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

Question # 1

If aand bare two vectors then a+b =

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

Question # 2

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

√3 A
1 B
√2 C
∞ D

Question # 3

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

1 A
√3 B
√2 C
7 D

Question # 4

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 # 5

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 # 6

Vector additon is:

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

Question # 7

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 # 8

The magnitude of vector a 2i-7j is

√23 A
√43 B
3 C
√53 D

Question # 9

If u = xi + yj, then|u|

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

Question # 10

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 # 11

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

3 A
√35 B
√17 C
√35 D

Question # 12

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 # 13

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 # 14

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

4 A
6 B
5 C
3 D

Question # 15

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 # 16

O (0,0)is called:

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

Question # 17

a ______quantity is one that possesses both magnitude and direction.

Scalar A
Vector B
Segment C
None of these D

Question # 18

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 # 19

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

5 A
5i B
-5 C
√5 D

Question # 20

Vector i =

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

Question # 21

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 # 22

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 # 23

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 # 24

The modulus of 12-5i is:

7 A
13 B
√7 C
119 D

Question # 25

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

√13 A
√7 B
1/√13 C
√29 D

Question # 26

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

√7 A
√41 B
√19 C
√(2&7) D

Question # 27

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 # 28

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

1 A
2 B
-1 C
-3 D

Question # 29

If a,b = 0 then

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

Question # 30

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

Sr.#	Question	Answer
1	Vector additon is:	A. Commutative B. Associative C. Commutative and Associative D. None of these
2	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
3	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
4	If u =[3,-4],then modulus of uis:	A. 5 B. 5i C. -5 D. √5
5	The vector i = [1,0] is called unit vector along:	A. x-axis B. y - axis C. z- axis D. Botha a and y-axis
6	Vector i =	A. [1,0] B. [0,1,0] C. [0,0,1] D. None of these
7	The modulus of a vector i-i+ k is:	A. √3 B. 1 C. √2 D. ∞
8	If u = xi + yj, then\|u\|	A. x² + y² B. (x² +y²)² C. x²-y² D. √(x²+y²)
9	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
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

If aand bare two vectors then a+b =

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

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:

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

Vector additon is:

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

The magnitude of vector a 2i-7j is

If u = xi + yj, then|u|

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

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 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| =

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

O (0,0)is called:

a ______quantity is one that possesses both magnitude and direction.

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

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

Vector i =

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:

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

The modulus of 12-5i is:

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

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

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=

If a,b = 0 then

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

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