Class 11 Mathematics Straight Lines MCQs

Question. The equation of a straight line which cuts off an intercept of 5 units on negative direction of y-axis and makes an angle of 120º with the positive direction of x-axis is    
(a) 3x + y + 5 = 0
(b) 3x + y - 5 = 0
(c) 3x - y - 5 = 0
(d) 3x - y + 5 = 0

Answer :  A

Question. The equation of the straight line that passes through the point (3, 4) and perpendicular to the line 3x + 2y + 5 = 0 is    
(a) 2x + 3y + 6 = 0
(b) 2x – 3y – 6 = 0
(c) 2x – 3y + 6 = 0
(d) 2x + 3y – 6 = 0

Answer :  C

Question. A point moves such that its distance from the point (4, 0) is half that of its distance from the line x = 16. The locus of the point is   
(a) 3x² + 4y² = 192
(b) 4x² + 3y² = 192
(c) x² + y² = 192
(d) None of these

Answer :  A

Question. If a, b, c are in A.P., then the straight lines ax + by + c = 0 will always pass through    
(a) (1, – 2)
(b) (1, 2)
(c) (– 1, 2)
(d) (– 1, – 2)

Answer :  A

Question. If the points (5, –1, 1), (–1, –3, 4) and (1, –6, 10) are the three vertices of a rhombus taken in order, then which one of the following is the fourth vertex?  
(a) (7, – 4, 11) 
(b) (3, 7/2,11/2)
(c) (7, – 4, 7)
(d) (7, 4, 11)

Answer :  C

Question. What is the area of the triangle whose vertices are (0,0,0) (3, 4, 0) and (3, 4, 6) ?    
(a) 12 square units
(b) 15 square units
(c) 30 square units
(d) 36 square units

Answer :  B

Question. The points (1,3) and (5,1) are two opposite vertices of a rectangle. The other two vertices lie on the line y = 2x + c, then one of the remaining vertices is    
(a) (4, 4)
(b) (2, 2)
(c) (0, 2)
(d) (4, 2)

Answer :  A

Question. Which one of the the following is the nearest point on the line 3x– 4y = 25 from the origin?     
(a) ( –1, –7)
(b) (3, –4)
(c) ( –5, –8)
(b) (3, 4)

Answer :  B
 
Question. If the mid point of the section of a straight line intercepted between the axes is (1, 1), then what is the equation of this line?     
(a) 2x + y = 3
(b) 2x – y = 1
(c) x – y = 0
(d) x + y = 2

Answer :  D

Question. What is the equation of the line which passes through (4, – 5) and is parallel to the line 3x + 4y +5 = 0 ?     
(a) 3x – 4y – 32 = 0
(b) 3x + 4y + 8 = 0
(c) 4x – 3y – 31 = 0
(d) 3x + 4y – 8 = 0

Answer :  B

Question. The point (x, y) lies on the line with slope m and through the fixed point (x0, y0) if and only if its coordinates satisfy the equation y – y0 is equal to ......... .   
(a) m(x – x₀)
(b) m(y – x₀)
(c) m(y – x)
(d) m(x – y₀)

Answer :  A

Question. The point (x, y) on the line with slope m and y-intercept c lies on the line if and only if :     
(a) y = mx + c
(b) x = my + c
(c) y = mc + y
(d) x = mc + y

Answer :  A

Question. The distances of the point (1, 2, 3) from the coordinate axes are A, B and C respectively. Now consider the following equations:   
(1) A2 = B2 + C2
(2) B2 = 2C2
(3) 2A2C2 = 13 B2
Which of these hold(s) true?
(a) 1 only
(b) 1 and 3
(c) 1 and 2
(d) 2 and 3

Answer :  D

Question. The intercept cut off by a line from y-axis twice than that from x-axis, and the line passes through the point (1, 2). The equation of the line is    
(a) 2x + y = 4
(b) 2x + y + 4 = 0
(c) 2x – y = 4
(d) 2x – y + 4 = 0

Answer :  A

Question. One vertex of the equilateral triangle with centroid at the origin and one side as x + y – 2 = 0 is    
(a) (–1, –1)
(b) (2, 2)
(c) (–2, – 2)
(d) (2, –2)

Answer :  B

Question. What is the angle between the two straight lines y = (2 - 3)x + 5 and y = (2 + 3) x - 7?     
(a) 60°
(b) 45°
(c) 30°
(d) 15°

