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

1 A
2 B
-1 C
-3 D

Question # 3

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 # 4

If u = xi + yj, then|u|

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

Question # 5

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 # 6

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 # 7

If aand bare two vectors then a+b =

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

Question # 8

The modulus of 12-5i is:

7 A
13 B
√7 C
119 D

Question # 9

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 # 10

a ______quantity is one that possesses both magnitude and direction.

Scalar A
Vector B
Segment C
None of these D

Question # 11

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

4 A
6 B
5 C
3 D

Question # 12

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 # 13

The magnitude of vector a 2i-7j is

√23 A
√43 B
3 C
√53 D

Question # 14

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 # 15

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 # 16

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

√13 A
√7 B
1/√13 C
√29 D

Question # 17

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 # 18

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 # 19

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

1 A
√3 B
√2 C
7 D

Question # 20

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 # 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

If a,b = 0 then

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

Vector i =

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

Question # 26

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

√21 A
√97 B
√39 C
None of these 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 additon is:

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

Question # 29

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

√3 A
1 B
√2 C
∞ D

Question # 30

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

Sr.#	Question	Answer
1	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
2	Vector additon is:	A. Commutative B. Associative C. Commutative and Associative D. None of these
3	If c = 2i+j+k and d= -1 + 4j +2k, then [c-d]=	A. √7 B. √41 C. √19 D. √(2&7)
4	a ______quantity is one that possesses both magnitude and direction.	A. Scalar B. Vector C. Segment D. None of these
5	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
6	If u =2i +pi + 5k and v = 3i + i +pk are perpendicular , then p=	A. 1 B. 2 C. -1 D. -3
7	If u = xi + yj, then\|u\|	A. x² + y² B. (x² +y²)² C. x²-y² D. √(x²+y²)
8	The magnitude of vector a=i-3j+5k is:	A. 3 B. √35 C. √17 D. √35
9	If a,b = 0 then	A. a \|b B. a\|\|b C. a = b D. None
10	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

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

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

If u = xi + yj, then|u|

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 aand bare two vectors then a+b =

The modulus of 12-5i is:

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

a ______quantity is one that possesses both magnitude and direction.

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 magnitude of vector a 2i-7j is

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:

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

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

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

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

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

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:

If a,b = 0 then

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

Vector i =

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

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

Vector additon is:

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

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

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