CBSE Class 10 All Subjects Revision Worksheet Set 02

Holiday Homework 

Class X - English Communicative

Question 1. Prepare a personality card about any poet/ writer from your literature reader. Find out his works and add photographs to make it more attractive. You must use the following points.
a) Name
b) Place of birth
c) Names of some books written by him
d) Types of stories or poems written
e) Any awards won
f) Some other information that you want to share
Use coloured A3 size cartridge sheet to make the personality card. It should be decorated beautifully to reflect your creativity. Use only black coloured sketch pens to write on the card.
Answer: Here is a comprehensive guide to preparing your personality card using the legendary poet Robert Frost:
- Name: Robert Lee Frost
- Place of birth: San Francisco, California, United States
- Famous books/collections: 'A Boy's Will', 'North of Boston', 'Mountain Interval', and 'New Hampshire'
- Genre/Type of works: Traditional rural life depictions, highly philosophical nature poems, and deep reflections on human choices (such as 'The Road Not Taken' and 'Stopping by Woods on a Snowy Evening')
- Key Awards: He was honored with four Pulitzer Prizes for Poetry and received the prestigious Congressional Gold Medal.
- Additional Information: Robert Frost was invited to read his poem 'The Gift Outright' at the presidential inauguration of John F. Kennedy in 1961, making him a central figure in American cultural history.
In simple words: This task requires making a colorful profile card for a famous writer on an A3 sheet. Robert Frost is an excellent option because of his famous poems about nature and human choices.

Exam Tip: When presenting a writer's profile, always match their poetic themes with their real-life experiences to score higher marks on research depth.

Question 2. Read the newspaper everyday, clip and paste articles (two each) related to the following topics:
a) Solar Efficiency
b) How to keep yourself fit
c) Save the environment
d) Sustaining Himalayas
e) Tiger in Trouble
Paste the newspaper clippings in the coloured scrap file. It should be decorated beautifully to reflect your creativity. Use only coloured pens to write in the file. Articles should be pasted properly under each category with proper heading mentioned at the top. Write these articles in your own words sharing your opinion about the topics.
Answer: Follow these personal commentary outlines for your scrap file write-ups:
- Solar Efficiency: Transitioning to solar power is no longer an option but a necessity. By investing in better photovoltaic tech, we can reduce our reliance on fossil fuels and cut carbon footprints.
- How to keep yourself fit: Daily exercise combined with a balanced diet forms the foundation of physical health. Simple acts like walking, yoga, and avoiding processed foods can increase longevity.
- Save the environment: Local action drives global change. Reducing single-use plastics and promoting recycling at the household level are crucial steps to restore ecological balance.
- Sustaining Himalayas: Rapid commercial construction in mountain regions threatens fragile ecosystems. We must enforce strict eco-tourism limits to prevent devastating landslides and protect natural water sources.
- Tiger in Trouble: Habitat loss and illegal poaching continue to threaten tiger populations. Protecting these apex predators is vital because their survival ensures the health of entire forest ecosystems.
In simple words: Collect two newspaper clippings for each of the five environmental and health topics, paste them neatly, and write your own thoughts next to them.

Exam Tip: For scrapbooks, clear structural headings and colorful borders help make the presentation visually appealing and highly graded.

Question 3. It has been rightly said that books are our friends for life. They give us knowledge and experience. Read the long reading text “The story of my life by Hellen Keller” (Lesson 1-10) Thereafter, Do the following work, related to the book read by You:
(i) Make a book cover based on the book read.
(ii) Select the character you liked the most and write a paragraph on him/her.
(iii) Plot of the story (in about 200 words).
(iv) Write the values you learnt from the life of Helen Keller in about 100 words.
(v) Answer the following questions in about 150 words each.
a) How did Helen Keller lose her faculties of seeing and hearing? (Chapter 1)
b) Helen was naughty and she indulged in pranks unmindful of their consequences. Describe the incidents to prove this. (Chapter 2)
c) A deaf and blind person pines for a life without disability. Why? (Chapter 3)
d) A teacher can play a very significant role in the life of her pupils. Justify the statement with special reference to Helen Keller. (Chapter 4)
e) Why did Helen start fearing of Nature? What lesson did she draw? (Chapter 5)
f) How can an abstract idea be made comprehensive to a challenged person? (Chapter 6)
g) Which subject Helen did not like? Why? (Chapter 7)
h) What happened to the canary presented to Helen? (Chapter 8)
i) What made Helen call Boston ‘The City of Kind Hearts’ how the journey to Boston was different from Helen’s earlier visit to Baltimore in 1886? (Chapter 9)
j) The episode of horseshoe crab taught Helen a great lesson. Explain. (Chapter 10)
Answer:
(i) Design a book cover featuring a silhouette of a young girl feeling a blooming flower, symbolizing Helen’s sensory connection with nature under the sunlight.
(ii) Anne Sullivan is the most inspiring figure. Her endless patience, creativity, and love unlocked the world for Helen. Rather than viewing Helen's condition as a barrier, she found innovative ways to communicate, transforming Helen's isolation into a bright future.
(iii) The story details Helen's early years after a childhood illness left her blind and deaf. Isolated in a world of silence and dark confusion, she struggled with frustration until her tutor, Miss Sullivan, arrived. Miss Sullivan introduced her to finger-spelling, starting with the breakthrough word 'water'. This opened the door to language, literature, and formal study, helping Helen overcome her limitations.
(iv) Helen's journey teaches us determination, resilience, and curiosity. She shows that limitations are physical, not mental. With hard work, patience, and assistance, any challenge can be overcome. Her story urges us to appreciate our physical senses and remain compassionate toward others.
(v) Detailed Chapter Answers:
a) At nineteen months old, Helen caught an acute stomach and brain congestion. Although the high fever passed quickly, it permanently took away her vision and hearing, plunging her into deep silence and darkness.
b) Helen's childhood mischief showed her stubborn nature. Once, she locked her mother in a pantry for hours. On another occasion, she nearly burned herself while drying her apron by the fire, demonstrating how she acted without realizing the dangers involved.
c) Lacking sight and hearing isolates an individual from normal human experiences. Being unable to speak or understand others easily creates frustration, prompting a strong desire to live a life free of these sensory barriers.
d) Miss Sullivan represents the ideal teacher. She arrived when Helen was wild and unreachable, using patience and gentle guidance to connect words with physical items, which helped Helen build her intelligence and self-confidence.
e) During a storm, Helen got stuck on a tree branch as the wind and dark sky grew intense. This scary experience taught her that nature can be both beautiful and dangerously unpredictable.
f) Abstract concepts can be explained using physical feelings. For instance, Miss Sullivan explained 'love' by pointing out the warmth of the sun and the gentle touch of a heartbeat, showing how abstract feelings connect to real experiences.
g) Helen struggled with arithmetic. Unlike languages, math felt too rigid and lacked the warm, descriptive qualities she enjoyed in literature and natural sciences.
h) Helen received a canary as a gift. Sadly, a house cat managed to reach the cage one morning and killed the bird, teaching Helen a sad lesson about life and loss.
i) In Boston, Helen was met with overwhelming kindness from members of the Perkins Institution. Unlike her exhausting 1886 journey to Baltimore, this trip was filled with joy, making her feel completely accepted.
j) Helen once caught a horseshoe crab and left it in a small bucket, only to find it gone the next morning. This taught her that wild creatures deserve to live freely in their natural habitats rather than being kept as pets.
In simple words: This section contains answers about the first ten chapters of Helen Keller's book, focusing on her struggles, her relationship with Miss Sullivan, and her life lessons.

Exam Tip: Use exact character quotes or specific event names (like the word 'water' at the pump house) to make your literary answers stand out.

Question 4. A poem always begins in delight and ends in wisdom. It helps us to understand the wonders of nature so let us turn to a famous poet this summer. You can choose any poem written by any of the following poets:
a) William Wordsworth
b) Robert Frost
c) William Blake
d) P.B Shelly
e) You can use any self composed poem.
Poem recitation activity will be conducted after the holidays. Also write the poem on A3 size white cartridge sheet. Draw related picture and make it more impressive and presentable. Make audio recording of your poem in a CD with proper annotations. The Poem must be of 3-4 minutes.
Answer: An excellent selection for this assignment is Robert Frost's classic poem, 'Stopping by Woods on a Snowy Evening'.
Text of the Poem:
Whose woods these are I think I know.
His house is in the village though;
He will not see me stopping here
To watch his woods fill up with snow.

My little horse must think it queer
To stop without a farmhouse near
Between the woods and frozen lake
The darkest evening of the year.

He gives his harness bells a shake
To ask if there is some mistake.
The only other sound’s the sweep
Of easy wind and downy flake.

The woods are lovely, dark and deep,
But I have promises to keep,
And miles to go before I sleep,
And miles to go before I sleep.

Recitation Guide: Speak slowly and clearly. Pause slightly between stanzas to let the quiet, snowy atmosphere sink in. Build up your vocal energy in the final stanza to emphasize the responsibilities of life over the desire to rest.
In simple words: Choose a poem like Robert Frost's famous winter piece, write it on an A3 sheet with drawings, and record your reading on a CD.

Exam Tip: Pronounce words clearly and vary your tone to capture the rhythmic flow of the poem during the recording.

Question 5. Movies are one of the most important sources of entertainment for our teenagers. Watch any English movies and write the review of any one English movie that you enjoyed the three most. Do your work on A4 size coloured sheets. You can add pictures, photographs or drawings to make it more impressive. Each review should include the following details about the film:
a) Its title
b) The name of the director
c) The names of the script writers
d) Some of the important dialogues
e) Genre - What kind of a film it is? whether it is a cartoon film /an adventurous story/ a comedy/a tragedy/a historical drama
f) The best thing about the film
g) The thing it that you did not like
h) Recommendation – Why people should see it?
Answer: Movie Review: 'The Lion King' (1994)
- Title: The Lion King
- Directors: Roger Allers and Rob Minkoff
- Script Writers: Irene Mecchi, Jonathan Roberts, and Linda Woolverton
- Key Dialogue: "The past can hurt. But the way I see it, you can either run from it or learn from it." (Rafiki)
- Genre: Animated Musical Drama / Adventure
- Best Aspect: The brilliant musical score by Elton John and Hans Zimmer, alongside stunning hand-drawn animation.
- Minor Drawback: The transition of the plot during the middle section feels a bit rushed, especially Simba's rapid growth into an adult.
- Recommendation: This film is highly recommended because it offers powerful lessons about family duty, loss, and finding the courage to face your responsibilities.
In simple words: Write a movie review on A4 paper covering the title, director, key lines, genre, positives, negatives, and reasons why others should watch it.

Exam Tip: When writing a movie review, focus on how the music and visuals support the main theme of the story.

Question 6. Read the extra reading text i.e “The hounds of Baskerville”. Prepare its central idea, list of important events, character sketches of main characters and get ready for your listening and speaking skills test to be conducted in the month of July.
Answer: Here is your study guide for 'The Hound of the Baskervilles':
- Core Theme: The conflict between rational science and superstitious myths. Sherlock Holmes uses logic to show that a seemingly supernatural beast is actually part of a human plot.
- Key Plot Points:
1. Dr. Mortimer asks Sherlock Holmes to investigate the mysterious death of Sir Charles Baskerville.
2. Sir Henry Baskerville arrives in London to claim his inheritance despite receiving warnings.
3. Watson travels to Baskerville Hall to guard Sir Henry and sends detailed letters back to Holmes.
4. Watson discovers a mysterious figure on the moor, who turns out to be Holmes working in secret.
5. Holmes exposes Stapleton's identity and plans a trap using Sir Henry as bait.
6. They shoot the glowing hound and Stapleton drowns in the treacherous Grimpen Mire.
- Character Summary:
1. Sherlock Holmes: A brilliant detective who values logic and evidence over superstition.
2. Dr. John Watson: Holmes's loyal, practical assistant who gathers crucial clues during his stay on the moor.
In simple words: This guide outlines the key events, themes, and characters in the Sherlock Holmes mystery to help you prepare for your upcoming speaking test.

Exam Tip: Focus on how Holmes solves the mystery using physical clues rather than accepting supernatural explanations.

Question 7. You are Sahil Madan, a Student Perfect of class X of SRSM School. You are highly upset with the rise in crime against women specially the sexual assault women is facing now a days. You personally feel that these types of crimes are big shame for any cultured society and it is the male section of the society that is responsible for the same So it is important to counsel men to improve their attitude towards women. Moreover sex education and gender sensitization is required at every level to reduce this shameful act. Prepare a speech in about 400-450 words to be delivered in the morning assembly of your school. Write it on A4 size sheet. Make audio recording of the same in the CD with proper voice modulations and expressions. Your speech should be of at least 4-5 minutes. You can use the same CD that is used in Ques 4.
Answer: Assembly Speech Draft:
Respected Principal, teachers, and my fellow peers,

My name is Sahil Madan, and I stand before you today to discuss an issue that threatens the moral fabric of our community - the rise in crimes against women. Every day, news reports highlight incidents of harassment and assault. These crimes are a severe blemish on any civil society.

We must address the root cause of this problem. This issue stems from how men are raised and the attitudes they develop. True change begins by counseling boys and men to treat women with respect. We must discard outdated notions of dominance and understand that respect and equality are non-negotiable.

To achieve this, we need to introduce gender sensitization and comprehensive education at all levels. Schools must become safe environments where students learn mutual respect. Let us pledge to stand up against inappropriate behavior and ensure our school lead by example.

Thank you.
In simple words: Write a speech for the school assembly focusing on respect, gender equality, and safe communities, and then record your delivery on a CD.

Exam Tip: Speak with a serious, respectful, and confident tone during your audio recording to emphasize the importance of the issue.

Question 9. Prepare “A Word Book” based on the reading text “The hounds of Baskerville” including:
a) 20 idioms, their meanings and sentence based on them.
b) 20 phrases, their meanings and sentence based on them.
Answer: Five sample entries for your Word Book:
Idioms:
1. 'Red herring' - Something that misleads or distracts from the relevant issue.
Example: The muddy footprints near the window were a red herring left to confuse the detective.
2. 'To keep at bay' - To prevent something dangerous from coming too close.
Example: Holmes used his lantern to keep the wild animals on the moor at bay.
3. 'In cold blood' - Done intentionally and without emotion.
Example: The villain planned the crime in cold blood.