Answer :  A

Question. The middle point of A (1, 2) and B (x, y) is C (2, 4).If BD is perpendicular to AB such that CD = 3 unit, then what is the length BD ?     
(a) 2 2 unit
(b) 2 unit
(c) 3 unit
(d) 3 2 unit

Answer :  B

Question. If A (2, 3), B (1, 4), C (0 – 2) and D (x, y) are the vertices of a parallelogram, then what is the value of (x, y) ?      
(a) (1, – 3)
(b) (2, 4)
(c) (1, 1)
(d) (0, 0)

Answer :  A

Question. If (a, b), (c, d) and (a – c, b – d) are collinear, then which one of the following is correct ?    
(a) bc – ad = 0
(b) ab – cd = 0
(c) bc + ad = 0
(d) ab + cd = 0

Answer :  A
  
Question. One of the equations of the lines passing through the point (3, – 2) and inclined at 60° to the line 3x+y = 1:     
(a) x – y = 3
(b) x + 2 = 0
(c) x + y = 0
(d) y + 2 = 0

Answer :  D

Question. The straight lines x + 2y – 9 = 0, 3x + 5y – 5 = 0 and ax + by = 1 are concurrent if the straight line 35x – 22y + 1 = 0 passes through :     
(a) (a, b)
(b) (b, a)
(c) (a, – b)
(d) (– a, b)

Answer :  A

Question. Let A (1, k), B(1, 1) and C (2, 1) be the vertices of a right angled triangle with AC as its hypotenuse.       
If the area of the triangle is 1square unit, then the set of values which 'k' can take is given by
(a) {–1, 3}
(b) {–3, –2}
(c) {1, 3}
(d) {0, 2}

Answer :  A

Question. P(3, 1), Q (6, 5) and R (x, y) are three points such that the angle RPQ is a right angle and the area of DRQP = 7, then the number of such points R is    
(a) 0
(b) 1
(c) 2
(d) 4

Answer :  C

Question. The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y – 11 = 0 are    
(a) (–6, 5)
(b) (5, 6)
(c) (–5, 6)
(d) (6, 5)

Answer :  B

Question. The reflection of the point (4, – 13) about the line 5x + y + 6 = 0 is    
(a) (–1, –14)
(b) (3, 4)
(c) (0, 0)
(d) (1, 2)

Answer :  A

Question. Locus of the mid-points of the portion of the line x sin q + y cos q = p intercepted between the axis is   
(a) 4xy = p²(x² + y²)
(b) 4x²y² = p²(x² + y²)
(c) 4x²y² = p(x + y)
(d) 4xy = p(x + y)

Answer :  B

Question. What is the locus of a moving point equidistant from the straight lines x + y = 0 and x – y = 0 ?   
(a) xy = 0
(b) xy = constant
(c) x = 0
(d) y = 0

Answer :  A

Question. What is the image of the point (2, 3) in the line y = – x ?    
(a) (– 3, – 2)
(b) (– 3, 2)
(c) (– 2, – 3)
(d) (3, 2)

Answer :  A

Question. If p be the length of the perpendicular from the origin on the straight line ax + by = p and b = √3/2 , then what is the angle between the perpendicular and the positive direction of x-axis?    
(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer :  C

Question. The coordinates of P and Q are (–3, 4) and (2, 1), respectively. If PQ is extended to R such that PR = 2QR, then what are the coordinates of R ?   
(a) (3, 7)
(b) (2, 4)
(c) (1/2, 5/2)
(d) (7, – 2)

Answer :  D

Question. A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). The co-ordinates of the point A is    
(a) (13/5 , 0)
(b) (5/13 , 0)
(c) (–7, 0)
(d) None of these

Answer :  A

Question. The coordinates of three points O, A and B are (0,0), (0, 4) and (6, 0), respectively. If a point P movesso that the area of D POA is always twice the area of D POB, then P lies on  
(a) 3x – y = 0
(b) x + y = 0
(c) x – 3y = 0
(d) x + 3y = 0

Answer :  A

Question. Let a, b, c and d be non- ero numbers. If the point of intersection of the lines 4ax + 2ay + c = 0 and 5bx + 2by + d = 0 lies in the fourth quadrant and is equidistant from the two axes then
(a) 3bc – 2ad = 0
(b) 3bc + 2ad = 0
(c) 2bc – 3ad = 0
(d) 2bc + 3ad = 0

