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

Question # 1

If the sum of two unit vectors is a unit vector the the magnitude of their difference is

√2 A
√3 B
1 C
None of these D

Question # 2

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 # 3

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

√21 A
√97 B
√39 C
None of these D

Question # 4

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

√3 A
1 B
√2 C
∞ D

Question # 5

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 # 6

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 # 7

Vector i =

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

Question # 8

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

3 A
√35 B
√17 C
√35 D

Question # 9

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

1 A
√3 B
√2 C
7 D

Question # 10

a ______quantity is one that possesses both magnitude and direction.

Scalar A
Vector B
Segment C
None of these D

Question # 11

Vector additon is:

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

Question # 12

The angle between the vectors u =2i - i + k and v = -i + i is:

3π/2 A
2π/3 B
5π/6 C
π/3 D

Question # 13

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 # 14

The magnitude of vector a 2i-7j is

√23 A
√43 B
3 C
√53 D

Question # 15

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 # 16

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

4 A
6 B
5 C
3 D

Question # 17

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 # 18

If u = xi + yj, then|u|

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

Question # 19

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

5 A
5i B
-5 C
√5 D

Question # 20

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

√7 A
√41 B
√19 C
√(2&7) D

Question # 21

The modulus of 12-5i is:

7 A
13 B
√7 C
119 D

Question # 22

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 # 23

If aand bare two vectors then a+b =

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

Question # 24

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

1 A
2 B
-1 C
-3 D

Question # 25

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

√13 A
√7 B
1/√13 C
√29 D

Question # 26

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 # 27

If a,b = 0 then

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

Question # 28

O (0,0)is called:

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

Question # 29

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

0 A
1 B
-1 C
3 D

Question # 30

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

Sr.#	Question	Answer
1	The modulus of a vector i-i+ k is:	A. √3 B. 1 C. √2 D. ∞
2	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
3	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
4	Vector additon is:	A. Commutative B. Associative C. Commutative and Associative D. None of these
5	If\|a\| =\|b\|=\|a + b\|=1, then\|a+ b\| = 5, then\|a-b\| =	A. 4 B. 6 C. 5 D. 3
6	I f a =5i + 2j, then\|a\| =	A. √13 B. √7 C. 1/√13 D. √29
7	Vector i =	A. [1,0] B. [0,1,0] C. [0,0,1] D. None of these
8	If u =2i +pi + 5k and v = 3i + i +pk are perpendicular , then p=	A. 1 B. 2 C. -1 D. -3
9	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
10	If a=5j + 2j,b=2i -3j, then\|a+2b\|=	A. √21 B. √97 C. √39 D. None of these

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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

If the sum of two unit vectors is a unit vector the the magnitude of their difference is

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

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

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

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

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

Vector i =

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

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

a ______quantity is one that possesses both magnitude and direction.

Vector additon is:

The angle between the vectors u =2i - i + k and v = -i + i is:

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

The magnitude of vector a 2i-7j is

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

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

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

If u = xi + yj, then|u|

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

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

The modulus of 12-5i is:

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

If aand bare two vectors then a+b =

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

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

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

If a,b = 0 then

O (0,0)is called:

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

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

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