Phrases:
1. 'On the brink of' - Extremely close to a major change or event.
Example: The family was on the brink of losing their ancestral estate.
2. 'To cast light upon' - To make something easier to understand.
Example: Watson's discoveries cast light upon the strange sounds heard at night.
In simple words: Create a vocabulary notebook containing 20 idioms and 20 phrases from the novel, complete with definitions and example sentences.

Exam Tip: Use sentences that relate directly to the characters and events of the novel to demonstrate your reading comprehension.

Question 10. Revise all the syllabus done so far and get ready for the surprise test after the vacation.
Answer: Make a study schedule that covers literature chapters, grammar concepts, and writing skills like letter writing and speech drafting. Reviewing these topics regularly during your break will help you perform well in the surprise test.
In simple words: Review your English notes and practice grammar exercises during the holidays to prepare for the test when school restarts.

Exam Tip: Focus on formal writing structures and grammar rules, as these are common areas where students lose marks.

Class X - Mathematics

Question 1. Represent the following graphically & find the value of x & y.
(a) 3x+7y=5; 5x-3y=1
(b) 3x-7y=4; 6x-14y=4
(c) 4x+6y=8; 7x+5y=2
(d) 3x-4y=1; 4x-8y=4
Answer: Let's solve each system of linear equations systematically:
(a) Given equations:
\( 3x + 7y = 5 \) --(1)
\( 5x - 3y = 1 \) --(2)
Multiply (1) by 3 and (2) by 7:
\( 9x + 21y = 15 \)
\( 35x - 21y = 7 \)
Add the equations:
\( 44x = 22 \)

\( \implies x = \frac{1}{2} = 0.5 \)
Substitute \( x = 0.5 \) into (1):
\( 3(0.5) + 7y = 5 \)

\( \implies 1.5 + 7y = 5 \)

\( \implies 7y = 3.5 \)

\( \implies y = 0.5 \)
The lines intersect at the point \( (0.5, 0.5) \).

(b) Given equations:
\( 3x - 7y = 4 \) --(1)
\( 6x - 14y = 4 \) --(2)
Divide (2) by 2:
\( 3x - 7y = 2 \)
Since the coefficients are identical but the constants differ (\( 4 \neq 2 \)), these equations represent parallel lines. This system has no solution.

(c) Given equations:
\( 4x + 6y = 8 \implies 2x + 3y = 4 \) --(1)
\( 7x + 5y = 2 \) --(2)
Multiply (1) by 5 and (2) by 3:
\( 10x + 15y = 20 \)
\( 21x + 15y = 6 \)
Subtract (1) from (2):
\( 11x = -14 \)

\( \implies x = -\frac{14}{11} \)
Substitute \( x \) into (1):
\( 2\left(-\frac{14}{11}\right) + 3y = 4 \)

\( \implies -\frac{28}{11} + 3y = \frac{44}{11} \)

\( \implies 3y = \frac{72}{11} \)

\( \implies y = \frac{24}{11} \)
The lines intersect at the point \( \left(-\frac{14}{11}, \frac{24}{11}\right) \).

(d) Given equations:
\( 3x - 4y = 1 \) --(1)
\( 4x - 8y = 4 \implies x - 2y = 1 \implies x = 2y + 1 \) --(2)
Substitute \( x \) into (1):
\( 3(2y + 1) - 4y = 1 \)

\( \implies 6y + 3 - 4y = 1 \)

\( \implies 2y = -2 \)

\( \implies y = -1 \)
Thus, \( x = 2(-1) + 1 = -1 \).
The lines intersect at the point \( (-1, -1) \).
In simple words: Find where the pairs of lines cross on a graph paper. If they cross, that point is the solution. If they are parallel, they will never meet and have no solution.

Exam Tip: Label the axes, write the equations on their respective lines, and plot at least three points per line to ensure accuracy.

Question 2. Present age of a father is nine times the age of his son. After five years, the age of father will be five times the age of his son. Represent the situation algebraically & graphically.
Answer: Let the father's current age be \( f \) and the son's current age be \( s \).
From the given information:
\( f = 9s \) --(1)
After 5 years:
\( f + 5 = 5(s + 5) \)

\( \implies f + 5 = 5s + 25 \) --(2)
Substitute (1) into (2):
\( 9s + 5 = 5s + 25 \)

\( \implies 4s = 20 \)

\( \implies s = 5 \)
Father's age \( f = 9(5) = 45 \).
To represent this graphically, plot the lines \( f - 9s = 0 \) and \( f - 5s = 20 \) using points like \( (5, 45) \) where they intersect.
In simple words: Set up the equations with the father's and son's ages. Solving them shows the son is 5 years old and the father is 45 years old.

Exam Tip: Clearly state the variables at the beginning of your solution to avoid mixing up the ages of the father and son.

Question 3. Determine the value of k for which the system has unique solution.
(a)(k+1) x+5y=4; 3x+5y=7;
(b)(k+1)x+2y=7; (4+k)x-y=7
(c) 6x-2y=7; 3x+ (k-3) y=4
Answer: For a linear system to have a unique solution, the condition is:
\( \frac{a_1}{a_2} \neq \frac{b_1}{b_2} \)

(a) Here, \( \frac{k+1}{3} \neq \frac{5}{5} \)

\( \implies \frac{k+1}{3} \neq 1 \)

\( \implies k + 1 \neq 3 \)

\( \implies k \neq 2 \)

(b) Here, \( \frac{k+1}{4+k} \neq \frac{2}{-1} \)

\( \implies k + 1 \neq -2(4 + k) \)

\( \implies k + 1 \neq -8 - 2k \)

\( \implies 3k \neq -9 \)

\( \implies k \neq -3 \)

(c) Here, \( \frac{6}{3} \neq \frac{-2}{k-3} \)

\( \implies 2 \neq \frac{-2}{k-3} \intertext{Dividing by 2:} \)

\( \implies 1 \neq \frac{-1}{k-3} \)

\( \implies k - 3 \neq -1 \)

\( \implies k \neq 2 \)
In simple words: Solve for the value of k that keeps the ratios of the x and y coefficients different. This ensures the lines cross at a single point.

Exam Tip: Make sure to use the 'not equal' sign (\( \neq \)) in your working steps when solving for a unique solution.

Question 4. Determine the value of k for which the system has no solution.
(2k+1)x+(k+1)y=7; (2k-1)x+(k+2)y=5
Answer: For the system to have no solution, the lines must be parallel, which requires:
\( \frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2} \)
Equating the first two ratios:
\( \frac{2k+1}{2k-1} = \frac{k+1}{k+2} \)
Cross-multiply:
\( (2k+1)(k+2) = (2k-1)(k+1) \)

\( \implies 2k^2 + 4k + k + 2 = 2k^2 + 2k - k - 1 \)

\( \implies 5k + 2 = k - 1 \)

\( \implies 4k = -3 \)

\( \implies k = -\frac{3}{4} \)
Checking the constant ratio with \( k = -0.75 \):
\( \frac{a_1}{a_2} = \frac{-1.5+1}{-1.5-1} = \frac{-0.5}{-2.5} = \frac{1}{5} \), which is not equal to \( \frac{7}{5} \).
Thus, \( k = -\frac{3}{4} \).
In simple words: Find the value of k that makes the lines parallel. This happens when \( k = -3/4 \).

Exam Tip: Always double check that your calculated value of k does not accidentally make the constant ratio equal to the coefficient ratio, which would result in infinite solutions.

Question 5. Determine the value of k for which the system has infinitely many solution.
(a) x+3y=1; 3x+9y=k-2
(b) (k-3)x+3y=k; kx+ky=12
Answer: For a system to have infinitely many solutions, the lines must coincide, requiring:
\( \frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} \)

(a) Using the ratios:
\( \frac{1}{3} = \frac{3}{9} = \frac{1}{k-2} \)

\( \implies \frac{1}{3} = \frac{1}{k-2} \)

\( \implies k - 2 = 3 \)

\( \implies k = 5 \)

(b) Using the ratios:
\( \frac{k-3}{k} = \frac{3}{k} = \frac{k}{12} \)
From the second and third parts:
\( \frac{3}{k} = \frac{k}{12} \implies k^2 = 36 \implies k = \pm 6 \)
If \( k = 6 \):
\( \frac{6-3}{6} = \frac{3}{6} = \frac{1}{2} \), which matches the other ratios.
If \( k = -6 \):
\( \frac{-6-3}{-6} = \frac{9}{6} = \frac{3}{2} \neq \frac{3}{-6} \).
Thus, the correct value is \( k = 6 \).
In simple words: Match the ratios of all coefficients and constant terms. For system (a), \( k = 5 \), and for system (b), \( k = 6 \).

Exam Tip: When you get two values from a quadratic step (like \( \pm 6 \)), test both values in all ratios to discard any incorrect options.

Question 6. Use graph paper to draw the graph for following lines. Also obtain the vertices of the triangle so formed.
(a) X+2y=0; 2x-y=0; &3x+y-5=0
(b) 4x+3y=12; 4x-3y=0& 4x+9y=0
Answer: Let's find the intersection points (vertices) by solving the pairs of equations algebraically:
(a) Line 1: \( x + 2y = 0 \), Line 2: \( 2x - y = 0 \), Line 3: \( 3x + y = 5 \)
- Intersection of Line 1 and Line 2:
Substituting \( x = -2y \) into Line 2 gives \( 2(-2y) - y = 0 \implies -5y = 0 \implies y = 0, x = 0 \). Vertex A: \( (0,0) \).
- Intersection of Line 1 and Line 3:
Substituting \( x = -2y \) into Line 3 gives \( 3(-2y) + y = 5 \implies -5y = 5 \implies y = -1, x = 2 \). Vertex B: \( (2, -1) \).
- Intersection of Line 2 and Line 3:
Substituting \( y = 2x \) into Line 3 gives \( 3x + 2x = 5 \implies 5x = 5 \implies x = 1, y = 2 \). Vertex C: \( (1, 2) \).
The vertices of the triangle are \( (0,0) \), \( (2, -1) \), and \( (1, 2) \).

(b) Line 1: \( 4x + 3y = 12 \), Line 2: \( 4x - 3y = 0 \), Line 3: \( 4x + 9y = 0 \)
- Intersection of Line 2 and Line 3:
Since both pass through the origin without constant terms, Vertex A is \( (0,0) \).
- Intersection of Line 1 and Line 2:
Adding the two equations: \( 8x = 12 \implies x = 1.5 \).
Substituting back: \( 4(1.5) - 3y = 0 \implies 3y = 6 \implies y = 2 \). Vertex B: \( (1.5, 2) \).
- Intersection of Line 1 and Line 3:
Subtracting Line 1 from Line 3: \( 6y = -12 \implies y = -2 \).
Substituting back: \( 4x + 3(-2) = 12 \implies 4x = 18 \implies x = 4.5 \). Vertex C: \( (4.5, -2) \).
The vertices of the triangle are \( (0,0) \), \( (1.5, 2) \), and \( (4.5, -2) \).
In simple words: Plot the three lines on a graph. The three points where the lines cross each other form the corners of a triangle.

Exam Tip: Shade the region bounded by the three lines to clearly highlight the triangle formed.

Question 7. Find the value of x&y:
3x+2y=2xy; 9x-4y=xy
Answer: Note that \( (0,0) \) is a trivial solution. Assuming \( x \neq 0 \) and \( y \neq 0 \), divide both equations by \( xy \):
\( \frac{3}{y} + \frac{2}{x} = 2 \) --(1)
\( \frac{9}{y} - \frac{4}{x} = 1 \) --(2)
Let \( \frac{1}{y} = u \) and \( \frac{1}{x} = v \). The system becomes:
\( 3u + 2v = 2 \) --(3)
\( 9u - 4v = 1 \) --(4)
Multiply (3) by 2:
\( 6u + 4v = 4 \) --(5)
Add (4) and (5):
\( 15u = 5 \implies u = \frac{1}{3} \)
Since \( u = \frac{1}{y} \), we have \( y = 3 \).
Substitute \( u = \frac{1}{3} \) into (3):
\( 3\left(\frac{1}{3}\right) + 2v = 2 \)

\( \implies 1 + 2v = 2 \)

\( \implies 2v = 1 \implies v = \frac{1}{2} \)
Since \( v = \frac{1}{x} \), we have \( x = 2 \).
The solutions are \( (0,0) \) and \( (2, 3) \).
In simple words: Divide the equations by \( xy \), substitute with new variables \( u \) and \( v \), solve the simpler equations, and then switch back to find \( x = 2 \) and \( y = 3 \).

Exam Tip: Do not forget to mention the \( (0,0) \) solution, as dividing by variables assumes they are non-zero.

Question 8. Solve the following for x & y
(a) 9/x+y +5/x-y =4; 15/x+y -3/x-y =1
(b) 22/3x+4y + 7/3x-4y; 33/3x+4 y + 14/3x-4y=1
Answer:
(a) Let \( \frac{1}{x+y} = u \) and \( \frac{1}{x-y} = v \). The equations are:
\( 9u + 5v = 4 \) --(1)
\( 15u - 3v = 1 \) --(2)
Multiply (1) by 3 and (2) by 5:
\( 27u + 15v = 12 \)
\( 75u - 15v = 5 \)
Adding these gives:
\( 102u = 17 \implies u = \frac{17}{102} = \frac{1}{6} \)
Thus, \( x + y = 6 \) --(3)
Substitute \( u = \frac{1}{6} \) into (1):
\( 9\left(\frac{1}{6}\right) + 5v = 4 \)

\( \implies 1.5 + 5v = 4 \)

\( \implies 5v = 2.5 \implies v = \frac{1}{2} \)
Thus, \( x - y = 2 \) --(4)
Solving (3) and (4) by addition:
\( 2x = 8 \implies x = 4 \)
\( y = 6 - 4 = 2 \).
The solution is \( x = 4, y = 2 \).

