ECAT Pre General Science MCQ Test With Answer for Mathematics Chapter 23

Question # 1

The angle between the vectors u = [-3 , 5] and v = [6 , -2] is:

π/2 A
-3π/2 B
π C
None of these D

Question # 2

The magnitude of vector a=i-3j+5k is:

3 A
√35 B
√17 C
√35 D

Question # 3

If u =2i +pi + 5k and v = 3i + i +pk are perpendicular , then p=

1 A
2 B
-1 C
-3 D

Question # 4

If u = xi + yj, then|u|

x² + y² A
(x² +y²)² B
x²-y² C
√(x²+y²) D

Question # 5

If a≠ , b≠ 0 and|a=b|=|a-b|,then vectors a and b are:

Parallel to each other A
Perpendicular to each other B
Inclined at 60^o C
neither parallel nor perpendicular D

Question # 6

If u = 2ai + i - k and v = i +ai + 4k are perpendicular then a =

4 A
1/2 B
3 C
4/3 D

Question # 7

If a = 2i +2j, b= 3i -j and c=4i +5j, the 3b -a-2c =

-i -15j A
i-15j B
i-3j C
None of these D

Question # 8

O (0,0)is called:

Position vector A
Free vector B
Unite vector C
Null vector D

Question # 9

If the angle between two vectors u and v is 0 orπ, then the vectors u and v are:

Orthogonal A
Collinear B
Perpendicular C
None of these D

Question # 10

If aand bare two vectors then a+b =

b + a A
b - a B
ab C
a^ b D

Question # 11

If|a| =|b|=|a + b|=1, then|a+ b| = 5, then|a-b| =

4 A
6 B
5 C
3 D

Question # 12

a ______quantity is one that possesses both magnitude and direction.

Scalar A
Vector B
Segment C
None of these D

Question # 13

Vector i =

[1,0] A
[0,1,0] B
[0,0,1] C
None of these D

Question # 14

If c = 2i+j+k and d= -1 + 4j +2k, then [c-d]=

√7 A
√41 B
√19 C
√(2&7) D

Question # 15

If|a| =|b| = |a+b|=1, then|a-b| is equal to:

1 A
√3 B
√2 C
7 D

Question # 16

If the angle between two vectors u and v is 0 orπ, then the vectors u and v are:

Orthogonal A
Collinear B
Perpendicular C
None of these D

Question # 17

If a = [1,4,3] and B= [2,-1,5] athen the mid point M of AB is:

[1,1,1.5] A
[2,2,1.5] B
[1.5,1.5,4] C
None of these D

Question # 18

The vector k = [0,0,1] is called unit vector along:

x -axis A
y - axis B
z- axis C
None of these D

Question # 19

The modulus of a vector i-i+ k is:

√3 A
1 B
√2 C
∞ D

Question # 20

The magnitude of vector a 2i-7j is

√23 A
√43 B
3 C
√53 D

Question # 21

If m and n be two scalars, then (m+n) g =

0 A
m+n
B
m▁a+n▁a C
ma - m▁a
D

Question # 22

The vector i = [1,0] is called unit vector along:

x-axis A
y - axis B
z- axis C
Botha a and y-axis D

Question # 23

The modulus of 12-5i is:

7 A
13 B
√7 C
119 D

Question # 24

If G is the centroid of the triangle, then GA +GB+GC=

0 A
1 B
-1 C
3 D

Question # 25

If u =[3,-4],then modulus of uis:

5 A
5i B
-5 C
√5 D

Question # 26

Vector additon is:

Commutative A
Associative B
Commutative and Associative C
None of these D

Question # 27

The positive real number which is the measure of the length of a vector is called the

Unit vector A
Modulus B
Inverse C
None of these D

Question # 28

If a,b = 0 then

a |b A
a||b B
a = b C
None D

Question # 29

I f a =5i + 2j, then|a| =

√13 A
√7 B
1/√13 C
√29 D

Question # 30

If a=5j + 2j,b=2i -3j, then|a+2b|=

√21 A
√97 B
√39 C
None of these D

Sr.#	Question	Answer
1	If m and n be two scalars, then (m+n) g =	A. 0 B. m+n C. m▁a+n▁a D. ma - m▁a
2	If u =[3,-4],then modulus of uis:	A. 5 B. 5i C. -5 D. √5
3	a ______quantity is one that possesses both magnitude and direction.	A. Scalar B. Vector C. Segment D. None of these
4	The vector k = [0,0,1] is called unit vector along:	A. x -axis B. y - axis C. z- axis D. None of these
5	If u = xi + yj, then\|u\|	A. x² + y² B. (x² +y²)² C. x²-y² D. √(x²+y²)
6	The angle between the vectors u =2i - i + k and v = -i + i is:	A. 3π/2 B. 2π/3 C. 5π/6 D. π/3
7	If the sum of two unit vectors is a unit vector the the magnitude of their difference is	A. √2 B. √3 C. 1 D. None of these
8	If a=5j + 2j,b=2i -3j, then\|a+2b\|=	A. √21 B. √97 C. √39 D. None of these
9	If the angle between two vectors u and v is 0 orπ, then the vectors u and v are:	A. Orthogonal B. Collinear C. Perpendicular D. None of these
10	If\|a\| =\|b\| = \|a+b\|=1, then\|a-b\| is equal to:	A. 1 B. √3 C. √2 D. 7

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ECAT Pre General Science MCQ Test With Answer for Mathematics Chapter 23

MCQ's Test For ECAT Mathematics Chapter 23 Conic Section

ECAT Mathematics Chapter 23 Conic Section

The angle between the vectors u = [-3 , 5] and v = [6 , -2] is:

The magnitude of vector a=i-3j+5k is:

If u =2i +pi + 5k and v = 3i + i +pk are perpendicular , then p=

If u = xi + yj, then|u|

If a≠ , b≠ 0 and|a=b|=|a-b|,then vectors a and b are:

If u = 2ai + i - k and v = i +ai + 4k are perpendicular then a =

If a = 2i +2j, b= 3i -j and c=4i +5j, the 3b -a-2c =

O (0,0)is called:

If the angle between two vectors u and v is 0 orπ, then the vectors u and v are:

If aand bare two vectors then a+b =

If|a| =|b|=|a + b|=1, then|a+ b| = 5, then|a-b| =

a ______quantity is one that possesses both magnitude and direction.

Vector i =

If c = 2i+j+k and d= -1 + 4j +2k, then [c-d]=

If|a| =|b| = |a+b|=1, then|a-b| is equal to:

If the angle between two vectors u and v is 0 orπ, then the vectors u and v are:

If a = [1,4,3] and B= [2,-1,5] athen the mid point M of AB is:

The vector k = [0,0,1] is called unit vector along:

The modulus of a vector i-i+ k is:

The magnitude of vector a 2i-7j is

If m and n be two scalars, then (m+n) g =

The vector i = [1,0] is called unit vector along:

The modulus of 12-5i is:

If G is the centroid of the triangle, then GA +GB+GC=

If u =[3,-4],then modulus of uis:

Vector additon is:

The positive real number which is the measure of the length of a vector is called the

If a,b = 0 then

I f a =5i + 2j, then|a| =

If a=5j + 2j,b=2i -3j, then|a+2b|=

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