Answer : A

Question. If the image of point P(2, 3) in a line L is Q(4, 5), then the image of point R(0, 0) in the same line is:
(a) (2, 2)
(b) (4, 5)
(c) (3, 4)
(d) (7, 7)

Answer : D

Question. If a, b, c Î R and 1 is a root of equation ax² + bx + c = 0, then the curve y = 4ax² + 3bx + 2c, a ≠ 0 intersect x-axis at
(a) two distinct points whose coordinates are always rational numbers
(b) no point
(c) exactly two distinct points
(d) exactly one point

Answer : D

Question. Let L be the line y = 2x, in the two dimensional plane.
Statement 1: The image of the point (0, 1) in L is the point (4/5, 3/5)
Statement 2: The points (0, 1) and (4/5, 3/5) lie on opposite sides of the line L and are at equal distance from it.
(a) Statement 1 is true, Statement 2 is false.
(b) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
(c) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
(d) Statement 1 is false, Statement 2 is true.

Answer : C

Question. Let θ₁ be the angle between two lines 2x + 3y + c₁ = 0 and – x + 5y + c₂ = 0 and θ₂ be the angle between two lines 2x + 3y + c₁ = 0 and – x + 5y + c₃ = 0, where c₁, c₂, c₃ are any real numbers :
Statement-1: If c₂ and c₃ are proportional, then θ₁ = θ₂.
Statement-2: θ₁ = θ₂ for all c₂ and c₃.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation of Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation of Statement-1.
(c) Statement-1 is false; Statement-2 is true.
(d) Statement-1 is true; Statement-2 is false.

Answer : A

Question. If the three lines x – 3y = p, ax + 2y = q and ax + y = r form a right-angled triangle then :
(a) a² – 9a + 18 = 0
(b) a² – 6a – 12 = 0
(c) a² – 6a – 18 = 0
(d) a² – 9a + 12 = 0

Answer : A

Question. The point of intersection of the lines
(a³ + 3)x + ay + a – 3 = 0 and
(a⁵ + 2)x + (a + 2)y + 2a + 3 = 0 (a real) lies on the y-axis for
(a) no value of a
(b) more than two values of a
(c) exactly one value of a
(d) exactly two values of a

Answer : A

Question. The equation y = sin x sin (x + 2) – sin² (x + 1) represents a straight line lying in :
(a) second and third quadrants only
(b) first, second and fourth quadrant
(c) first, third and fourth quadrants
(d) third and fourth quadrants only

Answer : D

Question. Let PS be the median of the triangle vertices P(2, 2), Q(6, –1) and R(7, 3). The equation of the line passing through (1, –1) and parallel to PS is:
(a) 4x + 7y + 3 = 0
(b) 2x – 9y – 11 = 0
(c) 4x – 7y – 11 = 0
(d) 2x + 9y + 7 = 0

Answer : D

Question. The base of an equilateral triangle is along the line given by 3x + 4y = 9. If a vertex of the triangle is (1, 2), then the length of a side of the triangle is:
(a) 2√3/15
(b) 4√3/15
(c) 4√3/5
(d) 2√3/5

Answer : B

Question. Consider the straight lines
L₁ : x – y = 1
L₂ : x + y = 1
L₃ : 2x + 2y = 5
L₄ : 2x – 2y = 7
The correct statement is
(a) L₁ P L₄ , L₂ P L₃ , L₁ intersect L₄.
(b) L₁ ⊥ L₂ , L₁ P L₃ , L₁ intersect L₂.
(c) L₁ ⊥ L₂ , L₂ P L₃ ,L₁ intersect L₄.
(d) L₁ ⊥ L₂ , L₁ ⊥ L₃ , L₂ intersect L₄.