(b) Assuming the first equation is equal to 2 (which is the standard textbook form for this problem):
\( \frac{22}{3x+4y} + \frac{7}{3x-4y} = 2 \) --(1)
\( \frac{33}{3x+4y} + \frac{14}{3x-4y} = 1 \) --(2)
Let \( \frac{1}{3x+4y} = u \) and \( \frac{1}{3x-4y} = v \):
\( 22u + 7v = 2 \) --(3)
\( 33u + 14v = 1 \) --(4)
Multiply (3) by 2:
\( 44u + 14v = 4 \) --(5)
Subtract (4) from (5):
\( 11u = 3 \implies u = \frac{3}{11} \)
Substitute \( u \) into (3):
\( 22\left(\frac{3}{11}\right) + 7v = 2 \implies 6 + 7v = 2 \implies 7v = -4 \implies v = -\frac{4}{7} \)
This gives:
\( 3x + 4y = \frac{11}{3} \) --(6)
\( 3x - 4y = -\frac{7}{4} \) --(7)
Adding (6) and (7):
\( 6x = \frac{11}{3} - \frac{7}{4} = \frac{44 - 21}{12} = \frac{23}{12} \implies x = \frac{23}{72} \)
Subtracting (7) from (6):
\( 8y = \frac{11}{3} + \frac{7}{4} = \frac{44 + 21}{12} = \frac{65}{12} \implies y = \frac{65}{96} \).
In simple words: Replace terms like \( x+y \) with new variables to simplify the equations, solve for them first, and then solve again to find \( x \) and \( y \).

Exam Tip: Be careful with signs when substituting fractional values back into your equations.

Question 9. Sum of ages of father& son is 62 years. Present age of father is 26 years more than son. Find the present age of father and son.
Answer: Let the present age of the father be \( x \) and the son be \( y \).
According to the problem:
\( x + y = 62 \) --(1)
\( x = y + 26 \) --(2)
Substitute (2) into (1):
\( (y + 26) + y = 62 \)

\( \implies 2y + 26 = 62 \)

\( \implies 2y = 36 \)

\( \implies y = 18 \)
Substitute \( y = 18 \) into (2):
\( x = 18 + 26 = 44 \).
The father is 44 years old, and the son is 18 years old.
In simple words: The sum of their ages is 62 and the father is 26 years older. This means the father is 44 and the son is 18.

Exam Tip: Check your final values at the end: \( 44 + 18 = 62 \) and \( 44 - 18 = 26 \), confirming the answer is correct.

Question 10. At present a father is three times as old as his son. After 12 years, his age will be twice the age of his son. Find their present age.
Answer: Let the son's age be \( s \) and the father's age be \( f \).
Given conditions:
\( f = 3s \) --(1)
After 12 years:
\( f + 12 = 2(s + 12) \)

\( \implies f + 12 = 2s + 24 \) --(2)
Substitute (1) into (2):
\( 3s + 12 = 2s + 24 \)

\( \implies s = 12 \)
Father's age \( f = 3(12) = 36 \).
The father is 36 years old, and the son is 12 years old.
In simple words: Set up the equations using their ages. Solving them shows the father is 36 and the son is 12.

Exam Tip: Remember to add 12 to both ages when writing the equation for their future ages.

Question 11. If the numerator & denominator of a fraction are both increased by 1, it becomes equal to 2/3. Also, the denominator is 4 more than the numerator. Find the reciprocal of the fraction.
Answer: Let the fraction be \( \frac{x}{y} \).
According to the first condition:
\( \frac{x+1}{y+1} = \frac{2}{3} \implies 3x + 3 = 2y + 2 \implies 3x - 2y = -1 \) --(1)
According to the second condition:
\( y = x + 4 \) --(2)
Substitute (2) into (1):
\( 3x - 2(x + 4) = -1 \)

\( \implies 3x - 2x - 8 = -1 \)

\( \implies x = 7 \)
Substitute \( x = 7 \) into (2):
\( y = 7 + 4 = 11 \).
The original fraction is \( \frac{7}{11} \).
The reciprocal of this fraction is \( \frac{11}{7} \).
In simple words: First find the fraction, which is \( 7/11 \). The question asks for the reciprocal, so flip it over to get \( 11/7 \).

Exam Tip: Read the final question carefully: it asks for the reciprocal of the fraction, not just the fraction itself.

Question 12. A fraction becomes 4/5 if 1 is added to both numerator and denominator If however 5 is subtracted to both, the fraction becomes 1/2. Find the fraction.
Answer: Let the fraction be \( \frac{x}{y} \).
First condition:
\( \frac{x+1}{y+1} = \frac{4}{5} \implies 5x + 5 = 4y + 4 \implies 5x - 4y = -1 \) --(1)
Second condition:
\( \frac{x-5}{y-5} = \frac{1}{2} \implies 2x - 10 = y - 5 \implies y = 2x - 5 \) --(2)
Substitute (2) into (1):
\( 5x - 4(2x - 5) = -1 \)

\( \implies 5x - 8x + 20 = -1 \)

\( \implies -3x = -21 \)

\( \implies x = 7 \)
Substitute \( x = 7 \) into (2):
\( y = 2(7) - 5 = 9 \).
The required fraction is \( \frac{7}{9} \).
In simple words: Set up the equations for both conditions. Solving them gives the fraction as \( 7/9 \).

Exam Tip: Be careful to subtract 5 from both the numerator and the denominator in the second step.

Question 13. 2 audio & 3 three video cassettes together cost Rs 425, where as 3 audio & 3 video cassettes cost Rs 350. What are the prices of an audio &video cassette?
Answer: Let's assume there is a typo in the second part of the question (it should be 3 audio & 2 video cassettes, as 3 audio & 3 video cassettes cannot cost less than 2 audio & 3 video cassettes).
Let the price of an audio cassette be \( a \) and a video cassette be \( v \).
\( 2a + 3v = 425 \) --(1)
\( 3a + 2v = 350 \) --(2)
Multiply (1) by 2 and (2) by 3:
\( 4a + 6v = 850 \)
\( 9a + 6v = 1050 \)
Subtract the first from the second:
\( 5a = 200 \)

\( \implies a = 40 \)
Substitute \( a = 40 \) into (1):
\( 2(40) + 3v = 425 \)

\( \implies 80 + 3v = 425 \)

\( \implies 3v = 345 \)

\( \implies v = 115 \)
The price of an audio cassette is Rs 40 and a video cassette is Rs 115.
In simple words: By correcting a typo in the question, we find that an audio cassette costs Rs 40 and a video cassette costs Rs 115.

Exam Tip: If a real exam question contains a typo that leads to a negative value, write down your steps clearly and state your assumptions to secure full marks.

Question 14. 2 belts & 3 ties cost Rs 400.Also,3 belts&2 ties cost Rs 350. Find the cost of a belt &a tie.
Answer: Let the cost of a belt be \( b \) and a tie be \( t \).
We have:
\( 2b + 3t = 400 \) --(1)
\( 3b + 2t = 350 \) --(2)
Multiply (1) by 2 and (2) by 3:
\( 4b + 6t = 800 \)
\( 9b + 6t = 1050 \)
Subtracting these equations gives:
\( 5b = 250 \)

\( \implies b = 50 \)
Substitute \( b = 50 \) into (1):
\( 2(50) + 3t = 400 \)

\( \implies 100 + 3t = 400 \)

\( \implies 3t = 300 \)

\( \implies t = 100 \)
A belt costs Rs 50 and a tie costs Rs 100.
In simple words: Solving the equations shows that one belt costs Rs 50 and one tie costs Rs 100.

Exam Tip: Since the equations are symmetric in their coefficients, you can also add and subtract them to get simpler equations to solve.

Question 15. In a two digit number, the unit digit is twice the tens digit .If 36 is added to the number, the digits interchange places. Find the number.
Answer: Let the tens digit be \( t \) and the units digit be \( u \).
The number is \( 10t + u \).
Given:
\( u = 2t \) --(1)
When 36 is added, the digits reverse:
\( 10t + u + 36 = 10u + t \)

\( \implies 9u - 9t = 36 \)

\( \implies u - t = 4 \) --(2)
Substitute (1) into (2):
\( 2t - t = 4 \implies t = 4 \)
Thus, \( u = 2(4) = 8 \).
The original number is 48.
In simple words: The tens digit is 4 and the units digit is 8, making the number 48. Adding 36 gives 84, which reverses the digits.

Exam Tip: Always write the general form of a two digit number as \( 10t + u \) rather than just \( tu \).

Question 16. The area of a rectangle is increased by 38 sq units if its length & breadth both are increased by 2 units each. If however length is increased by 3 units and breadth decreased by 3 units the area reduced by 18 sq units. Find the original dimension of the rectangle.
Answer: Let the original length be \( L \) and breadth be \( B \).
Original Area = \( LB \).
First condition:
\( (L + 2)(B + 2) = LB + 38 \)

\( \implies LB + 2L + 2B + 4 = LB + 38 \)

\( \implies 2L + 2B = 34 \implies L + B = 17 \) --(1)
Second condition:
\( (L + 3)(B - 3) = LB - 18 \)

\( \implies LB - 3L + 3B - 9 = LB - 18 \)

\( \implies -3L + 3B = -9 \implies L - B = 3 \) --(2)
Adding (1) and (2):
\( 2L = 20 \implies L = 10 \)
From (1), \( B = 17 - 10 = 7 \).
The length is 10 units and the breadth is 7 units.
In simple words: Solving the equations derived from the area changes reveals the rectangle's dimensions are 10 by 7.

Exam Tip: Be sure to expand algebraic products like \( (L+3)(B-3) \) carefully to avoid losing signs.

Question 17. A boat goes 16 km upstream and 24 km downstream in 6 hours.It can go 12 km upstream and 36 km downstream in same time.Find speed of boat in still water and speed of stream.
Answer: Let the speed of the boat in still water be \( x \) km/h and the speed of the stream be \( y \) km/h.
Upstream speed = \( x - y \), Downstream speed = \( x + y \).
We have:
\( \frac{16}{x-y} + \frac{24}{x+y} = 6 \) --(1)
\( \frac{12}{x-y} + \frac{36}{x+y} = 6 \) --(2)
Let \( \frac{1}{x-y} = u \) and \( \frac{1}{x+y} = v \):
\( 16u + 24v = 6 \implies 8u + 12v = 3 \) --(3)
\( 12u + 36v = 6 \implies 2u + 6v = 1 \) --(4)
Multiply (4) by 2:
\( 4u + 12v = 2 \) --(5)
Subtract (5) from (3):
\( 4u = 1 \implies u = \frac{1}{4} \implies x - y = 4 \) --(6)
Substitute \( u = \frac{1}{4} \) into (4):
\( 2\left(\frac{1}{4}\right) + 6v = 1 \implies 6v = \frac{1}{2} \implies v = \frac{1}{12} \implies x + y = 12 \) --(7)
Solving (6) and (7):
\( 2x = 16 \implies x = 8 \)
\( y = 12 - 8 = 4 \).
The speed of the boat is 8 km/h and the speed of the stream is 4 km/h.
In simple words: The boat's speed in calm water is 8 km/h and the water stream flows at 4 km/h.

Exam Tip: In boat problems, the speed of the boat in still water must always be greater than the speed of the stream.

Question 18. A boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream in same time. Find speed of boat in still water and speed of stream.
Answer: Let \( \frac{1}{x-y} = u \) and \( \frac{1}{x+y} = v \).
According to the problem:
\( 12u + 40v = 8 \implies 3u + 10v = 2 \) --(1)
\( 16u + 32v = 8 \implies 2u + 4v = 1 \) --(2)
Multiply (1) by 2 and (2) by 3:
\( 6u + 20v = 4 \)
\( 6u + 12v = 3 \)
Subtracting the second equation from the first:
\( 8v = 1 \implies v = \frac{1}{8} \implies x + y = 8 \)
Substitute \( v = \frac{1}{8} \) into (2):
\( 2u + 4\left(\frac{1}{8}\right) = 1 \implies 2u = \frac{1}{2} \implies u = \frac{1}{4} \implies x - y = 4 \)
Solving \( x+y=8 \) and \( x-y=4 \):
\( 2x = 12 \implies x = 6 \)
\( y = 8 - 6 = 2 \).
The speed of the boat is 6 km/h and the speed of the stream is 2 km/h.
In simple words: The boat travels at 6 km/h in calm water, while the stream flows at 2 km/h.

Exam Tip: Clearly show the substitution step to make your algebra easier to follow for the evaluator.

Question 19. Check if \(2x^3 +1\) is a factor of \(2x^5+10x^4+6x^3+2x^2+5x+1\).
Answer: Let's perform polynomial long division to check for a remainder:
Divide \( 2x^5 + 10x^4 + 6x^3 + 2x^2 + 5x + 1 \) by \( 2x^3 + 1 \):
1. First term: \( \frac{2x^5}{2x^3} = x^2 \).
Multiply: \( x^2(2x^3 + 1) = 2x^5 + x^2 \).
Subtract: \( (2x^5 + 10x^4 + 6x^3 + 2x^2 + 5x + 1) - (2x^5 + x^2) = 10x^4 + 6x^3 + x^2 + 5x + 1 \).
2. Next term: \( \frac{10x^4}{2x^3} = 5x \).
Multiply: \( 5x(2x^3 + 1) = 10x^4 + 5x \).
Subtract: \( (10x^4 + 6x^3 + x^2 + 5x + 1) - (10x^4 + 5x) = 6x^3 + x^2 + 1 \).
3. Next term: \( \frac{6x^3}{2x^3} = 3 \).
Multiply: \( 3(2x^3 + 1) = 6x^3 + 3 \).
Subtract: \( (6x^3 + x^2 + 1) - (6x^3 + 3) = x^2 - 2 \).
Since the remainder is \( x^2 - 2 \neq 0 \), \( 2x^3 + 1 \) is not a factor.
In simple words: Dividing the larger polynomial leaves a remainder of \( x^2 - 2 \), meaning it does not divide evenly.

