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

Question # 1

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 # 2

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 # 3

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

√7 A
√41 B
√19 C
√(2&7) D

Question # 4

Vector i =

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

Question # 5

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

3 A
√35 B
√17 C
√35 D

Question # 6

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

√21 A
√97 B
√39 C
None of these D

Question # 7

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

√3 A
1 B
√2 C
∞ D

Question # 8

a ______quantity is one that possesses both magnitude and direction.

Scalar A
Vector B
Segment C
None of these D

Question # 9

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 # 10

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 # 11

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 # 12

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 # 13

If aand bare two vectors then a+b =

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

Question # 14

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 # 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

O (0,0)is called:

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

Question # 18

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 # 19

If a,b = 0 then

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

Question # 20

The magnitude of vector a 2i-7j is

√23 A
√43 B
3 C
√53 D

Question # 21

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

1 A
2 B
-1 C
-3 D

Question # 22

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

√13 A
√7 B
1/√13 C
√29 D

Question # 23

The modulus of 12-5i is:

7 A
13 B
√7 C
119 D

Question # 24

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 # 25

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 # 26

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

0 A
1 B
-1 C
3 D

Question # 27

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

5 A
5i B
-5 C
√5 D

Question # 28

If u = xi + yj, then|u|

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

Question # 29

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 # 30

Vector additon is:

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

Sr.#	Question	Answer
1	If aand bare two vectors then a+b =	A. b + a B. b - a C. ab D. a^ b
2	If u = 2ai + i - k and v = i +ai + 4k are perpendicular then a =	A. 4 B. 1/2 C. 3 D. 4/3
3	If a=5j + 2j,b=2i -3j, then\|a+2b\|=	A. √21 B. √97 C. √39 D. None of these
4	The positive real number which is the measure of the length of a vector is called the	A. Unit vector B. Modulus C. Inverse D. None of these
5	If\|a\| =\|b\| = \|a+b\|=1, then\|a-b\| is equal to:	A. 1 B. √3 C. √2 D. 7
6	a ______quantity is one that possesses both magnitude and direction.	A. Scalar B. Vector C. Segment D. None of these
7	If u =2i +pi + 5k and v = 3i + i +pk are perpendicular , then p=	A. 1 B. 2 C. -1 D. -3
8	The modulus of a vector i-i+ k is:	A. √3 B. 1 C. √2 D. ∞
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 G is the centroid of the triangle, then GA +GB+GC=	A. 0 B. 1 C. -1 D. 3

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