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

Question # 1

The two lines 5x + 7y = 35 and 3x -7y=21, intersect at the point:

(7,5) A
(1,2) B
(2,7) C
(7,0) D

Question # 2

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 # 3

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 # 4

Shifting origin to (1,-2), the new coordinates of (4,5) are:

(3,7) A
(5,3) B
(-3,7) C
(3,-7) D

Question # 5

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 # 6

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 # 7

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 # 8

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 # 9

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 # 10

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 # 11

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

Question # 12

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

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

Question # 13

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 # 14

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

7 A
5 B
11 C
12 D

Question # 15

The medians of a triangle are:

Collinear A
Concurrent B
Perpendicular C
zero D

Question # 16

Bisectors of angles of a triangle are:

Collinear A
Concurrent B
Perpendicular C
zero D

Question # 17

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 # 18

The points (0,-1), (2,1),(0,3) and (-2,1) are the corner of:

Square A
rhombus B
Parallelogram C
rectangel D

Question # 19

Axes remain parallel to the old axes, in:

Translating of axes A
rotation of axes B
Translation and rotation of axes C
None of these D

Question # 20

If points (5 , 5), (10 , x) and (-5 , 1) are collinear, x =

5 A
3 B
9 C
7 D

Question # 21

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 # 22

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 # 23

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 # 24

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

a-axis A
y-axis B
origin C
Point 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 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 # 27

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

x A
x tanθ B
-tanθ C
-cotθ D

Question # 28

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 # 29

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 # 30

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

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

Sr.#	Question	Answer
1	The in-centre of triangle whose vertices are (0,0), (5,12) and (16,12) is:	A. (9,7) B. (2,7) C. (9,2) D. (7,9)
2	The points (0,-1), (2,1),(0,3) and (-2,1) are the corner of:	A. Square B. rhombus C. Parallelogram D. rectangel
3	The cartesian system of coordinates was introduced by:	A. Eulaer B. Euclid C. Descrates D. Maclream
4	The points A, B and C are said to be collinear if they:	A. be on same line B. have same slope C. Lie on a same plane D. options a & b
5	x-axis divides the line segment joining points (2,-3) and (5,6) in the ratio:	A. 2 : 1 B. -2 : 1 C. 1 : 2 D. -1 : 2
6	The distance of a point (x cosθ , x sinθ ) from origin is:	A. x B. x tanθ C. -tanθ D. -cotθ
7	The two lines 5x + 7y = 35 and 3x -7y=21, intersect at the point:	A. (7,5) B. (1,2) C. (2,7) D. (7,0)
8	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)
9	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
10	The length of perpendicular from (3,1) to the line 4x + 3y +20 = 0 is:	A. 7 B. 5 C. 11 D. 12

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