Exam Tip: Remember to align terms of the same degree during polynomial subtraction to avoid calculation mistakes.

Question 20. Divide \(3x^3-x^2-3x+5\) by \(x^2-x-1\) & verify the division algorithm.
Answer: Let's divide:
1. \( \frac{3x^3}{x^2} = 3x \).
Multiply: \( 3x(x^2 - x - 1) = 3x^3 - 3x^2 - 3x \).
Subtract: \( (3x^3 - x^2 - 3x + 5) - (3x^3 - 3x^2 - 3x) = 2x^2 + 5 \).
2. \( \frac{2x^2}{x^2} = 2 \).
Multiply: \( 2(x^2 - x - 1) = 2x^2 - 2x - 2 \).
Subtract: \( (2x^2 + 5) - (2x^2 - 2x - 2) = 2x + 7 \).
So, Quotient \( Q(x) = 3x + 2 \), Remainder \( R(x) = 2x + 7 \).
Verification of Division Algorithm:
\( \text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder} \)
\( = (x^2 - x - 1)(3x + 2) + (2x + 7) \)
\( = 3x^3 + 2x^2 - 3x^2 - 2x - 3x - 2 + 2x + 7 \)
\( = 3x^3 - x^2 - 3x + 5 \). This matches the Dividend. Verified!
In simple words: Dividing gives a quotient of \( 3x+2 \) and a remainder of \( 2x+7 \). Multiplying them back verifies the calculation is correct.

Exam Tip: Always state both the Quotient and Remainder clearly before starting your verification steps.

Question 21. Find all the zeroes of the polynomial \(2x^4-x^3-7x^2+2x+6\) if two of its zeroes are \(\sqrt{2}\) & \(-\sqrt{2}\).
Answer: Given zeroes: \( \sqrt{2} \) and \( -\sqrt{2} \).
The corresponding quadratic factor is:
\( (x - \sqrt{2})(x + \sqrt{2}) = x^2 - 2 \).
Divide \( 2x^4 - x^3 - 7x^2 + 2x + 6 \) by \( x^2 - 2 \):
- \( \frac{2x^4}{x^2} = 2x^2 \).
- Subtracting \( 2x^2(x^2-2) \) leaves \( -x^3 - 3x^2 + 2x + 6 \).
- \( \frac{-x^3}{x^2} = -x \).
- Subtracting \( -x(x^2-2) \) leaves \( -3x^2 + 6 \).
- \( \frac{-3x^2}{x^2} = -3 \).
- Subtracting \( -3(x^2-2) \) leaves a remainder of 0.
The quotient is \( 2x^2 - x - 3 \).
Solve \( 2x^2 - x - 3 = 0 \) to find the remaining zeroes:
\( 2x^2 - 3x + 2x - 3 = 0 \)

\( \implies x(2x - 3) + 1(2x - 3) = 0 \)

\( \implies (x + 1)(2x - 3) = 0 \implies x = -1, \frac{3}{2} \).
All zeroes of the polynomial are \( \sqrt{2} \), \( -\sqrt{2} \), \( -1 \), and \( \frac{3}{2} \).
In simple words: Divide the polynomial by \( x^2-2 \), then factor the resulting quadratic equation to find the other two zeroes as \( -1 \) and \( 1.5 \).

Exam Tip: Since the polynomial is of degree 4, make sure you write down exactly four zeroes in your final line.

Question 22. If two zeroes of the polynomial \(x^4-6x^3-26x^2+138x-35\) are \(2 \pm \sqrt{3}\)
Answer: Given zeroes are \( 2 + \sqrt{3} \) and \( 2 - \sqrt{3} \).
The sum of the zeroes is 4, and their product is \( (2+\sqrt{3})(2-\sqrt{3}) = 4 - 3 = 1 \).
The corresponding quadratic factor is:
\( x^2 - 4x + 1 \).
Divide \( x^4 - 6x^3 - 26x^2 + 138x - 35 \) by \( x^2 - 4x + 1 \):
- \( \frac{x^4}{x^2} = x^2 \). Product: \( x^4 - 4x^3 + x^2 \). Subtracting leaves \( -2x^3 - 27x^2 + 138x - 35 \).
- \( \frac{-2x^3}{x^2} = -2x \). Product: \( -2x^3 + 8x^2 - 2x \). Subtracting leaves \( -35x^2 + 140x - 35 \).
- \( \frac{-35x^2}{x^2} = -35 \). Product: \( -35x^2 + 140x - 35 \). Subtracting leaves a remainder of 0.
The quotient is \( x^2 - 2x - 35 \).
Solve \( x^2 - 2x - 35 = 0 \):
\( (x - 7)(x + 5) = 0 \implies x = 7, -5 \).
All the zeroes are \( 2 \pm \sqrt{3} \), \( 7 \), and \( -5 \).
In simple words: Divide by the quadratic factor representing the given roots to get \( x^2-2x-35 \). Factoring this gives the remaining zeroes, which are \( 7 \) and \( -5 \).

Exam Tip: Be methodical during the division step, as a simple arithmetic slip will prevent the remainder from canceling to zero.

Question 23. Find the missing frequency in the following frequency distribution if it is known that the mean of the distribution is 1.46.

Answer: Let the missing frequencies be \( f_1 \) and \( f_2 \) corresponding to \( x = 1 \) and \( x = 2 \).
Total frequency:
\( 46 + f_1 + f_2 + 25 + 10 + 5 = 200 \)

\( \implies 86 + f_1 + f_2 = 200 \implies f_1 + f_2 = 114 \) --(1)
Mean is 1.46:
\( \sum fx = 0(46) + 1(f_1) + 2(f_2) + 3(25) + 4(10) + 5(5) \)

\( \implies \sum fx = f_1 + 2f_2 + 75 + 40 + 25 = f_1 + 2f_2 + 140 \)
Since \( \text{Mean} = \frac{\sum fx}{\sum f} \):
\( 1.46 = \frac{f_1 + 2f_2 + 140}{200} \)

\( \implies f_1 + 2f_2 + 140 = 292 \)

\( \implies f_1 + 2f_2 = 152 \) --(2)
Subtract (1) from (2):
\( f_2 = 152 - 114 = 38 \)
Thus, \( f_1 = 114 - 38 = 76 \).
The missing frequencies are 76 and 38.
In simple words: Use the total frequency of 200 and the mean of 1.46 to set up two simple equations, giving the missing values as 76 and 38.

Exam Tip: Make a table containing columns for \( x \), \( f \), and \( fx \) to present your data clearly to the examiner.

Question 24. Apply step-deviation method to find the AM of the following frequency distribution.

Answer: Let the assumed mean be \( A = 25 \), and the class interval step be \( h = 5 \).
Define the deviation \( u_i = \frac{x_i - A}{h} \):
- For \( x = 5 \): \( u = -4 \), \( f = 20 \), \( fu = -80 \)
- For \( x = 10 \): \( u = -3 \), \( f = 43 \), \( fu = -129 \)
- For \( x = 15 \): \( u = -2 \), \( f = 75 \), \( fu = -150 \)
- For \( x = 20 \): \( u = -1 \), \( f = 67 \), \( fu = -67 \)
- For \( x = 25 \): \( u = 0 \), \( f = 72 \), \( fu = 0 \)
- For \( x = 30 \): \( u = 1 \), \( f = 45 \), \( fu = 45 \)
- For \( x = 35 \): \( u = 2 \), \( f = 39 \), \( fu = 78 \)
- For \( x = 40 \): \( u = 3 \), \( f = 9 \), \( fu = 27 \)
- For \( x = 45 \): \( u = 4 \), \( f = 8 \), \( fu = 32 \)
- For \( x = 50 \): \( u = 5 \), \( f = 6 \), \( fu = 30 \)

Summing the values:
\( \sum f = 384 \)
\( \sum fu = (-80 - 129 - 150 - 67) + (45 + 78 + 27 + 32 + 30) = -426 + 212 = -214 \)
Using the step-deviation formula:
\( \text{Mean} = A + h \left(\frac{\sum fu}{\sum f}\right) \)
\( \text{Mean} = 25 + 5 \left(\frac{-214}{384}\right) \)
\( \text{Mean} = 25 - \frac{1070}{384} \approx 25 - 2.79 = 22.21 \).
The Arithmetic Mean of the distribution is approximately 22.21.
In simple words: Pick 25 as the starting midpoint, calculate deviations in steps of 5, and find the weighted average, which gives 22.21.

Exam Tip: Show the calculations for your deviations \( u_i \) in a dedicated column to get full marks for methodology.

Question 25. If the mean of the following frequency table 50.But the frequencies f1 &f2 are missing .find the missing term.

Answer: Total frequency is 120:
\( 17 + f_1 + 32 + f_2 + 19 = 120 \)

\( \implies 68 + f_1 + f_2 = 120 \implies f_1 + f_2 = 52 \) --(1)
Find the class midpoints (\( x_i \)): 10, 30, 50, 70, 90.
Using the mean formula with \( \text{Mean} = 50 \):
\( \sum fx = 10(17) + 30(f_1) + 50(32) + 70(f_2) + 90(19) \)

\( \implies \sum fx = 170 + 30f_1 + 1600 + 70f_2 + 1710 = 30f_1 + 70f_2 + 3480 \)
Since \( \text{Mean} = \frac{\sum fx}{\sum f} \):
\( 50 = \frac{30f_1 + 70f_2 + 3480}{120} \)

\( \implies 6000 = 30f_1 + 70f_2 + 3480 \)

\( \implies 30f_1 + 70f_2 = 2520 \implies 3f_1 + 7f_2 = 252 \) --(2)
Multiply (1) by 3:
\( 3f_1 + 3f_2 = 156 \) --(3)
Subtract (3) from (2):
\( 4f_2 = 96 \implies f_2 = 24 \)
Thus, \( f_1 = 52 - 24 = 28 \).
The missing frequencies are \( f_1 = 28 \) and \( f_2 = 24 \).
In simple words: Write equations based on the sum of frequencies (120) and the mean (50) to find that \( f_1 = 28 \) and \( f_2 = 24 \).

Exam Tip: Grouped data requires you to calculate class midpoints (\( x_i \)) first before using the mean formulas.

Holiday Homework 

Class X - Science

Question 1. Board Project: Research on ‘ Air Pollution, Nicotine smoking and lung diseases in India’. Suggest some possible remedial measures. Click some real pictures and take the print out to show the deadly effects(on spiral binding project file only. Paste pictures on plain page with suitable captions. Remarks and bibliography at last. Total 6-7 pages).
Answer: Tobacco smoke contains harmful compounds like nicotine and carbon monoxide, which severely damage human lung tissues. To complete this board project, research the rise of respiratory ailments like COPD, emphysema, and lung cancer linked to active and passive smoking in urban India. Suggested remedial steps include: 1. Enforcing strict bans on smoking in public places to protect non-smokers from passive inhalation. 2. Increasing public awareness campaigns about the hazards of vaping and tobacco consumption. 3. Planting air-purifying trees and reducing vehicular emissions to lower general air pollution in cities. Include a comprehensive bibliography citing medical journals and environmental reports at the end of your 6-7 page report.
In simple words: Create a 6-to-7-page report about how dirty air and smoking cause lung sicknesses in India. Suggest ways to fix this, like banning smoking in public and planting trees.

Exam Tip: Include clear graphs showing the increase in lung disease cases over recent years to earn maximum marks for data representation.

Question 3. Why parents are advised to discourage their children to eat chips and junk food?
Answer: Junk foods like potato chips contain high levels of trans fats, sodium, and chemical preservatives, while offering almost zero essential vitamins, minerals, or fiber. Eating these foods regularly leads to childhood obesity, digestive issues, and a higher risk of developing type 2 diabetes or heart diseases later in life. They also replace healthy, nutrient-rich meals that are essential for a growing child's physical and mental development.
In simple words: Junk food has too much bad fat and salt but no healthy nutrients. Eating it makes children gain unhealthy weight and fall sick easily.

Exam Tip: Mention specific health conditions like "obesity", "hypertension", and "nutritional deficiency" to write a strong answer.

Question 4. Brushing our teeth twice a day is a well known saying. Justify this statement.
Answer: When we eat, tiny food particles and sugars stick to our teeth. Bacteria living in our mouth feed on these sugars and produce harmful acids. These acids gradually dissolve the tooth enamel, causing cavities and tooth decay. Brushing in the morning and before bed removes these food remnants and prevents plaque build-up, keeping our gums and teeth healthy.
In simple words: Food left in our mouth feeds bacteria, which make acids that ruin our teeth. Brushing twice a day washes away the food and stops cavities.

Exam Tip: Always highlight the role of "acid-producing bacteria" and "enamel decay" when explaining dental hygiene.

Question 5. Farmers are using a large number of Pesticides and fertilizers in their fields to increase the crop production and to enhance their profits. But by doing so they are causing damage to the soil as well as to the environment. Do you agree with this statement? Why should we avoid eating fruits and vegetables without washing them properly?
Answer: Yes, this statement is accurate. While chemical fertilizers and pesticides boost crop yields in the short term, their excessive use degrades soil fertility by killing beneficial microbes and earthworms. These chemicals run off into nearby water bodies during rains, causing water pollution and eutrophication, which destroys aquatic ecosystems. We must wash fruits and vegetables thoroughly before eating because they often carry toxic pesticide residues on their skin, which can cause severe health issues and poisoning if ingested.
In simple words: Chemical sprays help grow more crops but ruin the soil and pollute water. Washing fruits before eating is necessary to clean off these poisonous chemical residues.

Exam Tip: Explain "bio-accumulation" of pesticides in the food chain to show a deep understanding of environmental impact.

Question 6. Suddenly your friend has fallen down in the assembly ground. You are standing next to him/her. What will you do? What could be the probable causes? His/her parents should be informed or not?
Answer: If a friend collapses, my immediate action will be to help them lie down in a safe, shaded spot, elevate their legs slightly to improve blood flow to the brain, and loosen any tight clothing around their neck. I will call for school medical help immediately. The collapse could be caused by dehydration, low blood sugar (hypoglycemia), heat exhaustion, or prolonged standing in the sun. Yes, their parents must be informed promptly by the school authorities to ensure they get proper medical evaluation and follow-up care.
In simple words: If a friend faints, help them lie down in the shade, raise their legs, and get the school nurse. Fainting can happen from not drinking enough water or standing in the heat too long. Their parents must be notified.

