CBSE Class 11 Mathematics Straight Lines Worksheet

Multiple Choice Questions

Question. The tangent of angle between the lines whose intercepts on the axes are a, −b and b, −a respectively, is
(a) a² - b²/ab
(b) b² - a²/2
(c) b² - a²/2ab
(d) None of these
Answer : B

Question. The coordinates of a point which divides externally the line joining (1, −3) and (− 3, 9) in the ratio 1 : 3 are
(a) (3, − 6)
(b) (− 6, 3)
(c) (3, −9)
(d) (−9, 3)
Answer : C

Question. The equation of the line through (− 2, 3) with slope − 4 is
(a) x + 4y −10 = 0
(b) 4x + y + 5 = 0
(c) x + y −1 = 0
(d) 3x + 4y − 6 = 0
Answer : B

Question. The equation of line passing through the points (−1, 1) and (2, − 4).
(a) 5x + 2y + 2 = 0
(b) 5x + 3y −2 = 0
(c) 5x + 2y + 3 = 0
(d) 5x + 3y + 2 = 0
Answer : D

Question. Using slope of line, till, are A(4, 4), B(3, 5) andC(−1, 1) the vertices of a right angled triangle.
(a) Yes
(b) No
(c) Cannot say
(d) Insufficient Information
Answer : A

Question. The points (1, − 1), (5, 2) and (9, 5) collinear.
(a) Yes
(b) No
(c) Cannot say
(d) Insufficient information
Answer : A

Question. The equations of the line which have slope 1/2 and cuts-off an intercept 4 on X -axis is
(a) x −2y −4 = 0
(b) x + 2y −4 = 0
(c) x + 2y + 4 = 0
(d) x −2y + 4 = 0
Answer : A

Question. The equation of the line passing through the point (1, 2) and perpendicular to the line x + y + 1 = 0 is
(a) y − x + 1 = 0
(b) y − x −1 = 0
(c) y − x + 2 = 0
(d) y − x −2 = 0
Answer : B

Question. If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is (3, 2), then the equation of the line will be
(a) 2x + 3y = 12
(b) 3x + 2y = 12
(c) 4x − 3y = 6
(d) 5x −2y = 10
Answer : A

Question. The distance of the point of intersection of the lines 2x − 3y + 5 = 0 and 3x + 4y = 0 from the line 5x − 2y = 0 is
(a) 130 / 17√29
(b) 13 / 7√29
(c) 130/7
(d) None of these
Answer : A

Question. The equation of a line perpendicular to the line x − 2y + 3 = 0 and passing through the point (1, – 2) is
(a) y = 2x
(b) x = 2y
(c) x = −2y
(d) y = −2x
Answer : D

Question. Slope of a line which cuts off intercepts of equal lengths on the axes is
(a) −1
(b) 0
(c) 2
(d) 3
Answer : A

Question. If the normal form of the equation √3x + y − 8 = 0 is x cos w + y sin w = p, then p and w respectively are
(a) 4, 45°
(b) 4, 30°
(c) 3, 45°
(d) 3, 30°
Answer : B

Question. The coordinates of a point which divides the line segment joining A (1, − 3) and B (− 3, 9) internally in the ratio 1 : 3, are given by
(a) (−2, 6)
(b) (0,0)
(c) (-6/3. 18/4)
(d) (-10/4. 30/4)
Answer : B

 

Question. A point on the straight line, 3x + 5y = 15 which is equidistant from the coordinate axes will lie only in :
(a) 4^th quadrant
(b) 1^st quadrant
(c) 1^st and 2^nd quadrants
(d) 1^st, 2^nd and 4^th quadrants
Answer : C

Question. If in a parallelogram ABDC, the coordinates of A, B and C are respectively (1, 2), (3, 4) and (2, 5), then the equation of the diagonal AD is :
(a) 5x – 3y + 1 = 0
(b) 5x + 3y – 11 = 0
(c) 3x – 5y + 7 = 0
(d) 3x + 5y – 13 = 0
Answer : A