Answer : D

Question. If two vertices of a triangle are (5, –1) and (–2, 3) and its orthocentre is at (0, 0), then the third vertex is
(a) (4, – 7)
(b) (– 4, – 7)
(c) (– 4, 7)
(d) (4, 7)

Answer : B

Question. The lines L1 : y – x = 0 and L₂ : 2x + y = 0 intersect the line L₃ : y + 2 = 0 at P and Q respectively. The bisector of the acute angle between L₁ and L₂ intersects L₃ at R.
Statement-1: The ratio PR : RQ equals 2√2: √5
Statement-2: In any triangle, bisector of an angle divides the triangle into two similar triangles.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is false.
(c) Statement-1 is false, Statement-2 is true.
(d) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Answer : B

Question. If a line L is perpendicular to the line 5x – y = 1, and the area of the triangle formed by the line L and the coordinate axes is 5, then the distance of line L from the line x + 5y = 0 is:
(a) 7/√5
(b) 5/√13
(c) 7/√13
(d) 5/√7

Answer : B

Question. The shortest distance between the line y – x = 1 and the curve x = y² is : 
(a) 2√3/8
(b) 3√2/5
(c) 3√4
(d) 3√2/8

Answer : D

Question. If two vertical poles 20 m and 80 m high stand apart on a hori ontal plane, then the height (in m) of the point of intersection of the lines oining the top of each pole to the foot of other is
(a) 16
(b) 18
(c) 50
(d) 15

Answer : A

Question. If one of the lines of my² + (1– m²) xy – mx² = 0 is a bisector of the angle between the lines xy = 0, then m is
(a) 1
(b) 2
(c) –1/2
(d) –2

Answer : A

Question. The lines x + y = a and ax – y = 1 intersect each other in the first quadrant. Then the set of all possible values of a in the interval :
(a) (0,∞)
(b) [1,∞)
(c) (-1,∞)
(d) (-1,1)

Answer : B

Question. The perpendicular bisector of the line segment oining P (1, 4) and Q(k, 3) has y-intercept –4. Then a possible value of k is 
(a) 1
(b) 2
(c) –2
(d) – 4

Answer : D

Question. If the three distinct lines x + 2ay + a = 0, x + 3by + b = 0 and x + 4ay + a = 0 are concurrent, then the point (a, b) lies on a: 
(a) circle
(b) hyperbola
(c) straight line
(d) parabola

Answer : C

Question. The lines p(p² +1)x – y + q = 0 and (p² + 1)² x + (p² + 1)y + 2q = 0 are perpendicular to a common line for :
(a) exactly one values of p
(b) exactly two values of p
(c) more than two values of p
(d) no value of p

Answer : A

Question. Let P = (–1, 0), Q = (0, 0) and R = (3, 3 √3) be three point.
The equation of the bisector of the angle PQR is
(a) √3/2 x + y = 0
(b) x + √3y = 0
(c) √3x + y = 0
(d) X + √3/2 y = 0

Answer : C

Question. The pair of lines represented by 3ax² + 5xy + (a² – 2)y² = 0 are perpendicular to each other for
(a) two values of a
(b) ∀ a
(c) for one value of a
(d) for no values of a

Answer : A

Question. A square of side a lies above the x-axis and has one vertex at the origin. The side passing through the origin makes an angle (0 < a < π/4) with the positive direction of x axis. The equation of its diagonal not passing through the origin is
(a) y(cosa + sin a) + x(cos a - sin a) = a
(b) y(cosa - sin a) - x(sin a - cosa) = a
(c) y(cosa + sina) + x(sin a - cosa) = a
(d) y(cosa + sina) + x(sin a + cosa) = a

Answer : A

Question. If one of the lines given by 6x²- xy + 4cy² = 0 is 3x + 4y = 0, then c equals
(a) –3
(b) 1
(c) 3
(d) 1

Answer : A

Question. If the sum of the slopes of the lines given by x² - 2cxy - 7y² = 0 is four times their product c has the value
(a) –2
(b) –1
(c) 2
(d) 1

Answer : C

Question. If x₁, x₂ , x₃ and y₁, y₂ , y₃ are both in G.P. with the same common ratio, then the points (x₁, y₁),(x₂, y₂) and (x₃, y₃)
(a) are vertices of a triangle
(b) lie on a straight line
(c) lie on an ellipse
(d) lie on a circle.

Answer : B

Question. If the pair of straight lines x² - 2pxy - y² = 0 and x² - 2qxy - y² = 0 be such that each pair bisects the angle between the other pair, then
(a) pq = –1
(b) p = q
(c) p = –q
(d) pq = 1.

Answer : A

Question. If the pair of lines ax² + 2hxy + by² + 2gx + 2fy + c = 0 intersect on the y-axis then
(a) 2fgh = bg² + ch²
(b) bg² ¹ ch²
(c) abc = 2fgh
(d) none of these

Answer : A