Exam Tip: Write down step-by-step first-aid actions clearly, starting with basic physical comfort followed by professional medical contact.

Question 7. Reena is an unhappy girl because he loves her father very much. But her father is a chain smoker. Often he comes home late at night. Those days Reena gets some fruity smells from his cloths. That time he behaves unusually, abuses his wife and talks loudly. Her mother sobs quietly. What is the problem? What are the consequences of these addictions? Suggest some ways so that Reena can get back a doting father?
Answer: Reena's father is suffering from substance abuse, specifically tobacco addiction (chain smoking) and alcohol addiction, indicated by his late nights, unusual loud behavior, domestic abuse, and the sweet, fruity odor of alcohol on his clothes. The consequences of these addictions are: 1. Physical health deterioration, including high risk of lung cancer, liver cirrhosis, and cardiovascular disease. 2. Emotional and psychological trauma for the family, leading to domestic violence, broken relationships, and constant fear. To help her father recover, Reena and her mother should: 1. Seek professional medical help, such as addiction therapists, psychiatrists, and rehabilitation centers. 2. Join support groups and gently counsel him during his sober hours about how much his family loves and needs him.
In simple words: Reena's father is addicted to smoking and drinking alcohol, which makes him act angry and hurt his family. To help him, they need to take him to a doctor or a rehab center and talk to him with love when he is sober.

Exam Tip: Address all three parts of the question separately: identifying the addiction, stating the health/social consequences, and proposing recovery solutions.

Science (Biology) Class - X

Question 1. Draw a flow chart of Blood Circulation through Human Heart.
Answer: Here is the step-by-step pathway of blood flow through the human heart:
1. Deoxygenated blood from body tissues \( \rightarrow \) Superior and Inferior Vena Cava \( \rightarrow \) Right Atrium
2. Right Atrium \( \rightarrow \) Tricuspid Valve \( \rightarrow \) Right Ventricle
3. Right Ventricle \( \rightarrow \) Pulmonary Artery \( \rightarrow \) Lungs (for oxygenation)
4. Oxygenated blood from Lungs \( \rightarrow \) Pulmonary Veins \( \rightarrow \) Left Atrium
5. Left Atrium \( \rightarrow \) Bicuspid (Mitral) Valve \( \rightarrow \) Left Ventricle
6. Left Ventricle \( \rightarrow \) Aorta \( \rightarrow \) Oxygenated blood distributed to body tissues
In simple words: Blood low in oxygen enters the right side of the heart, gets pumped to the lungs to get oxygen, returns to the left side of the heart, and is then pumped out to the rest of the body.

Exam Tip: Use arrows and clear labeling to show the distinct separation between oxygen-rich and oxygen-poor pathways.

Question 2. Write short notes on the following (5points each):- a) ECG b) Hill Reaction c) Osmoregulation d) Pace Maker e) Ivory
Answer:
a) ECG (Electrocardiogram): 1. It is a diagnostic test that records the electrical activity of the heart over a period of time. 2. Electrodes are placed on the skin to detect tiny electrical changes during cardiac muscle depolarization and repolarization. 3. The recording displays typical waves labeled P, Q, R, S, and T. 4. It helps doctors detect irregular heartbeats, heart attacks, and other cardiac abnormalities. 5. The device used to perform this recording is called an electrocardiograph.
b) Hill Reaction: 1. It represents the light-dependent phase of photosynthesis discovered by Robert Hill. 2. It occurs within the thylakoid membranes of chloroplasts in the presence of light. 3. Light energy splits water molecules into hydrogen ions, electrons, and oxygen in a process called photolysis. 4. The electrons and protons are transferred to convert NADP+ into NADPH. 5. This reaction produces oxygen as a byproduct, which is released into the atmosphere.
c) Osmoregulation: 1. It is the active regulation of the osmotic pressure of bodily fluids to maintain homeostasis. 2. It keeps the water and salt balance in organisms within optimal limits. 3. In humans, the kidneys play a primary role in filtering blood and regulating water reabsorption. 4. It prevents body cells from swelling up with too much water or shrinking from dehydration. 5. Freshwater and marine organisms have specialized adaptations to handle salt differences in their environments.
d) Pace Maker: 1. It is a specialized bundle of cardiac muscle fibers, called the Sinoatrial (SA) node, located in the right atrium. 2. It naturally generates electrical impulses that spread across the heart muscle to initiate contraction. 3. This electrical signaling sets the natural rhythm and rate of the heartbeat. 4. If the natural SA node fails, an artificial pacemaker can be surgically implanted to regulate the heart. 5. The artificial device runs on a small battery and sends electrical pulses to keep the heart beating regularly.
e) Ivory: 1. It is a hard, white, opaque dentine material that forms the main part of the tusks of elephants and some other mammals. 2. It is highly valued for carving intricate art pieces, piano keys, and decorative items. 3. The high demand for ivory has led to illegal poaching, threatening elephant populations with extinction. 4. Most countries have banned the international trade of ivory to protect wild elephants. 5. Synthetic alternatives are now used to replace natural ivory in manufacturing.
In simple words: This section provides short five-point notes on medical, biological, and natural science terms like heart tests, plant reactions, and water balance.

Exam Tip: For five-point notes, write short, distinct sentences with key definitions in the first point to secure maximum marks.

Question 3. Distinguish between : a) Xylem / Phloem b) RBC / WBC c) Blood / Lymph d) Artery / Vein / Capillary e) Left Lung / Right Lung f) Pulmonary Circulation / Systemic Circulation g) Photosynthesis / Respiration h) Light Reaction / Dark Reaction i) Bicuspid Valves / Tricuspid Valves
Answer: Let's present the differences clearly:
a) Xylem vs Phloem: - Xylem transports water and dissolved mineral salts from the roots up to the leaves. Phloem distributes prepared organic food from the leaves to all other parts of the plant. - Xylem cells are mostly dead at maturity, while phloem consists of living cells.
b) RBC (Red Blood Cells) vs WBC (White Blood Cells): - RBCs contain hemoglobin to transport oxygen. WBCs lack hemoglobin and protect the body against pathogens. - RBCs are biconcave and lack a nucleus at maturity. WBCs have distinct nuclei and varying shapes.
c) Blood vs Lymph: - Blood is a red fluid connective tissue that flows through blood vessels. Lymph is a colorless fluid that flows through lymphatic channels. - Blood contains red blood cells, white blood cells, platelets, and plasma. Lymph lacks red blood cells and platelets, containing mostly lymphocytes.
d) Artery vs Vein vs Capillary: - Arteries carry oxygen-rich blood away from the heart under high pressure (except the pulmonary artery). Veins return oxygen-poor blood to the heart under low pressure. Capillaries connect arteries and veins to allow direct nutrient exchange with tissues. - Arteries have thick, elastic walls. Veins have thinner walls with valves to prevent backflow. Capillaries have ultra-thin, single-layered walls.
e) Left Lung vs Right Lung: - The left lung is slightly smaller and divided into two lobes. The right lung is larger and divided into three lobes. - The left lung has a cardiac notch to accommodate the heart, which the right lung lacks.
f) Pulmonary Circulation vs Systemic Circulation: - Pulmonary circulation is the short loop that carries deoxygenated blood from the heart to the lungs and returns oxygenated blood to the heart. Systemic circulation is the larger loop that delivers oxygenated blood from the heart to the rest of the body and returns deoxygenated blood.
g) Photosynthesis vs Respiration: - Photosynthesis is an anabolic process in plants that uses light to build glucose and releases oxygen. Respiration is a catabolic process in all living organisms that breaks down glucose to release carbon dioxide and energy (ATP).
h) Light Reaction vs Dark Reaction: - The light reaction happens in the thylakoid membranes of chloroplasts and requires direct sunlight to produce ATP and NADPH. The dark reaction (Calvin cycle) happens in the stroma, does not need direct sunlight, and uses ATP and NADPH to fix carbon dioxide into glucose.
i) Bicuspid Valves vs Tricuspid Valves: - The bicuspid valve (mitral valve) is located between the left atrium and left ventricle. The tricuspid valve is situated between the right atrium and right ventricle. - The bicuspid valve has two flaps (cusps), while the tricuspid valve has three.
In simple words: This compares different body parts and plant processes, like how water and food move in plants, and how our blood vessels work.

Exam Tip: When answering "distinguish between" questions, presenting the differences in a comparative table makes it easier for examiners to award full marks.

Question a. Suddenly your friend has collapsed in the assembly ground. Suppose you are standing next to him/her. What will you do? What could be the reasons behind this? His/her parents should be informed or not? Who will inform them?
Answer: If my classmate collapses, I will quickly help them lie down in a shaded spot, raise their legs to improve circulation, and call the school medical team. The collapse may be due to dehydration, physical fatigue, low blood sugar, or heat stroke from standing in the sun. Yes, their parents must be informed immediately. This communication should be handled by the class teacher or school administration to convey the situation calmly and accurately.
In simple words: Help a fainted classmate into the shade, lift their feet, and notify the school medical staff. Parents must be contacted by the school office.

Exam Tip: Point out that professional administrative staff should contact the parents to prevent unnecessary panic or miscommunication.

Question B. Ritik’s grandmother is suffering from acute abdominal pain for the last 10-12 days .She has not visited any doctor so far. But daily she taking Devi Mata’s “charnamrit” supplied by the panditji of a local temple. Yesterday she found blood in her faeces. She is really scared now .How can Ritwik (a 10th standard boy) provide her comfort? What are the probable causes? Do you support him for going against the religious faith? Why or why not?
Answer: Ritwik can comfort his grandmother by listening to her worries calmly, reassuring her that seeking medical help does not disrespect her faith, and gently convincing her to see a doctor immediately. The presence of blood in her faeces coupled with severe abdominal pain could indicate serious medical conditions such as stomach ulcers, gastrointestinal bleeding, severe infections, or inflammatory bowel disease. I support Ritwik in guiding her toward medical care. This action does not contradict religious faith; science and medical treatments are essential tools to heal physical illnesses. Relying solely on ritual water for physical ailments while ignoring severe symptoms like internal bleeding is unsafe and life-threatening.
In simple words: Ritwik should comfort his grandmother and take her to a clinic immediately because blood in stool is a medical emergency. Seeking medical treatment works alongside faith to ensure health and safety.

Exam Tip: Maintain a balanced and highly respectful tone while emphasizing that medical science is essential to resolve physical emergencies.

Science (Physics) - Chapter-1. Energy

Question 1. A solar water heater cannot be used to get hot water on
(a) a sunny day.
(b) a cloudy day.
(c) a hot day.
(d) a windy day.
Answer: (b) a cloudy day.
In simple words: A solar water heater needs direct sunlight to heat up water. On a cloudy day, the sun is blocked, so the heater cannot work.

Exam Tip: Solar thermal devices rely on direct infrared radiation from the sun, which is largely absorbed or scattered by clouds.

Question 2. Compare and contrast fossil fuels and the Sun as direct sources of energy.
Answer: Fossil fuels (like coal, petroleum, and natural gas) are non-renewable, exhaustible, and highly polluting energy sources that release greenhouse gases when burned. In contrast, the Sun is a renewable, virtually inexhaustible, and clean source of energy that does not cause direct pollution. While fossil fuels provide highly concentrated and continuous energy on demand, solar energy is dilute and depends on weather conditions and daylight hours.
In simple words: Fossil fuels pollute the air and will run out eventually, but they are easy to use anytime. The Sun's energy is clean and unlimited, but we can only collect it during the day.

Exam Tip: Mention keywords like "renewable vs non-renewable" and "continuous availability vs weather dependence" to write a high-scoring comparison.

Question 3. Compare and contrast bio-mass and hydro electricity as sources of energy.
Answer: Bio-mass energy is obtained from organic materials like wood, agricultural waste, and cow dung, whereas hydroelectricity is generated from the kinetic energy of flowing water turning turbines. Both are renewable sources of energy, but burning bio-mass releases carbon dioxide and air pollutants, while generating hydroelectricity is completely clean. Additionally, establishing hydroelectric plants requires large dams that can disrupt local river ecosystems, whereas bio-mass systems are typically small-scale and easier to manage locally.
In simple words: Bio-mass comes from organic waste and releases smoke when burned, while hydroelectricity comes from water and is clean but requires building large dams.

Exam Tip: Discuss the environmental impact of both sources, specifically focusing on air pollution for biomass and habitat disruption for hydro dams.

Question 4. What are the limitations of extracting energy from—
(a) the wind? (b) waves? (c) tides?
Answer:
**(a) Wind Energy:** It requires large areas of land to set up wind farms, and the wind speed must be consistently high (above 15 km/h) to turn the turbines effectively. It also has high initial setup costs and can pose a danger to birds.
**(b) Wave Energy:** It can only be harvested in coastal areas with strong, consistent waves. The machinery must be strong enough to withstand severe ocean storms and salt corrosion.
**(c) Tidal Energy:** It depends on the gravitational pull of the moon, which only creates high tides a few times a day. There are also very few coastal locations suitable for constructing tidal dams.
In simple words: Wind needs big open spaces and constant breezes. Ocean waves and tides are hard to capture because salt ruins machinery and strong currents only happen in specific places.

Exam Tip: List at least two distinct geographical or technical limitations for each energy source.

Question 5. On what basis would you classify energy sources as
(a) renewable and non-renewable?
(b) exhaustible and inexhaustible?
Are the options given in (a) and (b) the same?
Answer:
**(a) Renewable and non-renewable:** Classified based on their ability to regenerate naturally over a short period. Renewable sources (like solar and wind) replenish quickly, while non-renewable sources (like coal and petroleum) take millions of years to form.
**(b) Exhaustible and inexhaustible:** Classified based on whether they will run out due to continuous human consumption. Exhaustible sources have limited reserves, whereas inexhaustible sources are unlimited. Yes, these two classifications are practically the same because renewable sources are inexhaustible, and non-renewable sources are exhaustible.
In simple words: Renewable and inexhaustible mean the energy will never run out (like the sun). Non-renewable and exhaustible mean we will eventually use it all up (like coal).

