ECAT Pre General Science MCQ Test With Answer for Mathematics Chapter 20

Question # 1

Shifting origin to (-4,-6), the new coordinates of (-6,-8) are:

(-1,2) A
(-2,-2) B
(1,-2) C
(3.-2) D

Question # 2

The distance of a point (x cosθ , x sinθ ) from origin is:

x A
x tanθ B
-tanθ C
-cotθ D

Question # 3

The length of perpendicular from (3,1) to the line 4x + 3y +20 = 0 is:

7 A
5 B
11 C
12 D

Question # 4

If a point (p,q) is equidistant from the points (5,3) and (-2,-4), then p+ q =

-1 A
1 B
3 C
-3 D

Question # 5

If the line is parallel to they y-axis, then m is said to be:

zero A
undefined B
1/2 C
-1 D

Question # 6

In 𝜟ABC the mid points of AB and AC are (3,5) and -3,-1) respectively, then the length of the side BC is:

15 A
10 B
30 C
20 D

Question # 7

Shifting origin to (-3,2), the new coordinates of (-6,9) are:

(-9,7) A
(3,7) B
(-3,7) C
(3,-7) D

Question # 8

If points A (6,-1), B ( 1,3) and C (x,8) are such that AB=BC, then x =

3,5 A
-3,5 B
3,-5 C
-3,-5 D

Question # 9

In translation of axes,________is shifted to another point in the plane.

a-axis A
y-axis B
origin C
Point D

Question # 10

The distance between two parallel lines 2x - 5y + 13 = 0 and -2x +5y -6 = 0 is:

√29 A
8/√29 B
7 /√29 C
29√7 D

Question # 11

The in-centre of triangle whose vertices are (0,0), (5,12) and (16,12) is:

(9,7) A
(2,7) B
(9,2) C
(7,9) D

Question # 12

If points (-1 , h), (3,2) and (7,3) are collinear then h=

3 A
4 B
0 C
None of these D

Question # 13

The equation of the line through (-8, 5) having slope undefined is:

y + 8 = 0 A
y = 8 B
y = x + 8 C
x + 8 = 0 D

Question # 14

The points (5,2),(-2,3),(-3,-4) and (4,-5) are the vertices of:

rhombus A
Parallelogram B
rectangle C
square D

Question # 15

The distance between the parallel lines 3x - 4y + 3 =0 and 3x -4y + 7 = 0 is:

2/3 A
9/13 B
4/5 C
7/12 D

Question # 16

If the points (a,b), (x,y) and (a-x, b-y) are collinear, then ay =

bx A
b-y B
a-x C
x D

Question # 17

The distance between lines 3x + 4y = 9 and 6x +8y = 15 is:

2/3 A
3/10 B
8 C
6/5 D

Question # 18

Bisectors of angles of a triangle are:

Collinear A
Concurrent B
Perpendicular C
zero D

Question # 19

Shifting origin to (-3,2), the new coordinate of (-2,6) are:

(1,4) A
(2,4) B
(-1,3) C
(-1,4) D

Question # 20

The distance from the point P(6,-1) to the line 6x - 4x + 9 = 0 is:

5/7 A
√52/7 B
2/48 C
49 /√52 D

Question # 21

The quadrilateral with the vertices (-3,-2), (2,-1), (3,4) and (-2,3) is a:

Square A
Rectangle B
rhombus C
parallelogram D

Question # 22

The points A, B and C are said to be collinear if they:

be on same line A
have same slope B
Lie on a same plane C
options a & b D

Question # 23

Three points (-2,2) (8,-2) and (-4,3) are vertices of a :

Isosceles triangle A
right-angled triangle B
Equilateral trainagle C
Rectangle D

Question # 24

The distance from the point P(3,4) to the line y = 2x - 3 is:

√5 A
√3 B
2√3 C
1/√5 D

Question # 25

The slope of the line from B (2,-3) through A (0,3) is:

-3 A
1/3 B
0 C
undefined D

Question # 26

The length of perpendicular form(-2,3) to the line y=2x-3 is:

5√2 A
6 B
2√5 C
7.5 D

Question # 27

x-axis divides the line segment joining points (2,-3) and (5,6) in the ratio:

2 : 1 A
-2 : 1 B
1 : 2 C
-1 : 2 D

Question # 28

The coordinates of a point which trisects segment joining (0,0) and (9,12) are:

(4,3)(8,6) A
(4,3)(6,8) B
(3,4)(6,8) C
(3,4)(8,6) D

Question # 29

The two vertices of a triangle are (-2,4)and (5,4). If its centroid is (5,6), then third vertex is:

(-10,12) A
(12,-10) B
(12,10) C
(10,12) D

Question # 30

The points (3,1), (-2,-3) and (2,2) are the vertices of :

Equilateral triangle A
Isosceles triangle B
right -angled triangle C
rhombus D

Sr.#	Question	Answer
1	The length of perpendicular from (3,1) to the line 4x + 3y +20 = 0 is:	A. 7 B. 5 C. 11 D. 12
2	In translation of axes,________is shifted to another point in the plane.	A. a-axis B. y-axis C. origin D. Point
3	The coordinates of a point which trisects segment joining (0,0) and (9,12) are:	A. (4,3)(8,6) B. (4,3)(6,8) C. (3,4)(6,8) D. (3,4)(8,6)
4	In 𝜟ABC the mid points of AB and AC are (3,5) and -3,-1) respectively, then the length of the side BC is:	A. 15 B. 10 C. 30 D. 20
5	The length of perpendicular form(-2,3) to the line y=2x-3 is:	A. 5√2 B. 6 C. 2√5 D. 7.5
6	The distance of a point (x cosθ , x sinθ ) from origin is:	A. x B. x tanθ C. -tanθ D. -cotθ
7	The distance from the point P(6,-1) to the line 6x - 4x + 9 = 0 is:	A. 5/7 B. √52/7 C. 2/48 D. 49 /√52
8	The distance between lines 3x + 4y = 9 and 6x +8y = 15 is:	A. 2/3 B. 3/10 C. 8 D. 6/5
9	The points (5,2),(-2,3),(-3,-4) and (4,-5) are the vertices of:	A. rhombus B. Parallelogram C. rectangle D. square
10	The points (3,1), (-2,-3) and (2,2) are the vertices of :	A. Equilateral triangle B. Isosceles triangle C. right -angled triangle D. rhombus

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