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

Question # 1

The modulus of 12-5i is:

7 A
13 B
√7 C
119 D

Question # 2

Vector additon is:

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

Question # 3

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 # 4

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

0 A
1 B
-1 C
3 D

Question # 5

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 # 6

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

5 A
5i B
-5 C
√5 D

Question # 7

a ______quantity is one that possesses both magnitude and direction.

Scalar A
Vector B
Segment C
None of these D

Question # 8

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

4 A
6 B
5 C
3 D

Question # 9

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

1 A
2 B
-1 C
-3 D

Question # 10

If aand bare two vectors then a+b =

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

Question # 11

Vector i =

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

Question # 12

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 # 13

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 # 14

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

3 A
√35 B
√17 C
√35 D

Question # 15

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 # 16

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 # 17

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

√7 A
√41 B
√19 C
√(2&7) D

Question # 18

The magnitude of vector a 2i-7j is

√23 A
√43 B
3 C
√53 D

Question # 19

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 # 20

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 # 21

If a,b = 0 then

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

Question # 22

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

√13 A
√7 B
1/√13 C
√29 D

Question # 23

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

√21 A
√97 B
√39 C
None of these D

Question # 24

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 # 25

O (0,0)is called:

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

Question # 26

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 # 27

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 # 28

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

√3 A
1 B
√2 C
∞ D

Question # 29

If u = xi + yj, then|u|

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

Question # 30

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

Sr.#	Question	Answer
1	If u = 2ai + i - k and v = i +ai + 4k are perpendicular then a =	A. 4 B. 1/2 C. 3 D. 4/3
2	Vector i =	A. [1,0] B. [0,1,0] C. [0,0,1] D. None of these
3	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
4	If a≠ , b≠ 0 and\|a=b\|=\|a-b\|,then vectors a and b are:	A. Parallel to each other B. Perpendicular to each other C. Inclined at 60^o D. neither parallel nor perpendicular
5	The magnitude of vector a 2i-7j is	A. √23 B. √43 C. 3 D. √53
6	If\|a\| =\|b\| = \|a+b\|=1, then\|a-b\| is equal to:	A. 1 B. √3 C. √2 D. 7
7	The modulus of a vector i-i+ k is:	A. √3 B. 1 C. √2 D. ∞
8	I f a =5i + 2j, then\|a\| =	A. √13 B. √7 C. 1/√13 D. √29
9	If a,b = 0 then	A. a \|b B. a\|\|b C. a = b D. None
10	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

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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 modulus of 12-5i is:

Vector additon is:

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

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

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

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

a ______quantity is one that possesses both magnitude and direction.

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

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

If aand bare two vectors then a+b =

Vector i =

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

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

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

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

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

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

The magnitude of vector a 2i-7j is

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

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

If a,b = 0 then

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

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

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

O (0,0)is called:

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

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

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

If u = xi + yj, then|u|

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

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