Exam Tip: Clarify that although the criteria differ slightly (regeneration rate vs consumption limit), the resulting categories contain the exact same energy sources.

Question 6. What are the qualities of an ideal source of energy?
Answer: An ideal energy source should have the following qualities: 1. High calorific value, meaning it produces a large amount of heat energy per unit mass. 2. Easy availability and accessibility over a long period. 3. Safe and convenient to store and transport. 4. Clean and environmentally friendly, producing minimal pollution or waste residue. 5. Highly economical and cost-effective for general public use.
In simple words: A perfect fuel should give a lot of heat, be cheap, easy to carry, safe to use, and not make any smoke or pollution.

Exam Tip: Remember to mention "high calorific value" and "low pollution" as these are the primary scientific criteria for evaluating fuels.

Question 7. What are the advantages and disadvantages of using a solar cooker? Are there places where solar cookers would have limited utility?
Answer: Advantages of a solar cooker: It uses free, renewable sunlight, requires no fuel, and produces zero smoke or greenhouse gases. Disadvantages: It cannot be used at night, on cloudy days, or indoors. The cooking process is slow and it cannot be used for baking or deep-frying. Solar cookers have very limited utility in polar regions, heavily forested areas, and places with long winters or frequent rainfall, where sunlight is weak or inconsistent.
In simple words: Solar cookers save fuel and do not pollute, but they work slowly and only work when the sun is shining. They are not useful in cloudy or rainy regions.

Exam Tip: Group your answer into three clear sections: advantages, disadvantages, and geographical limitations to ensure a structured response.

Question 8. What are the environmental consequences of the increasing demand for energy?
Answer: The rising demand for energy has led to several severe environmental issues: 1. Air pollution and global warming caused by burning fossil fuels, which releases carbon dioxide, sulfur, and nitrogen oxides. 2. Acid rain, which damages forests, soils, and aquatic ecosystems. 3. Habitat destruction and loss of biodiversity due to coal mining, oil drilling, and flooding lands for large hydro dams. 4. Large amounts of toxic fly ash and radioactive waste from thermal and nuclear power plants.
In simple words: Demanding more energy makes us burn more fossil fuels, which pollutes the air, heats up the earth, and destroys forests to build power plants.

Exam Tip: Use scientific terms like "greenhouse effect", "acid rain", and "habitat destruction" to describe the consequences.

Question 9. What are the disadvantages of fossil fuels?
Answer: The main disadvantages of fossil fuels are: 1. They are non-renewable and their limited reserves will eventually run out. 2. Burning them releases carbon dioxide, which is the primary cause of global warming. 3. They release harmful pollutants like sulfur dioxide and carbon monoxide, which cause respiratory illnesses and acid rain. 4. Accidental oil spills during extraction and transport cause massive damage to marine life.
In simple words: Fossil fuels are running out, they cause climate change, and their smoke makes people sick and creates acid rain.

Exam Tip: Focus on two distinct aspects: their exhaustible nature and their damaging emissions.

Question 10. Why are we looking at alternate sources of energy?
Answer: We are searching for alternative energy sources because our current reliance on fossil fuels is unsustainable. Fossil fuel reserves are depleting rapidly and will soon run out. Additionally, burning them releases greenhouse gases that drive global climate change and cause severe air pollution. Developing clean, renewable alternatives like solar, wind, and tidal energy ensures long-term energy security while protecting our environment.
In simple words: We need alternative energy because fossil fuels are running out and burning them causes climate change and air pollution.

Exam Tip: Mention both "depletion of fossil reserves" and "environmental protection" as the two main reasons for this transition.

Question 11. How has the traditional use of wind and water energy been modified for our convenience?
Answer: Traditionally, wind energy was used only for sailing ships and running mechanical windmills to grind grain or lift water. Today, it has been modified using large wind turbines connected to generators to produce electricity. Similarly, water energy, which was once used simply to turn watermills for mechanical tasks, is now harnessed by constructing large dams where falling water turns high-speed turbines to generate hydroelectricity.
In simple words: We used to use wind and water only for mechanical work like grinding grain. Now, we use modern wind turbines and water dams to generate electricity.

Exam Tip: Contrast the historical mechanical uses of wind and water with their modern conversion into electricity.

Question 12. What kind of mirror – concave, convex or plain – would be best suited for use in a solar cooker? Why?
Answer: A concave mirror is best suited for a solar cooker. This is because concave mirrors are converging mirrors; they focus parallel rays of sunlight coming from a large area onto a single focal point. Placing the cooking pot at this focus concentrates the heat energy, raising the temperature quickly and making the cooker much more efficient than one using plain or convex mirrors.
In simple words: A concave mirror is best because it acts like a lens, focusing all the sun's rays onto one hot spot where the cooking pot sits.

Exam Tip: Explain the optical property of a concave mirror as "converging parallel rays to a single focus" to secure full marks.

Question 13. What is geothermal energy?
Answer: Geothermal energy is heat energy derived from deep within the Earth's crust. Radioactive decay and geological activity heat up underground rocks. When groundwater contacts these hot rocks, it turns into high-pressure steam. This steam can be piped to the surface to turn turbines and generate clean, continuous electricity.
In simple words: Geothermal energy is heat from deep inside the earth. We use the steam from hot underground water to spin turbines and make electricity.

Exam Tip: Explain how underground heat turns water into steam to drive electric generators.

Question 14. What are the advantages of nuclear energy?
Answer: The key advantages of nuclear energy are: 1. It produces an exceptionally large amount of energy from a very small amount of fuel compared to coal or oil. 2. It does not release greenhouse gases or air pollutants during electricity generation, helping combat climate change. 3. It provides a highly reliable, continuous base-load power supply that does not depend on weather conditions.
In simple words: Nuclear power produces massive amounts of energy without creating dirty smoke, and it can run continuously day and night.

Exam Tip: Highlight its "high energy density" and "low greenhouse emissions" as its primary benefits.

Question 15. Hydrogen has been used as a rocket fuel. Would you consider it a cleaner fuel than CNG? Why or why not?
Answer: Yes, hydrogen is a much cleaner fuel than CNG (Compressed Natural Gas). When hydrogen burns in oxygen, its only byproduct is water vapor, which is completely harmless to the environment. CNG, being a hydrocarbon, releases carbon dioxide (a greenhouse gas) and small amounts of carbon monoxide when burned, contributing to global warming and air pollution.
In simple words: Yes, hydrogen is cleaner because burning it only makes water. Burning CNG releases carbon dioxide, which heats up the earth.

Exam Tip: Support your answer with the simple chemical combustion reactions of both fuels to show their byproducts.

Class - X - Social Science

Question 1. Prepare a project on Disaster management.
Answer: Here are brief content structures for each disaster management topic: - **Tsunami (Roll 1-10):** Focus on how underwater earthquakes generate massive waves. Discuss warning systems, coastal evacuation protocols, and planting mangroves to reduce wave impact. - **First-Aid (Roll 11-20):** Outline critical emergency steps for handling fractures, burns, severe bleeding, and CPR (Cardiopulmonary Resuscitation). - **Communication Facilities (Roll 21-30):** Detail how HAM radio, satellite phones, and emergency broadcasts remain operational when mobile networks collapse during a disaster. - **Disaster Resilient Structures (Roll 31-40):** Explain engineering techniques used to build earthquake-resistant houses and flood-safe raised structures in high-risk zones.
In simple words: Create a handwritten 15-page project file on your assigned disaster safety topic using newspapers, books, and diagrams.

Exam Tip: Ensure your project contains an index page, introduction, neat diagrams, and a detailed bibliography to score full marks.

Question 2. Make a PPT on PROJECT RHINO.
Answer: Your presentation on 'Project Rhino' should include: 1. Introduction to the Indian One-Horned Rhinoceros and its natural habitat in Assam (Kaziranga National Park). 2. The main threats to their survival, such as poaching for their horns and habitat loss. 3. The launch of Project Rhino (and Indian Rhino Vision 2020) to protect and increase their population. 4. Key conservation strategies: anti-poaching patrols, habitat restoration, and local community involvement.
In simple words: Prepare a digital presentation showing how conservation projects are saving the one-horned rhinos in India.

Exam Tip: Use high-quality pictures of Kaziranga National Park and bullet points on each slide instead of long paragraphs to keep your presentation engaging.

Question 3. Visit Parliament Museum, Pandit Pant Marg, New Delhi. Write a report on the “Story of Indian Democratic Heritage”. Write report on A4 size sheet. Use blue or black gel pen.
Answer: Your report on the Indian Democratic Heritage should highlight: 1. The historical evolution of democracy in India, from ancient janapadas and panchayats to the modern constitution. 2. Key museum exhibits: interactive displays showing the transfer of power and the drafting of the Constitution by Dr. B.R. Ambedkar. 3. The struggle for independence and how universal adult suffrage was established to give every citizen a voice.
In simple words: Write a neat report on A4 paper describing your visit to the Parliament Museum and what you learned about how India became a democracy.

Exam Tip: Mention specific historical milestones like the "republics of ancient India" and the "Constituent Assembly debates" to write an outstanding report.

Question 1. “Resources are regarded as free gifts of nature”. Discuss.
Answer: Although resources like water, soil, air, and minerals exist naturally, they are not entirely "free gifts." They only become valuable resources when humans use technology and skills to transform them into usable forms. For example, crude oil underground is useless until refined into fuel. Treating them as free gifts leads to over-exploitation and pollution; we must manage them carefully to ensure sustainable development.
In simple words: Natural materials are not just free gifts because we have to work to make them useful. If we treat them as free, we will pollute and waste them.

Exam Tip: Emphasize that human skills and technology are necessary to transform natural elements into valuable resources.

Question 2. Write a short note on PROJECT TIGER.
Answer: Project Tiger is a major wildlife conservation initiative launched by the Government of India in 1973. Its primary goal is to protect the declining population of Bengal tigers and preserve their natural habitats. The project established specialized tiger reserves across the country, using anti-poaching squads and scientific monitoring to help tiger populations recover.
In simple words: Project Tiger is a wildlife program started in 1973 that sets up safe forest reserves to save Indian tigers from poachers.

Exam Tip: Mention key terms like "habitat preservation", "anti-poaching patrols", and "ecological balance" in your note.

Question 3. Give advantages of Himalayan Yew Tree.
Answer: The Himalayan Yew (Taxus wallichiana) is a valuable medicinal plant found in parts of the Himalayas. Its bark, needles, and seeds contain a chemical compound called 'Taxol', which is used to manufacture highly effective anti-cancer drugs. It also plays a vital role in protecting soil from erosion on steep mountain slopes.
In simple words: The Himalayan Yew is a mountain tree that produces 'Taxol', a compound used to make life-saving cancer medicines.

Exam Tip: Highlight the chemical "Taxol" and its medical use in treating cancer as its primary benefit.

Question 4. What is Bio-diversity? Why bio-diversity important for human life?
Answer: Biodiversity refers to the wide variety of plant and animal species living within an ecosystem. It is essential for human survival because different species work together to provide clean air, purified water, fertile soil for crops, and natural pollination. It also serves as a vital source of medicines, food, and raw materials for industries.
In simple words: Biodiversity means the variety of life on Earth. It is important because plants and animals keep our air, water, and soil clean and healthy.

Exam Tip: Discuss "ecological balance" and "ecosystem services" to write a strong, scientific answer.

Question 5. How is urban development directly related to the cost of ecology and environment?
Answer: Rapid urban development often occurs at the expense of local ecosystems. Building roads and cities requires clearing forests, which destroys wildlife habitats and reduces biodiversity. Concrete surfaces prevent rainwater from soaking into the ground, lowering water tables and causing urban floods. Additionally, rising populations in cities increase energy demand and waste generation, leading to severe air and water pollution.
In simple words: Building cities destroys forests, pollutes water, and causes flooding because concrete blocks rain from soaking into the ground.

Exam Tip: Explain how concrete surfaces cause "groundwater depletion" and "urban heat islands" to show a deep understanding of urban geography.

