CBSE Class 9 Maths Number Systems MCQs

Question: The rationalsing factor of a² + ab + b² is
a) a – b
b) a + b
c) a² – b²
d) a² + b²

Answer: a – b

Question: The value of (3° – 4°) × 5² is
a) 0
b) none
c) 25
d) – 25

Answer: 0

Question: The solution of 3^3x-5 = 1/9^{x is}
a) 1
b) 5
c) 7/3
d) 5/2

Answer: 1

Question: The value of [(-2)^(-2)]^(-3) is
a) 64
b) cannot be determined
c) 32
d) none of these

Answer: 64

Question: (16/81)^3/4
a) 8/27
b) 9/2
c) 2/9
d) 27/8

Answer: 8/27

Question: √2 - 1÷√ 2+ 1
a) 1/4
b) 4
c) 2
d) None of these

Answer: 1/4

Question: Simplify (32)^-2/5 ÷ (125) ^-2/3
a) 25/4
b) 5/2
c) 2/5
d) 4/25

Answer: 25/4

Question: The value of x + x (x^x) when x = 2 is
a) 10
b) 18
c) 16
d) 36

Answer: 10

Question: When simplified, (x^–1 + y^–1)–1 is equal to
a) xy/x+y
b) x+y
c) xy
d) None of these

Answer: xy/x+y

Question: The standard form of 15240000 is
a) 1.524 × 10⁷
b) 15.24 × 10⁷
c) 1.524 × 10⁶
d) 1.524 × 10⁸

Answer: 1.524 × 10⁷

Question:

a) 2
b) 0
c) 1
d) 3

Answer: 2

Question: The value of (512)^-2/9 is
a) 1/4
b) 2
c) 1/2
d) 4

Answer: 1/4

Question: Which one of the following is a rational number:
(a) √3
(b) √2
(c) 0
(d) √5

Question: 0.6666 in p/q form is:
(a) 6/99
(b) 2/3
(c) 3/5
(d) 1/66

Question: 4 1/8 in decimal form is:
(a) 4.125
(b) 4.15
(c) 4.15
(d) 0.415

Question: The value of (3+√3)(3-√3)is:
(a) 0
(b) 6
(c) 9
(d) 3

Question: The value of ( √5+√2)² is:
(a) 7+2√5
(b) 1+5√2
(c) 7 + 2√10
(d) 7- 2√10

Question: The value of ( √5+√2) ( √5-√2) is:
(a) 10
(b) 7
(c) 3
(d) √3

Question: The value of (3+√3)(2+√2) is:
(a) 6 +3√2+2√3+√6
(b) 3 +3√2+3√3+6
(c) 6-3√2-2√3-√6
(d) 6-3√2+2√3-√6

Question: The value of (√11+√7) (√11-√7)  is
(a) 4
(b) – 4
(c) 18
(d) – 18

Question: The value of (5+√5)(5-√5) is :
(a) 0
(b) 25
(c) 20
(d) – 20

Question: On rationalizing the denominator of 1/√7 , we get
(a) 7
(b) √7/7
(c) -√7/7
(d) 7

Question: An irrational number is
a) a nonterminating and non-repeating decimal
b) a nonterminating and repeating decimal
c) a terminating and non-repeating decimal
d) a terminating and repeating decimal

Question: Multiplicative inverse of ‘O’ is

Question. Which of the following is true?
(a) Every whole number is a natural number
(b) Every integer is a rational number
(c) Every rational number is an integer
(d) Every integer is a whole number

Question. Out of the following, the irrational number is 

Question. To rationalize the denominator of 1/√a+b , we multiply this by
(a) 1/√a+b
(b) 1/√a-b
(c) √a+b/√a+b
(d) √a-b/√a-b

Question. For Positive real numbers a and b, which is not true?
(a) √ab = √a √b
(b) (a+√b)(a-√b) =a2 - b2
(c) √a/b = √a/√b
(d) (√a+√b)(√a-√b) = a+b

Question. The number of rational numbers between √3 and √5 is
(a) One
(b) 3
(c) none
(d) infinitely many

Question. If we add two irrational numbers, the resulting number
(a) is always an irrational number
(b) is always a rational number
(c) may be a rational or an irrational number
(d) always an integer

Question. The rationalizing factor of 7-2√3 is
(a) 7-2√3 
(b) 7+2√3 
(c) 5+2√ 3
(d) 4+2√ 3

Question.

