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

Vector i =

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

Question # 3

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 # 4

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

√3 A
1 B
√2 C
∞ 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

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 # 7

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

3 A
√35 B
√17 C
√35 D

Question # 8

The magnitude of vector a 2i-7j is

√23 A
√43 B
3 C
√53 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|a| =|b|=|a + b|=1, then|a+ b| = 5, then|a-b| =

4 A
6 B
5 C
3 D

Question # 11

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 # 12

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

5 A
5i B
-5 C
√5 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| is equal to:

1 A
√3 B
√2 C
7 D

Question # 15

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

0 A
1 B
-1 C
3 D

Question # 16

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 # 17

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 # 18

a ______quantity is one that possesses both magnitude and direction.

Scalar A
Vector B
Segment C
None of these D

Question # 19

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 # 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

Vector additon is:

Commutative A
Associative B
Commutative and Associative 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 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=5j + 2j,b=2i -3j, then|a+2b|=

√21 A
√97 B
√39 C
None of these D

Question # 26

The modulus of 12-5i is:

7 A
13 B
√7 C
119 D

Question # 27

If u = xi + yj, then|u|

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

Question # 28

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 # 29

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 # 30

O (0,0)is called:

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

Sr.#	Question	Answer
1	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
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	I f a =5i + 2j, then\|a\| =	A. √13 B. √7 C. 1/√13 D. √29
4	If u =2i +pi + 5k and v = 3i + i +pk are perpendicular , then p=	A. 1 B. 2 C. -1 D. -3
5	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
6	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
7	If a=5j + 2j,b=2i -3j, then\|a+2b\|=	A. √21 B. √97 C. √39 D. None of these
8	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
9	If u =[3,-4],then modulus of uis:	A. 5 B. 5i C. -5 D. √5
10	The magnitude of vector a 2i-7j is	A. √23 B. √43 C. 3 D. √53

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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:

Vector i =

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

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

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:

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

The magnitude of vector a 2i-7j is

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

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

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

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

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

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

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

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

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

a ______quantity is one that possesses both magnitude and direction.

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

If a,b = 0 then

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

Vector additon is:

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

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

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

The modulus of 12-5i is:

If u = xi + yj, then|u|

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

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

O (0,0)is called:

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