ग्रीष्मकालीन अवकाश हेतु गृह कार्य
विषय : हिन्दी | कक्षा : X

Question क. निबंध लेखन (शब्द सीमा 280 शब्द) । भ्रष्टाचार निवारण अथवा वही मनुष्य है कि जो मनुष्य के लिए मरे
Answer: भ्रष्टाचार हमारे समाज और राष्ट्र के विकास में एक बहुत बड़ी बाधा है। यह देश की प्रगति को धीमा करता है और पात्र लोगों तक उनके बुनियादी अधिकार पहुँचने नहीं देता। इसे पूरी तरह समाप्त करने के लिए हमें सबसे पहले कड़े कानून लागू करने होंगे। साथ ही, सरकारी कार्यालयों में डिजिटल प्रक्रियाओं और पारदर्शी व्यवस्था को बढ़ावा देना चाहिए। सबसे जरूरी बात यह है कि बचपन से ही बच्चों में ईमानदारी और नैतिक मूल्य विकसित किए जाने चाहिए। एक जागरूक और जिम्मेदार नागरिक ही एक ईमानदार एवं भ्रष्टाचार मुक्त समाज का निर्माण कर सकता है।
In simple words: भ्रष्टाचार को खत्म करने के लिए सख्त नियमों, डिजिटल तकनीक और बच्चों में अच्छे नैतिक संस्कारों का होना बेहद जरूरी है।

Exam Tip: निबंध लिखते समय सबसे पहले एक आकर्षक प्रस्तावना लिखें, फिर मुख्य विषय पर विस्तार से चर्चा करें और अंत में एक सकारात्मक निष्कर्ष के साथ समाप्त करें।

Question ख. पत्र लेखन । सड़क परिवहन के प्रबंधक को बसों की व्यवस्था के लिए शिकायती पत्र लिखिए।
Answer: सेवा में,
प्रबंधक महोदय,
सड़क परिवहन निगम,
[शहर का नाम]

विषय: हमारे क्षेत्र में बसों की अनियमितता एवं खराब व्यवस्था के संबंध में शिकायती पत्र।

महोदय,
मैं इस पत्र के माध्यम से आपका ध्यान हमारे क्षेत्र में बसों की अनुपलब्धता की ओर आकर्षित करना चाहता हूँ। यहाँ सुबह और शाम के समय दफ्तर जाने वाले लोगों और स्कूली बच्चों की भीड़ बहुत अधिक होती है, लेकिन बसों की संख्या काफी कम है। जो बसें चलती भी हैं, उनका कोई निश्चित समय नहीं होता। इस वजह से स्थानीय निवासियों को प्रतिदिन भारी समस्याओं का सामना करना पड़ रहा है। आपसे सविनय अनुरोध है कि व्यस्त समय के दौरान बसों के फेरे बढ़ाए जाएं ताकि यात्रियों को आवश्यक सुविधा मिल सके।

भवदीय,
[आपका नाम]
In simple words: इस पत्र में बसों की कमी और उनके अनिश्चित समय के कारण हो रही परेशानियों को बताते हुए बस सेवा सुधारने की मांग की गई है।

Exam Tip: औपचारिक पत्र लिखते समय हमेशा विषय (Subject) स्पष्ट रूप से लिखें और भाषा को अत्यंत शिष्ट एवं मर्यादित रखें।

Question ग. लेखन एवं रिकॉर्डिंग।पाँच ऐसे व्यक्तियों को चुनो जो सफलता प्राप्त कर चुके हैं। किसी समसामयिक विषय पर साक्षात्कार को सुनें एवं रिकॉर्ड करें, बाद में उसे संवाद रूप में लिख कर प्रस्तुत करें।
Answer: इस रचनात्मक गतिविधि को पूरा करने के लिए आप डॉ. ए.पी.जे. अब्दुल कलाम, सचिन तेंदुलकर, मैरी कॉम, डॉ. बी.आर. अंबेडकर और स्वामी विवेकानंद जैसी महान हस्तियों के प्रेरणादायी जीवन का चयन कर सकते हैं। इसके बाद, पर्यावरण संरक्षण या शिक्षा प्रणाली जैसे किसी समसामयिक विषय पर एक साक्षात्कार (इंटरव्यू) सुनें। इस वार्तालाप को संवाद शैली (Dialogue Format) में इस प्रकार लिखें:
प्रश्नकर्ता: सर, वर्तमान समय में पर्यावरण को बचाने के लिए सबसे आवश्यक कदम क्या है?
विशेषज्ञ: सबसे पहला कदम है कि हम एकल-उपयोग वाले प्लास्टिक का इस्तेमाल बंद करें और अधिक से अधिक पौधे लगाएं।
इस प्रकार पूरे संवाद को अपनी रचनात्मकता के साथ कॉपी में दर्ज करें और इसकी एक ऑडियो क्लिप भी तैयार रखें।
In simple words: पाँच सफल लोगों को चुनें और पर्यावरण या किसी अन्य मुख्य विषय पर एक बातचीत (संवाद) लिखकर उसे अपनी आवाज में रिकॉर्ड करें।

Exam Tip: संवाद लेखन में भाषा हमेशा सरल, स्वाभाविक और पात्रों के अनुकूल होनी चाहिए ताकि पढ़ने वाले को संवाद सहज लगे।

Question घ. याद करने का कार्य:- मुहावरे:- मक्खियाँ मारना, हाथ-पैर मारना, खून का घूँट पीकर रह जाना, कोरा जवाब देना, कीचड़ उछालना, हथेली पर सरसों उगाना, बाजी मारना, हाथ बँटाना, होश उड़ जाना, हाथ पसारना, लकीर का फकीर, लोहे के चने चबाना, श्री गणेश करना, लोहा लेना, रंगा सियार, रंग में भंग पड़ना, मुट्ठी गर्म करना, मजा किरकिरा करना, माथा ठनकना, सिर पर चढ़ना, हवा से बातें करना।
Answer: यहाँ दिए गए प्रमुख मुहावरों के अर्थ और उनके वाक्य प्रयोग प्रस्तुत हैं:
1. मक्खियाँ मारना (बेकार बैठे रहना) - नौकरी छूटने के बाद से सोहन घर पर बैठकर सिर्फ मक्खियाँ मार रहा है।
2. हाथ-पैर मारना (काफी प्रयास करना) - उसने परीक्षा में सफल होने के लिए बहुत हाथ-पैर मारे, लेकिन सफलता नहीं मिली।
3. खून का घूँट पीकर रह जाना (क्रोध को भीतर ही दबा लेना) - मालिक के अपमानजनक शब्दों को सुनकर नौकर खून का घूँट पीकर रह गया।
4. कोरा जवाब देना (साफ मना करना) - जब मैंने रमेश से मदद मांगी, तो उसने मुझे कोरा जवाब दे दिया।
5. कीचड़ उछालना (बदनाम करना) - बिना किसी ठोस प्रमाण के दूसरों पर कीचड़ उछालना बहुत बुरी बात है।
6. हथेली पर सरसों उगाना (असंभव कार्य को तुरंत करने की कोशिश करना) - कठिन परीक्षा एक ही रात में पास करना हथेली पर सरसों उगाने जैसा है।
7. बाजी मारना (जीत जाना) - इस बार वार्षिक दौड़ प्रतियोगिता में राहुल ने बाजी मार ली।
8. हाथ बँटाना (मदद करना) - हमें घरेलू कार्यों में अपनी माताजी का हाथ बँटाना चाहिए।
9. होश उड़ जाना (घबरा जाना) - अचानक सामने जंगली जानवर को देखकर राहगीर के होश उड़ गए।
10. हाथ पसारना (याचना करना या मदद माँगना) - एक स्वाभिमानी व्यक्ति कभी किसी के सामने हाथ नहीं पसारता।
11. लकीर का फकीर (पुरानी रूढ़ियों पर चलना) - दुनिया आगे बढ़ गई, पर वह आज भी लकीर का फकीर बना हुआ है।
12. लोहे के चने चबाना (कठिन परिस्थितियों का सामना करना) - भारतीय सेना से मुकाबला करना दुश्मनों के लिए लोहे के चने चबाने जैसा है।
13. श्री गणेश करना (कार्य का प्रारंभ करना) - आज शुभ मुहूर्त देखकर पिताजी ने अपनी नई दुकान का श्री गणेश किया।
14. लोहा लेना (सामना करना) - स्वतंत्रता सेनानियों ने अंग्रेजी हुकूमत से डटकर लोहा लिया था।
15. रंगा सियार (ढोंगी व्यक्ति) - उस पर विश्वास मत करना, वह तो असल में एक रंगा सियार है।
16. रंग में भंग पड़ना (विघ्न आना) - शादी के उत्सव के दौरान अचानक तेज आंधी आने से रंग में भंग पड़ गया।
17. मुट्ठी गर्म करना (रिश्वत देना) - आज के समय में कुछ दफ्तरों में मुट्ठी गर्म किए बिना कोई काम आसानी से नहीं होता।
18. मजा किरकिरा करना (आनंद बिगाड़ना) - फिल्म के बीच में बिजली चले जाने से हमारा सारा मजा किरकिरा हो गया।
19. माथा ठनकना (संदेह होना) - उसकी संदेहास्पद बातें सुनकर ही मेरा माथा ठनक गया था।
20. सिर पर चढ़ना (अधिक ढील देना) - बच्चों को बहुत ज्यादा लाड-प्यार देकर सिर पर नहीं चढ़ाना चाहिए।
21. हवा से बातें करना (बहुत तेज दौड़ना) - मैदान में उतरते ही महाराणा प्रताप का घोड़ा हवा से बातें करने लगता था।
In simple words: यहाँ सभी मुहावरों के अर्थ और वाक्य इस प्रकार दिए गए हैं ताकि आप इन्हें आसानी से समझकर याद कर सकें।

Exam Tip: बोर्ड परीक्षा में मुहावरों के वाक्य प्रयोग इस तरह करें जिससे मुहावरे का अंतर्निहित अर्थ पूरी तरह स्पष्ट हो जाए।

Question घ. लोकोक्तियाँ:- ओस चाटे प्यास नहीं बुझती, दोनों हाथों में लड्डू, जैसी करनी वैसी भरनी, हाथी के दाँत खाने के और दिखाने के और, हाथ कंगन को आरसी क्या, सौ सुनार की एक लुहार की, साँप भी मरे लाठी भी न टूटे, रस्सी जल गई मगर बल नहीं गया, मन चंगा तो कठौती में गंगा, बोया पेड़ बबूल का तो आम कहाँ से होय, पर उपदेश कुशल बहुतेरे, न रहेगा बाँस न बजेगी बाँसुरी, नाम बड़े दर्शन छोटे, झूठ के पाँव नहीं होते, धोबी का कुत्ता न घर का न घाट का, जाको राखे साइयाँ मार सके न कोए, गंगा गए गंगादास जमुना गए जमुनादास, खिसियानी बिल्ली खंभा नोचे, खरबूजे को देखकर खरबूजा रंग बदलता है, कंगाली में आटा गीला।
Answer: यहाँ दी गई लोकोक्तियों के अर्थ और उनके वाक्य प्रयोग निम्नलिखित हैं:
1. ओस चाटे प्यास नहीं बुझती (कम मात्रा में मिलने पर आवश्यकता पूरी न होना) - इतनी बड़ी भूख में केवल एक बिस्कुट खाने से क्या होगा, ओस चाटे प्यास नहीं बुझती।
2. दोनों हाथों में लड्डू (हर परिस्थिति में लाभ होना) - सोहन की लॉटरी भी लग गई और नौकरी भी मिल गई, उसके तो दोनों हाथों में लड्डू हैं।
3. जैसी करनी वैसी भरनी (कर्म के अनुसार फल मिलना) - शाम ने मेहनत नहीं की और अनुत्तीर्ण हो गया; सच है, जैसी करनी वैसी भरनी।
4. हाथी के दाँत खाने के और दिखाने के और (कथनी और करनी में अंतर होना) - कुछ लोग बाहर से सीधे दिखते हैं पर अंदर से कपटी होते हैं, इसे कहते हैं हाथी के दाँत खाने के और दिखाने के और।
5. हाथ कंगन को आरसी क्या (प्रत्यक्ष को प्रमाण की आवश्यकता नहीं) - जब चोर चोरी के माल के साथ रंगे हाथों पकड़ा गया, तो सबूत क्या चाहिए; हाथ कंगन को आरसी क्या।
6. सौ सुनार की एक लुहार की (सौ निर्बल प्रहारों पर एक सबल प्रहार भारी होना) - उसने मेरे खिलाफ कई छोटी साजिशें कीं, लेकिन मैंने एक ही सच सबके सामने लाकर उसका काम तमाम कर दिया; सौ सुनार की एक लुहार की।
7. साँप भी मरे लाठी भी न टूटे (बिना किसी नुकसान के काम बन जाना) - हमें इस पारिवारिक समस्या को इस तरह सुलझाना चाहिए कि काम भी हो जाए और संबंध भी न बिगड़ें; साँप भी मरे लाठी भी न टूटे।
8. रस्सी जल गई मगर बल नहीं गया (सब कुछ नष्ट होने पर भी अहंकार न जाना) - राजा साहब की जमींदारी चली गई, पर उनका रौब आज भी वैसा ही है; इसे कहते हैं रस्सी जल गई मगर बल नहीं गया।
9. मन चंगा तो कठौती में गंगा (हृदय शुद्ध हो तो घर पर ही तीर्थ है) - यदि आपका मन साफ है, तो आपको पवित्रता के लिए कहीं बाहर जाने की आवश्यकता नहीं; मन चंगा तो कठौती में गंगा।
10. बोया पेड़ बबूल का तो आम कहाँ से होय (बुरे कार्यों का अच्छा परिणाम नहीं मिलता) - जीवन भर दूसरों का अहित करने वाले को सुख कैसे मिल सकता है; बोया पेड़ बबूल का तो आम कहाँ से होय।
11. पर उपदेश कुशल बहुतेरे (दूसरों को उपदेश देना सरल है पर स्वयं अमल करना कठिन) - वह सबको जल्दी उठने की सलाह देता है पर खुद देर से जागता है; पर उपदेश कुशल बहुतेरे।
12. न रहेगा बाँस न बजेगी बाँसुरी (विवाद की जड़ को ही नष्ट कर देना) - रोज-रोज के झगड़े से बचने के लिए उसने वह विवादित वस्तु ही बेच दी; न रहेगा बाँस न बजेगी बाँसुरी।
13. नाम बड़े दर्शन छोटे (प्रसिद्धि अधिक पर गुणवत्ता कम होना) - उस महंगे होटल का भोजन बहुत साधारण था; इसे कहते हैं नाम बड़े दर्शन छोटे।
14. झूठ के पाँव नहीं होते (झूठ अधिक समय तक टिक नहीं पाता) - पुलिस की पूछताछ में उसका सच बाहर आ ही गया, क्योंकि झूठ के पाँव नहीं होते।
15. धोबी का कुत्ता न घर का न घाट का (कहीं का न रहना) - उसने दो अलग-अलग नौकरियों के चक्कर में दोनों खो दीं; वह अब धोबी का कुत्ता न घर का न घाट का बनकर रह गया है।
16. जाको राखे साइयाँ मार सके न कोए (ईश्वर जिसकी रक्षा करे उसका कोई कुछ नहीं बिगाड़ सकता) - भयंकर हादसे में भी वह बच्चा सुरक्षित बच गया; सच है, जाको राखे साइयाँ मार सके न कोए।
17. गंगा गए गंगादास जमुना गए जमुनादास (अवसरवादी होना) - उसका कोई एक सिद्धांत नहीं है, वह तो बस गंगा गए गंगादास जमुना गए जमुनादास की तरह व्यवहार करता है।
18. खिसियानी बिल्ली खंभा नोचे (शर्मिंदा होने पर अकारण गुस्सा निकालना) - खेल में पराजित होने के बाद वह अपनी ही टीम के सह-खिलाड़ियों पर चिल्लाने लगा; खिसियानी बिल्ली खंभा नोचे।
19. खरबूजे को देखकर खरबूजा रंग बदलता है (संगति का असर पड़ना) - कक्षा के पढ़ने वाले छात्रों को देखकर सोहन ने भी पढ़ाई शुरू कर दी; खरबूजे को देखकर खरबूजा रंग बदलता है।
20. कंगाली में आटा गीला (विपत्ति पर और विपत्ति आना) - व्यापार में घाटा तो हुआ ही था, ऊपर से घर में चोरी भी हो गई; कंगाली में आटा गीला।
In simple words: समाज के दीर्घकालिक अनुभवों से बनी इन लोकोक्तियों के अर्थ और व्यावहारिक उदाहरण यहाँ दिए गए हैं।

