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

Question # 1

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 # 2

Vector i =

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

Question # 3

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

√13 A
√7 B
1/√13 C
√29 D

Question # 4

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

√7 A
√41 B
√19 C
√(2&7) 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 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 # 7

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 # 8

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

3 A
√35 B
√17 C
√35 D

Question # 9

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

√3 A
1 B
√2 C
∞ 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

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 # 13

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

5 A
5i B
-5 C
√5 D

Question # 14

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 # 15

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 # 16

The modulus of 12-5i is:

7 A
13 B
√7 C
119 D

Question # 17

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 # 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

The magnitude of vector a 2i-7j is

√23 A
√43 B
3 C
√53 D

Question # 20

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

√21 A
√97 B
√39 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

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 # 23

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

1 A
2 B
-1 C
-3 D

Question # 24

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 # 25

O (0,0)is called:

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

Question # 26

If aand bare two vectors then a+b =

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

Question # 27

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

0 A
1 B
-1 C
3 D

Question # 28

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

4 A
6 B
5 C
3 D

Question # 29

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 # 30

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

Sr.#	Question	Answer
1	Vector i =	A. [1,0] B. [0,1,0] C. [0,0,1] D. None of these
2	Vector additon is:	A. Commutative B. Associative C. Commutative and Associative 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	If a = 2i +2j, b= 3i -j and c=4i +5j, the 3b -a-2c =	A. -i -15j B. i-15j C. i-3j D. None of these
5	The angle between the vectors u = [-3 , 5] and v = [6 , -2] is:	A. π/2 B. -3π/2 C. π D. None of these
6	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
7	If\|a\| =\|b\| = \|a+b\|=1, then\|a-b\| is equal to:	A. 1 B. √3 C. √2 D. 7
8	If c = 2i+j+k and d= -1 + 4j +2k, then [c-d]=	A. √7 B. √41 C. √19 D. √(2&7)
9	O (0,0)is called:	A. Position vector B. Free vector C. Unite vector D. Null vector
10	The modulus of 12-5i is:	A. 7 B. 13 C. √7 D. 119

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

Vector i =

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

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

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

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

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

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

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

a ______quantity is one that possesses both magnitude and direction.

Vector additon is:

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

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

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

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

The modulus of 12-5i is:

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

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

The magnitude of vector a 2i-7j is

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

If a,b = 0 then

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

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

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

O (0,0)is called:

If aand bare two vectors then a+b =

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

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

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

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

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