Question. Two sides of a rhombus are along the lines, x – y + 1 = 0 and 7x – y – 5 = 0. If its diagonals intersect at (–1, –2), then which one of the following is a vertex of this rhombus?
(a) (1/3, - 8/3)
(b) (- 10/3, - 7/3)
(c) (–3, –9)
(d) (–3, –8)
Answer : A

Question. If a vertex of a triangle is (1, 1) and the mid points of two sides through this vertex are (–1, 2) and (3, 2) then the centroid of the triangle is
(a) (-1, 7/3)
(b) (-1/3, 7/3)
(c) (1, 7/3)
(d) (1/3, 7/3)
Answer : C

Question. Two vertical poles of heights, 20 m and 80 m stand apart on a hori ontal plane. The height (in meters) of the point of intersection of the lines oining the top of each pole to the foot of the other, from this hori ontal plane is :
(a) 15
(b) 18
(c) 12
(d) 16
Answer : D

Question. If the line 3x + 4y – 24 = 0 intersects the x-axis at the point A and the y-axis at the point B, then the incentre of the triangle OAB, where O is the origin, is:
(a) (3, 4)
(b) (2, 2)
(c) (4, 3)
(d) (4, 4)
Answer : B

Question. A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is :
(a) 2x + 3y = xy
(b) 3x + 2y = xy
(c) 3x + 2y = 6xy
(d) 3x + 2y = 6
Answer : B

Question. In a triangle ABC, coordianates of A are (1, 2) and the equations of the medians through B and C are x + y = 5 and x = 4 respectively. Then area of ΔABC (in sq. units) is
(a) 5
(b) 9
(c) 12
(d) 4
Answer : B

Question. If the point (1, a) lies between the straight lines x + y = 1 and 2(x + y) = 3 then a lies in interval
(a) (3/1, ∞)
(b) (1,3/2)
(c) (- ∞, 0)
(d) (0, 3/1)
Answer : D

Question. The point (2, 1) is translated parallel to the line L : x – y = 4 by 2√3 units. If the new points Q lies in the third quadrant, then the equation of the line passing through Q and perpendicular to L is :
(a) x + y = 2 - √6
(b) 2x + 2y =1- √6
(c) x + y = 3- 3√6
(d) x + y = 3- 2√6
Answer : D

Question. Given three points P, Q, R with P(5, 3) and R lies on the x-axis. If equation of RQ is x – 2y = 2 and PQ is parallel to the x-axis, then the centroid of DPQR lies on the line:
(a) 2x + y – 9 = 0
(b) x – 2y + 1 = 0
(c) 5x – 2y = 0
(d) 2x – 5y = 0
Answer : D

Question. A straight line through origin O meets the lines 3y = 10 – 4x and 8x + 6y + 5 = 0 at points A and B respectively. Then O divides the segment AB in the ratio :
(a) 2 : 3
(b) 1 : 2
(c) 4 : 1
(d) 3 : 4
Answer : C

Question. A point P moves on the line 2x – 3y + 4 = 0. If Q(1, 4) and R(3, –2) are fixed points, then the locus of the centroid of ΔPQR is a line:
(a) with slope 3/2
(b) parallel to x-axis
(c) with slope 2/3
(d) parallel to y-axis
Answer : C

Question. A ray of light along x + √3y = √3 gets reflected upon reaching x-axis, the equation of the reflected ray is
(a) y = x + √3
(b) √3y = x – √3
(c) y = 3x - √3
(d) √3y = x -1
Answer : B

Question. If a line intercepted between the coordinate axes is trisected at a point A(4, 3), which is nearer to x-axis, then its equation is: 
(a) 4x – 3y = 7
(b) 3x + 2y = 18
(c) 3x + 8y = 36
(d) x + 3y = 13
Answer : B

Question. Let A (–3, 2) and B (–2, 1) be the vertices of a triangle ABC. If the centroid of this triangle lies on the line 3x + 4y + 2 = 0, then the vertex C lies on the line :
(a) 4x + 3y + 5 = 0
(b) 3x + 4y + 3 = 0
(c) 4x + 3y + 3 = 0
(d) 3x + 4y + 5 = 0
Answer : B

Question. If the straight lines x + 3y = 4, 3x + y = 4 and x + y = 0 form a triangle, then the triangle is
(a) scalene
(b) equilateral triangle
(c) isosceles
(d) right angled isosceles
Answer : C

