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

Question # 1

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 # 2

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 # 3

Vector additon is:

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

Question # 4

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 # 5

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

√7 A
√41 B
√19 C
√(2&7) D

Question # 6

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

√13 A
√7 B
1/√13 C
√29 D

Question # 7

The modulus of 12-5i is:

7 A
13 B
√7 C
119 D

Question # 8

If u = xi + yj, then|u|

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

Question # 9

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 # 10

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

0 A
1 B
-1 C
3 D

Question # 13

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

√21 A
√97 B
√39 C
None of these D

Question # 14

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 # 15

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

1 A
2 B
-1 C
-3 D

Question # 16

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

5 A
5i B
-5 C
√5 D

Question # 17

Vector i =

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

Question # 18

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

3 A
√35 B
√17 C
√35 D

Question # 19

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 # 20

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

4 A
6 B
5 C
3 D

Question # 21

If a,b = 0 then

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

Question # 22

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

√3 A
1 B
√2 C
∞ D

Question # 23

a ______quantity is one that possesses both magnitude and direction.

Scalar A
Vector B
Segment C
None of these D

Question # 24

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 # 25

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

1 A
√3 B
√2 C
7 D

Question # 26

The magnitude of vector a 2i-7j is

√23 A
√43 B
3 C
√53 D

Question # 27

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 # 28

O (0,0)is called:

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

Question # 29

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 # 30

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

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	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
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	The magnitude of vector a 2i-7j is	A. √23 B. √43 C. 3 D. √53
5	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
6	If a,b = 0 then	A. a \|b B. a\|\|b C. a = b D. None
7	The modulus of 12-5i is:	A. 7 B. 13 C. √7 D. 119
8	If u = 2ai + i - k and v = i +ai + 4k are perpendicular then a =	A. 4 B. 1/2 C. 3 D. 4/3
9	I f a =5i + 2j, then\|a\| =	A. √13 B. √7 C. 1/√13 D. √29
10	If u = xi + yj, then\|u\|	A. x² + y² B. (x² +y²)² C. x²-y² D. √(x²+y²)

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

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

Vector additon is:

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

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

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

The modulus of 12-5i is:

If u = xi + yj, then|u|

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

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

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

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

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

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

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

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

Vector i =

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

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

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

If a,b = 0 then

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

a ______quantity is one that possesses both magnitude and direction.

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

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

The magnitude of vector a 2i-7j is

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

O (0,0)is called:

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

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

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