Question. The value of √n for which n be a rational number is
(a) 2
(b) 4
(c) 3
(d) 5

Question. 3√12/6√27 equals
(a) 1/2 
(b) √2 
(c) √3
(d) 1/3

Question. (3+√3) (3-√2) equals
(a) 9 -5 √2 - √6
(b) 9 -√6
(c) 3+√2
(d) 9-3√2 + 3√3 - √6

Question. The arrangement of √2 , √5 , √3 in ascending order is
(a) √2,√3,√5
(b) √2,√5,√3
(c) √5,√3,√2
(d) √3,√2,√5

Question. If √10 = 3.162 , then the value of 1/√10 is
(a) 0.3162
(b) 3.162
(c) 31.62
(d) 316.2

Question. If (3/4)⁶ x (16/9)⁵ = (4/3)^x+2 , then the value of x is
(a) 2
(b) 4
(c) -2
(d) 6

Question. If m and n are two natural numbers and mⁿ = 32, then n^mn is
(a) 5²
(b) 5³
(c) 5¹⁰
(d) 5¹²

Question. (3+√3)(3-√2) equals
(a) 9-5 √2-√6
(b) 9-√6
 (c) 3+√2
(d) 9-3√2+3√3-√6

Question. The arrangement of √2, √5, √3 in ascending order is
(a) √2, √3, √5
(b) √2, √5, √3
(c) √5, √3, √2
(d) √3, √2, √5

Question. If m and n are two natural numbers and mⁿ = 32, then n^mn is
(a) 5²
(b) 5³
(c) 5¹⁰
(d) 5¹²

Exponents and Radicals

1.. An equation which has an unknown quantity as an exponent is called an exponential equation.
e.g., (i) 5^x = 625
(ii) 3^x–5 = 1

2. a^1/n is called then nth root of ‘a’ and may be written as n√a

3. n√a is called a radical of index ‘n’ and ‘a’ is called the radicand.

4. Law of exponents:
If ‘a’ and ‘b’ are any rational numbers different from zero and if x, y are any rational numbers, then
(i) a^x × ay = a^x+y
(ii) a^x ÷ ay = a^x–y
(iii) (a^x)^y = a^xy
(iv) (ab)^x = a^x × b^x
(v) (a/b)^x = a^x/b^x
(vi) a° = 1

5. Radicals of index 2 are know as square root radicals. e.g., √3, 7√5, √39,....etc.

6. A radical consisting of the product of an irrational and a rational is called a mixed radical. e.g., 5√7, 23√11,......etc.

7. A radical that contains no rational factor is called a pure radical e.g., √143, √20, √45,.....etc.

8. An expression of the from a + √b, where ‘a’ and ‘b’ are rational and non-zero is called a bionomial surd. e.g., 3 + √5, 2 – √3, 9 + √11,......., etc.
Note: The surd (a – √b) is called the conjugate surd of a + √b.

9. A square root radical is in simplest form if
(i) there is no fraction in the radicand.
(ii) no perfect square is a factor of the radicand and
(iii) there is no radical on the denominator e.g., √75 = 5√3

Question. 7/√10 + √3 =
(A) (√10 + √3)2
(B) 7(√10 - √3)
(C) √10 - √3
(D) none

Answer : C

Question. The value of 4√3 -4/√3+1 - 2-√3/2+√3/ is
(A) 0
(B) 1
(C) 8√3
(D) 15

Answer : B

Question. If x^y = y^x, then (x/y)^x/y is equal to
(A) x^{x /y}
(B) x ^{x/y 1}
(C) x ^y/x
(D) x ^{y/x 1}

Answer : B

Question. If x/y = 6/5 then x2+y2/x2 - y2 is
(A) 36/25
(B) 25/36
(C) 61/11
(D) 11/61

Answer : C

Question. (64)-2/3 x (1/4)-3 equals to
(A) 4
(B) 1/4
(C) 1
(D) 16

Answer : A

Question. The value of (5)^0.25 x (12.5)^0.25/(256)^0.10 x (253)^0.15 is
(A) √5/2
(B) 5/4
(C) 25/2
(D) 25/16

Answer : B

Question. The value of (67.542)² - (32.458)²/75.458 40.374 is
(A) 1
(B) 10
(C) 100
(D) none

Answer : C

Question. Which of the following values are equals?
I. 1⁴ II. 4⁰ III. 0⁴ IV. 4¹
(A) I and II 
(B) II and III
(C) I and III 
(D) I and IV

Answer : A

Question. The sum of the powers of the prime factors in 108 × 192 is
(A) 5 
(B) 7
(C) 8 
(D) 12

Answer : D

Question. The value of √1³ + 2³ + 3³ is
(A) 5 
(B) 6
(C) 7
(D) 8

Answer : B

Question. The value of 3³√2 x 7 ³√6 x 5³√18 is
(A) 545 
(B) 500
(C) 630
(D) none

Answer : C

Question. Conjugate sure of a – √b is
(A) a + √b 
(B) √a – b
(C) √a – √b 
(D) √a + b