Question. If A (2, – 3) and B (– 2, 1) are two vertices of a triangle and third vertex moves on the line 2x + 3y = 9, then the locus of the centroid of the triangle is :
(a) x - y =1
(b) 2x + 3y =1
(c) 2x + 3y = 3
(d) 2x - 3y = 1
Answer : B

Question. If the extremities of the base of an isosceles triangle are the points (2a, 0) and (0, a) and the equation of one of the sides is x = 2a, then the area of the triangle, in square units, is : 
(a) (5/4)a²
(b) (5/2)a²
(c) 25a²/4
(d) 5a²
Answer : B

Question. The circumcentre of a triangle lies at the origin and its centroid is the mid point of the line segment oining the points (a² + 1, a² + 1) and (2a, – 2a), a ≠ 0. Then for any a, the orthocentre of this triangle lies on the line:
(a) y – 2ax = 0
(b) y – (a² + 1)x = 0
(c) y + x = 0
(d) (a – 1)²x – (a + 1)2y = 0
Answer : D

Question. If the line 2x + y = k passes through the point which divides the line segment oining the points (1,1) and (2,4) in the ratio 3 :2, then k equals :
(a) 29/5
(b) 5
(c) 6
(d) 11/5
Answer : C

Question. If 2 (a,a²) falls inside the angle made by the lines y = x/2, x > 0 and y = 3x , x > 0 , then a belong to
(a) (0, 1/2)
(b) (3, ∞)
(c) (1/2, 3)
(d) (-3, - 1/2)
Answer : C

Question. If the x-intercept of some line L is double as that of the line, 3x + 4y = 12 and the y-intercept of L is half as that of the same line, then the slope of L is :
(a) – 3
(b) – 3/8
(c) – 3/2
(d) – 3/16
Answer : D

Question. A straight line L through the point (3, – 2) is inclined at an angle of 60 to the line √3 x + y = 1. If L also intersects the x-axis, then the equation of L is :
(a) y + √3 x + 2 – 3√3 = 0
(b) √3 y + x – 3 + 2√3 = 0
(c) y – √3 x + 2 + 3√3 = 0
(d) √3 y – x + 3 + 2√3 = 0
Answer : C

Case Based MCQs

Population vs Year graph given below.

Based on the above information answer the following questions.

Question. The slope of line AB is
(a) 2
(b) 1
(c) 1/2
(d) 1/3
Answer : C

Question. The equation of line AB is
(a) x + 2y = 1791
(b) x −2y = 1801
(c) x −2y = 1791
(d) x −2y + 1801 = 0
Answer : B

Question. The population in year 2010 is (in crores)
(a) 104.5
(b) 119.5
(c) 109.5
(d) None of these
Answer : A

Question. The equation of line perpendicular to line AB and passing through (1995, 97) is
(a) 2x − y = 4087
(b) 2x + y = 4087
(c) 2x + y = 1801
(d) None of the above
Answer : B

Question. In which year the population becomes 110 crores is
(a) 2020
(b) 2019
(c) 2021
(d) 2022
Answer : C

 

If A and B are two persons sitting at the positions (2, − 3) and (6, − 5). IfC is a third person who is sitting between A and B such that it divides the line AB in 1 : 3 ratio

Based on the above information, answer the following questions.

Question. The distance between A and B is
(a) √5
(b) 2√5
(c) 3√5
(d) 4√5
Answer : B

Question. The equation of AB is
(a) x + 2y + 4 = 0
(b) x + 2y −4 = 0
(c) x −2y + 4 = 0
(d) None of these
Answer : A

Question. Coordinates of pointC are
(a) (7/2, - 3)
(b) (3, 7/2)
(c) (3,3)
(d) (3, - 7/2)
Answer : D

Question. Distance between A andC is
(a) √5
(b) 2√5
(c) √5/2
(d) √5/2
Answer : C

Question. Distance betweenC and B is
(a) 3√5/2
(b) 3√5
(c) 2√5/3
(d) None of these
Answer : A

Please click on below link to download CBSE Class 11 Mathematics Straight Lines Worksheet