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 a,b = 0 then

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

Question # 3

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

√3 A
1 B
√2 C
∞ D

Question # 4

Vector i =

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

Question # 5

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

3 A
√35 B
√17 C
√35 D

Question # 6

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

√7 A
√41 B
√19 C
√(2&7) D

Question # 7

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 # 8

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

√21 A
√97 B
√39 C
None of these D

Question # 9

a ______quantity is one that possesses both magnitude and direction.

Scalar A
Vector B
Segment C
None of these D

Question # 10

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 # 11

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

0 A
1 B
-1 C
3 D

Question # 12

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

1 A
√3 B
√2 C
7 D

Question # 13

If u = xi + yj, then|u|

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

Question # 14

The magnitude of vector a 2i-7j is

√23 A
√43 B
3 C
√53 D

Question # 15

If aand bare two vectors then a+b =

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

Question # 16

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 # 17

Vector additon is:

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

Question # 18

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

√13 A
√7 B
1/√13 C
√29 D

Question # 19

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

4 A
6 B
5 C
3 D

Question # 20

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 # 21

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 # 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 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 # 24

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 # 25

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 # 26

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 # 27

The modulus of 12-5i is:

7 A
13 B
√7 C
119 D

Question # 28

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 # 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

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

5 A
5i B
-5 C
√5 D

Sr.#	Question	Answer
1	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
2	If aand bare two vectors then a+b =	A. b + a B. b - a C. ab D. a^ b
3	Vector i =	A. [1,0] B. [0,1,0] C. [0,0,1] D. None of these
4	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
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	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
7	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
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 a=5j + 2j,b=2i -3j, then\|a+2b\|=	A. √21 B. √97 C. √39 D. None of these
10	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

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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 a,b = 0 then

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

Vector i =

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

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 =

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

a ______quantity is one that possesses both magnitude and direction.

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

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

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

If u = xi + yj, then|u|

The magnitude of vector a 2i-7j is

If aand bare two vectors then a+b =

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

Vector additon is:

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

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

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

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

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

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

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

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 = [-3 , 5] and v = [6 , -2] is:

The modulus of 12-5i is:

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

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

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

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