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

Question # 1

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 # 2

If aand bare two vectors then a+b =

b + a A
b - a B
ab C
a^ b 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 vector k = [0,0,1] is called unit vector along:

x -axis A
y - axis B
z- axis C
None of these D

Question # 5

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

1 A
2 B
-1 C
-3 D

Question # 6

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 # 7

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

1 A
√3 B
√2 C
7 D

Question # 8

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 # 9

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

4 A
6 B
5 C
3 D

Question # 10

The magnitude of vector a 2i-7j is

√23 A
√43 B
3 C
√53 D

Question # 11

O (0,0)is called:

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

Question # 12

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 # 13

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

3 A
√35 B
√17 C
√35 D

Question # 14

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

5 A
5i B
-5 C
√5 D

Question # 15

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 # 16

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 # 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

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

The modulus of 12-5i is:

7 A
13 B
√7 C
119 D

Question # 20

If a,b = 0 then

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

Question # 21

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 # 22

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 # 23

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 # 24

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

√3 A
1 B
√2 C
∞ D

Question # 25

Vector additon is:

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

Question # 26

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 # 27

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

0 A
1 B
-1 C
3 D

Question # 28

Vector i =

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

Question # 29

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 # 30

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

√13 A
√7 B
1/√13 C
√29 D

Sr.#	Question	Answer
1	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
2	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
3	Vector i =	A. [1,0] B. [0,1,0] C. [0,0,1] 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	I f a =5i + 2j, then\|a\| =	A. √13 B. √7 C. 1/√13 D. √29
6	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
7	If a = [1,4,3] and B= [2,-1,5] athen the mid point M of AB is:	A. [1,1,1.5] B. [2,2,1.5] C. [1.5,1.5,4] D. None of these
8	The modulus of 12-5i is:	A. 7 B. 13 C. √7 D. 119
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	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

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

If aand bare two vectors then a+b =

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

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:

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:

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

The magnitude of vector a 2i-7j is

O (0,0)is called:

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

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

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

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

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

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

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

The modulus of 12-5i is:

If a,b = 0 then

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

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

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

Vector additon is:

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

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

Vector i =

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

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

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