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

Question # 1

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

3 A
√35 B
√17 C
√35 D

Question # 2

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 # 3

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

√21 A
√97 B
√39 C
None of these D

Question # 4

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 # 5

If aand bare two vectors then a+b =

b + a A
b - a B
ab C
a^ b 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|a| =|b|=|a + b|=1, then|a+ b| = 5, then|a-b| =

4 A
6 B
5 C
3 D

Question # 8

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

0 A
1 B
-1 C
3 D

Question # 9

Vector additon is:

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

Question # 10

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

1 A
√3 B
√2 C
7 D

Question # 11

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

√3 A
1 B
√2 C
∞ D

Question # 12

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 # 13

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

1 A
2 B
-1 C
-3 D

Question # 14

If u = xi + yj, then|u|

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

Question # 15

O (0,0)is called:

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

Question # 16

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 # 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,b = 0 then

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

Question # 19

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

√13 A
√7 B
1/√13 C
√29 D

Question # 20

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 # 21

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

√7 A
√41 B
√19 C
√(2&7) D

Question # 22

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 # 23

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 # 24

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

5 A
5i B
-5 C
√5 D

Question # 25

The magnitude of vector a 2i-7j is

√23 A
√43 B
3 C
√53 D

Question # 26

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 # 27

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 # 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

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

Vector i =

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

Sr.#	Question	Answer
1	Vector i =	A. [1,0] B. [0,1,0] C. [0,0,1] D. None of these
2	If u =[3,-4],then modulus of uis:	A. 5 B. 5i C. -5 D. √5
3	If u =2i +pi + 5k and v = 3i + i +pk are perpendicular , then p=	A. 1 B. 2 C. -1 D. -3
4	If\|a\| =\|b\| = \|a+b\|=1, then\|a-b\| is equal to:	A. 1 B. √3 C. √2 D. 7
5	If a=5j + 2j,b=2i -3j, then\|a+2b\|=	A. √21 B. √97 C. √39 D. None of these
6	The modulus of a vector i-i+ k is:	A. √3 B. 1 C. √2 D. ∞
7	The vector k = [0,0,1] is called unit vector along:	A. x -axis B. y - axis C. z- axis D. None of these
8	The modulus of 12-5i is:	A. 7 B. 13 C. √7 D. 119
9	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
10	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

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

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

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

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

If aand bare two vectors then a+b =

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

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

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

Vector additon is:

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

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

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

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

If u = xi + yj, then|u|

O (0,0)is called:

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

a ______quantity is one that possesses both magnitude and direction.

If a,b = 0 then

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

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

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

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

The magnitude of vector a 2i-7j is

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

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

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

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

Vector i =

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