Answer : A

Question. The value of (√5 + √2)² + (√5 – √2)² is
(A) 7 
(B) 14
(C) 2√10 
(D) none

Answer : B

Question. If √2 = 1.414 then the value of 5 + √2 / 5 - √2 is
(A) 1.787 
(B) 1.525
(C) 1.828 
(D) 1.326

Answer : A

Question. The rationalsing factor of a² + ab + b² is
(A) a + b 
(B) a² + b²
(C) a² – b² 
(D) a – b

Answer : D

Question. The value of (3° – 4°) × 52 is
(A) 25 
(B) 0
(C) – 25 
(D) none

Answer : B

Question. The solution of 3^{3x – 5} = 1/9x is
(A) 5/2
(B) 5
(C) 1 
(D) 7/3

Answer : C

Question. The value of [(-2)^(-2)]^(-3) is
(A) 64 
(B) 32
(C) cannot be determined 
(D) none of these

Answer : A

Question. (16/81)3∫4 =
(A) 9/2
(B) 2/9
(C) 8/27
(D) 27/8

Answer : C

Question. √2 - 1 √2 + 1 =
(A) 3 – 2√2 
(B) 3 + 2√2
(C) 1/√2
(D) 1.732

Answer : A

Question. The value of (512)-2/9 is
(A) 1/2
(B) 2
(C) 4 
(D) 1/4

Answer : D

Question. Simplify (32)-2/5 ÷ (125)-2/ 3
(A) 4/25
(B) 25/4
(C) 2/5
(D) 5/2

Answer : B

Question. The rationalising factor of 5 + 2√6 is
(A) –2√6 – 5
(B) √6 – 10
(C) 6 – √5
(D) 5 – 2√6

Answer : D

Question. Simplify: √300 - √48 + √75 - √147
(A) 2√3
(B) √3
(C) 4√3
(D) none

Answer : C

Question. Similify: (√3 + 2)² - (√3 - 2)²
(A) 8√3
(B) 14
(C) 14 + 8√3
(D) 14 – 8√3

Answer : A

Question. Match the following provided that a and b are any rational numbers different from zero and x, y are any rational numbers
(1) a^x × a^y (a) a^x – y
(2) a^x ÷ a^y (b) a^xy
(3) (a^x)^y (c) a^{x + y}
(4) (ab)^x (d) a^x/b^x
(5) (a/b)^x (e) a^x × b^x
(A) 1 - c, 2 - a, 3 - b, 4 - e, 5 - d
(B) 1 - b, 2 - c, 3 - a, 4 - e, 5 - d
(C) 1 - a, 2 - c, 3 - a, 4 - e, 5 - d
(D) 1 - a, 2 - b, 3 - c, 4 - d, 5 - e

Answer : A

Question. The value of expression (8° – 3°) × (8° + 3°) is equal to
(A) 0 
(B) 1
(C) 2 
(D) 3

Answer : A

Question. The value of expression (1/3)³ x (-2/5)² x (-3/2)³ is
(A) 1/50 
(B) –1/50
(C) 1 
(D) 0

Answer : B

Question. If 36a⁴ = a⁶, then a³ is euqal to
(A) (1/6)a⁶
(B) 6a⁴
(C) (1/6)a²
(D) 6a²

Answer : D

Question. The reciprocal of the rational number (3/2)^-2 ÷ (1/3)^-3 is
(A) 240/4
(B) 241/2
(C) 243/4
(D) 241/4

Answer : C

Question. The value of expression -2/7 x -2/7 x -2/7 in power notation is
(A) (-2/7)³
(B) (2/7)³
(C) 2/7
(D) -2/7

Answer : A

Question. The quotient of 100¹⁰⁰ and 50⁵⁰ is
(A) 50⁵⁰ 
(B) 50¹⁰⁰
(C) 200⁵⁰ 
(D) 400⁵⁰

Answer : C

Question. √300 √48 √75 √147 =
(A) 2√3 
(B) √3
(C) 4√3 
(D) √3

Answer : C

Question. The value of expression 3√64/125 in the exponential form is
(A)  (64)^{1/ 3} / (125)^{1/ 3}
(B) (64)^{1/ 2} / (125)^{1/ 2}
(C) 0 
(D) 1

Answer : A

Question. Which expression is equivalent to the number 8, 006 425 ?
(A) (8 × 107) + (6 × 106) + (4 × 103) + (2 × 102) + (5 × 101)
(B) (8 × 10) + (6 × 10) + (4 × 10) + (2 × 10) + (5 × 10)
(C) (8 × 106) + (6 × 105) + (4 × 104) + (2 × 103) + (5 × 102)
(D) (8 × 106) + (6 × 103) + (4 × 102) + (2 × 101) + (5 × 100)