Exam Tip: लोकोक्ति का प्रयोग करते समय यह ध्यान रखें कि वह किसी प्रसंग या घटना के अंत में एक सार्थक टिप्पणी के रूप में आए।

Question घ. समानार्थक शब्द:- दो-दो समानार्थक शब्द लिखिए:- सरस्वती, समुद्र, सिंह, मित्र, लक्ष्मी, भौंरा, बिजली, युद्ध, चमक, पवन, नौका, दुख, गरीब, ताल, नक्षत्र, जंगल, कुशल, गंगा, कपड़ा, अहंकार।
Answer: दिए गए शब्दों के दो-दो पर्यायवाची (समानार्थक) शब्द निम्नलिखित हैं:
1. सरस्वती - शारदा, वीणापाणि
2. समुद्र - सागर, जलधि
3. सिंह - शेर, वनराज
4. मित्र - दोस्त, सखा
5. लक्ष्मी - रमा, कमला
6. भौंरा - भ्रमर, अलि
7. बिजली - विद्युत, चंचला
8. युद्ध - रण, संग्राम
9. चमक - कांति, प्रभा
10. पवन - वायु, हवा
11. नौका - नाव, तरणी
12. दुख - कष्ट, पीड़ा
13. गरीब - निर्धन, दरिद्र
14. ताल - तालाब, सरोवर
15. नक्षत्र - तारा, सितारा
16. जंगल - वन, कानन
17. कुशल - निपुण, योग्य
18. गंगा - भागीरथी, सुरसरि
19. कपड़ा - वस्त्र, पट
20. अहंकार - घमंड, दर्प
In simple words: यहाँ दिए गए सभी शब्दों के दो-दो समान अर्थ वाले शब्द सरल रूप में प्रस्तुत किए गए हैं।

Exam Tip: समानार्थक शब्द याद करते समय उनकी वर्तनी (Spelling) पर विशेष ध्यान दें ताकि लेखन में कोई अशुद्धि न हो।

Question घ. विलोम शब्द:- अल्पायु, अनुकूल, विराग, अनुचित, आलसी, निराहार, मुक्ति, दानव, निश्चल, क्रय, कृतघ्न, ऊसर, निषेध, निर्गुण, स्थूल, दीर्घ, निष्क्रिय, अशिष्ट, वक्र, राग।
Answer: यहाँ दिए गए शब्दों के विलोम (विपरीतार्थक) शब्द प्रस्तुत हैं:
1. अल्पायु - दीर्घायु
2. अनुकूल - प्रतिकूल
3. विराग - अनुराग
4. अनुचित - उचित
5. आलसी - परिश्रमी
6. निराहार - साहार (या आहार)
7. मुक्ति - बंधन
8. दानव - मानव
9. निश्चल - चंचल
10. क्रय - विक्रय
11. कृतघ्न - कृतज्ञ
12. ऊसर - उर्वर (या उपजाऊ)
13. निषेध - विधि
14. निर्गुण - सगुण
15. स्थूल - सूक्ष्म
16. दीर्घ - लघु
17. निष्क्रिय - सक्रिय
18. अशिष्ट - शिष्ट
19. वक्र - ऋजु (या सरल)
20. राग - विराग (या द्वेष)
In simple words: इन सभी मुख्य शब्दों के ठीक विपरीत अर्थ रखने वाले विलोम शब्दों की सूची यहाँ दी गई है।

Exam Tip: तत्सम शब्दों का विलोम हमेशा तत्सम ही होना चाहिए (जैसे - अशिष्ट का विलोम शिष्ट होगा, न कि अच्छा)।

Question घ. अनेक शब्दों के लिए एक शब्द:- शीघ्र टूटने वाला, किए गए उपकार को मानने वाला, जो उच्च कुल में पैदा हुआ हो, जिसकी आशा न की गई हो, जो हर स्थान पर विद्यमान हो, जिसमें संदेह हो, इस लोक से संबंधित हो, जिसकी मरने की अवस्था हो, इच्छा के अनुकूल, जो घना न हो, साधु स्वभाव की स्त्री, जो आँखों के सामने हो, पर देश में जाकर बसने वाला, छिप कर टोह लेने वाला, मरते दम तक, जो दिखाई न दें, उपजाऊ भूमि, जो बर्फ से घिरा हुआ हो, शक्ति का उपासक, पृथ्वी से संबंध रखने वाला, जो दर्द से भरा हो।
Answer: अनेक शब्दों के स्थान पर प्रयुक्त होने वाले उपयुक्त एक शब्द निम्नलिखित हैं:
1. शीघ्र टूटने वाला - क्षणभंगुर
2. किए गए उपकार को मानने वाला - कृतज्ञ
3. जो उच्च कुल में पैदा हुआ हो - कुलीन
4. जिसकी आशा न की गई हो - अप्रत्याशित
5. जो हर स्थान पर विद्यमान हो - सर्वव्यापी
6. जिसमें संदेह हो - संदेहास्पद (या संदिग्ध)
7. इस लोक से संबंधित हो - ऐहिक (या लौकिक)
8. जिसकी मरने की अवस्था हो - मुमूर्षु (या मरणासन्न)
9. इच्छा के अनुकूल - यथेच्छ (या इच्छानुकूल)
10. जो घना न हो - विरल
11. साधु स्वभाव की स्त्री - आर्या (या सुशीला)
12. जो आँखों के सामने हो - प्रत्यक्ष
13. पर देश में जाकर बसने वाला - प्रवासी (या अप्रवासी)
14. छिप कर टोह लेने वाला - गुप्तचर
15. मरते दम तक - आमरण (या जीवनपर्यंत)
16. जो दिखाई न दे - अदृश्य
17. उपजाऊ भूमि - उर्वरा
18. जो बर्फ से घिरा हुआ हो - हिमाच्छादित
19. शक्ति का उपासक - शाक्त
20. पृथ्वी से संबंध रखने वाला - पार्थिव
21. जो दर्द से भरा हो - दर्दनाक
In simple words: विस्तृत अर्थ वाली बात को संक्षेप में प्रभावी ढंग से कहने के लिए इन एकार्थी शब्दों का अभ्यास करें।

Exam Tip: "कृतज्ञ" (उपकार मानने वाला) और "कृतघ्न" (उपकार न मानने वाला) के सूक्ष्म अंतर को ध्यान से समझें, ये अक्सर परीक्षाओं में पूछे जाते हैं।

Question इ. पढ़ो और रिपोर्ट तैयार करो:- हिन्दी समाचार पत्र पढ़ो, उसकी 10 कटिंग(चित्र सहित) काटो और उस पर स्वतः अपने विचार लिखो।
Answer: इस रचनात्मक गृहकार्य को पूरा करने के लिए दैनिक जागरण, अमर उजाला या नवभारत टाइम्स जैसे किसी प्रतिष्ठित हिंदी समाचार पत्र से 10 महत्वपूर्ण सामाजिक, वैज्ञानिक या खेल संबंधी समाचारों की कटिंग काटें। प्रत्येक कटिंग को अपनी स्क्रैपबुक में व्यवस्थित रूप से चिपकाने के बाद उसके नीचे निम्नलिखित बिंदुओं के आधार पर अपनी व्यक्तिगत टिप्पणी दर्ज करें:
- मुख्य समाचार का संक्षिप्त सारांश (घटना की संक्षिप्त जानकारी)
- इस विषय पर आपकी व्यक्तिगत सोच या राय
- इस समस्या या घटना का समाज पर होने वाला प्रभाव
In simple words: समाचार पत्र से 10 सचित्र खबरें काटें, उन्हें चिपकाएं और नीचे अपने शब्दों में लिखें कि आपको उस खबर के बारे में क्या लगता है।

Exam Tip: समसामयिक मुद्दों (जैसे पर्यावरण संरक्षण, विज्ञान और खेल) से जुड़ी खबरों का चयन करने से आपकी रिपोर्ट अधिक ज्ञानवर्धक बनेगी।

Question च. गिरिराज शरण अग्रवाल द्वारा रचित पुस्तक "पक्ष और विपक्ष" में से कम से कम 5 ऐसे विषय चुनो और लिखो जो समसामयिक हो। (उस पर अपनी विचार रिपोर्ट तैयार करना)
Answer: गिरिराज शरण अग्रवाल की चर्चित पुस्तक "पक्ष और विपक्ष" में से आप निम्नलिखित 5 अत्यंत समसामयिक विषयों का चयन करके उन पर दोनों दृष्टिकोणों (पक्ष और विपक्ष) से अपनी विचार रिपोर्ट तैयार कर सकते हैं:
1. **सोशल मीडिया का युवा पीढ़ी पर प्रभाव**
- *पक्ष:* त्वरित सूचना का आदान-प्रदान, रचनात्मकता की अभिव्यक्ति और वैश्विक संपर्क।
- *विपक्ष:* समय का दुरुपयोग, मानसिक स्वास्थ्य पर विपरीत प्रभाव और साइबर सुरक्षा संबंधी खतरे।
2. **ऑनलाइन शिक्षा बनाम पारंपरिक शिक्षा प्रणाली**
- *पक्ष:* सीखने की सुविधा, संसाधनों की बचत और डिजिटल कौशल का विकास।
- *विपक्ष:* व्यावहारिक शिक्षण का अभाव, शारीरिक स्वास्थ्य पर बुरा प्रभाव और सामाजिक अलगाव।
3. **महानगरों का जीवन: सुखद या जटिल**
- *पक्ष:* रोजगार के उत्कृष्ट अवसर, आधुनिक स्वास्थ्य और शिक्षा सुविधाएं।
- *विपक्ष:* प्रदूषण की समस्या, मानसिक तनाव और पारंपरिक सामाजिक संबंधों में कमी।
4. **प्लास्टिक का बढ़ता उपयोग और पर्यावरण संरक्षण**
- *पक्ष:* सस्ता, टिकाऊ और विभिन्न वस्तुओं के निर्माण के लिए उपयोगी।
- *विपक्ष:* मृदा और जल प्रदूषण का प्रमुख कारण, पशु-पक्षियों के स्वास्थ्य के लिए अत्यंत हानिकारक।
5. **एकल परिवार बनाम संयुक्त परिवार**
- *पक्ष (एकल):* व्यक्तिगत स्वतंत्रता और कम जिम्मेदारियाँ।
- *पक्ष (संयुक्त):* बच्चों को बड़ों का स्नेह और उचित संस्कार, संकट के समय सामूहिक सहयोग।
In simple words: पुस्तक से 5 विषय चुनकर उनके पक्ष (फायदे) और विपक्ष (नुकसान) दोनों दृष्टिकोणों को स्पष्ट करते हुए अपनी रिपोर्ट लिखें।

Exam Tip: रिपोर्ट लिखते समय दोनों पक्षों (सकारात्मक और नकारात्मक) को बिल्कुल निष्पक्ष होकर संतुलित एवं साहित्यिक भाषा में प्रस्तुत करना चाहिए।

Holiday Homework 
Class 10th - Arts & Craft

Question Craft (i) Glass painting (ii) Your city made with boxes & use in any material.
Answer: To complete the craft section of your art folder, implement the following practical design steps:
(i) **Glass Painting:** Obtain an OHP sheet or a small clear glass frame. Outline your chosen design (such as a peacock, floral pattern, or geometric mandala) using a black glass outliner. Once dry, fill the compartments with vibrant water-based glass colors. Keep it flat until completely dry to prevent color running.
(ii) **Your City Made with Boxes:** Collect discarded small cardboard boxes (like toothpaste cartons, soap boxes, and matchboxes). Wrap them neatly in colorful chart paper to represent buildings, houses, and factories. Arrange them on a sturdy cardboard base, using paints to draw roads and small twigs to create roadside trees.
In simple words: Make a colorful painting on glass or plastic sheets, and build a mini model of a city using empty cardboard boxes.

Exam Tip: Secure all cardboard elements firmly on the base board using strong adhesive so the model is sturdy enough to transport to school.

Question Draw & colour on full sized ivory sheet (i) Village scene (ii) My Delhi on poster (iii) 2 Abstract paintings.
Answer: Follow these compositional ideas on your full-sized ivory sheets:
(i) **Village Scene:** Draw a serene countryside featuring a couple of thatched huts under a spreading banyan tree, a winding river path, and a farmer guiding bullocks through green crop fields. Use warm poster colors or oil pastels to complete the rural aesthetic.
(ii) **My Delhi Poster:** Create a collage of Delhi's heritage monuments like the India Gate, Qutub Minar, and Lotus Temple. Add a modern touch by sketching a metro train in the background. Use bold, contrasting watercolours and write a catchy slogan like "Dilwalon Ki Dilli" in neat calligraphy.
(iii) **2 Abstract Paintings:** Explore emotions through colors and textures. In the first piece, use fluid acrylic pours of blues and greens to represent natural serenity. In the second piece, use sharp geometric blocks in contrasting warm colors (red, orange, black) to depict the energy of urban environments.
In simple words: Draw a peaceful village scene, a colorful poster of Delhi's monuments, and two modern abstract paintings on large ivory sheets.

Exam Tip: Maintain neat margins on your ivory sheets and write clear titles at the bottom of each artwork.