Answer : D

Question. The value of [(-2)^(-2)]^(-3) is
(A) 64
(B) 32
(C) Cannot be determined
(D) 14

Answer: A

Question. The value of x in exponential equation 2x – 4 = 1 is equal to
(A) 4
(B) 3
(C) 2
(D) 1

Answer: A

Question. The standard form of 0.00000037 is
(A) 3.7 × 10–6
(B) 3.7 × 10–7
(C) 3.7 × 10–5
(D) 3.7

Answer: B

Question. If {(1/3)^-1 - (1/4)^-1}^m = 1 , then least positive integral value of m is
(A) 0
(B) 2
(C) 1
(D) 3

Answer: B

Question. The value of the expression (1³ + 2³ + 3³ + 4³)^–3/2 is
(A) 1
(B) 1/1000
(C) 1/100
(D) 0

Answer: B

Question. The distance between Sun and Earth is 1.496 × 1011 m and the distance between Earth and Moon is 3.84 × 108 m. During solar eclipse, Moon comes in between Earth and Sun. At that time the distance between Moon and Sun is
(A) 149.216 × 10⁸ m
(B) 1492.16 × 10⁸ m
(C) 14.9216 × 10⁸ m
(D) 1.49216 × 108 m

Answer: B

Question. The least number of numbers to be deleted from the set {1, 2, 3..., 13, 14, 15} so that the product of the remaining numbers is a perfect square is
(A) 1
(B) 3
(C) 2
(D) 4

Answer: B

Question. Let the length of a positive integer n be defined as the number of prime foctors of n, counting perpetitions. Length of 36 is 4 as 36 = 2.2.3.3. Length of 64 is 6 as 64 = 2.2.2.2.2.2. The number of numbers less than 100 with maximum length is
(A) 5
(B) 4
(C) 3
(D) 2

Answer: D

Question. (36 + 64)^{1/ 3} + (1+ 4^3/2 )^{1/ 2}+√20 + √45 equals
(A) 13 + 2 √5
(B) 10 + 5 √5
(C) 10 + 2 √5
(D) 13 + 5 √5

Answer: D

Question. (1024)^4/5 x (1/4)^-3 equals to
(A) 4
(B) 1/4
(C) 1
(D) 16

Answer: A

Question. The value of (3²)³ + (2/3)⁰ + 3⁵ is
(A) 930
(B) 973
(C) 932
(D) 950

Answer: B

Question. 16^5/2 ÷ 16^1/2 =
(A) 250 
(B) 256
(C) 255 
(D) 200

Answer : B

Question. (32)^-2/5 ÷ (125)^-2/3 =
(A) 4/25 
(B) 25/4
(C) 2/5 
(D) 5/2

Answer : B

Question. The value of (512) ^-2/9 is
(A) 1/2 
(B) 2
(C) 4 
(D) 1/4

Answer : D

Question.  

(A) 0
(B) 1
(C) 2
(D) 3

Answer : 

Question. 4^-3/2 +8^2/3 = ? 

Answer :

Question. The value of 

(A) 1/4
(B) 1/8
(C) 16
(D) 1/16 

Answer: D

Question. If 10/3 x 3^x - 3^x-1 = 81, then the value of x is
(A) 2 
(B) 1
(C) 3 
(D) 0

Answer : C

Question. The standard form of 15240000 is
(A) 1.524 × 10⁷ 
(B) 1.524 × 10⁶
(C) 15.24 × 10⁷ 
(D) 1.524 × 10⁸

Answer : A

Question. (√3 +2)² - (√3 - 2)² =
(A) 8√3 
(B) 14
(C) 14 + 8√3 
(D) 14 - 8√3

Answer : A

Question. The value of 2²⁰⁰¹ + 2¹⁹⁹⁹ / 2²⁰⁰⁰ - 2¹⁹⁹⁸ is
(A) 2 
(B) 10/3
(C) 2¹⁰⁰⁰ + 1 
(D) 10

Answer : B

Question. When simplified, (x^–1 + y^–1)^–1 is equal to
(A) x + y 
(B) xy/x + y
(C) xy 
(D) 1/xy

Answer : B

Question. The value of x + x (x^x) when x = 2 is
(A) 10 
(B) 16
(C) 18 
(D) 36

Answer : A

Question. Multiplicative inverse of 1/10^–100 is
(A) 10^–100 
(B) 1/10^-100
(C) (10)^–100 
(D) (10–50)³

Answer : B

Question. The value of (1024)^-(4/5) is
(A) 1/64 
(B) 1/128
(C) 1/256 
(D) 1/512

Answer : C