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

Question # 1

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 # 2

If a,b = 0 then

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

Question # 3

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

5 A
5i B
-5 C
√5 D

Question # 4

If aand bare two vectors then a+b =

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

Question # 5

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 # 6

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

4 A
6 B
5 C
3 D

Question # 7

If u = xi + yj, then|u|

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

Question # 8

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

√7 A
√41 B
√19 C
√(2&7) D

Question # 9

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

√21 A
√97 B
√39 C
None of these D

Question # 10

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

3 A
√35 B
√17 C
√35 D

Question # 11

O (0,0)is called:

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

Question # 12

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 # 13

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 # 14

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

1 A
2 B
-1 C
-3 D

Question # 15

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 # 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

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 # 18

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 # 19

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

0 A
1 B
-1 C
3 D

Question # 20

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

√13 A
√7 B
1/√13 C
√29 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

a ______quantity is one that possesses both magnitude and direction.

Scalar A
Vector B
Segment C
None of these D

Question # 23

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

1 A
√3 B
√2 C
7 D

Question # 24

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

√3 A
1 B
√2 C
∞ D

Question # 25

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 # 26

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 # 27

Vector additon is:

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

Question # 28

Vector i =

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

Question # 29

The magnitude of vector a 2i-7j is

√23 A
√43 B
3 C
√53 D

Question # 30

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

4 A
1/2 B
3 C
4/3 D

Sr.#	Question	Answer
1	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
2	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
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	If u = 2ai + i - k and v = i +ai + 4k are perpendicular then a =	A. 4 B. 1/2 C. 3 D. 4/3
5	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
6	The modulus of a vector i-i+ k is:	A. √3 B. 1 C. √2 D. ∞
7	Vector additon is:	A. Commutative B. Associative C. Commutative and Associative D. None of these
8	If c = 2i+j+k and d= -1 + 4j +2k, then [c-d]=	A. √7 B. √41 C. √19 D. √(2&7)
9	If u =2i +pi + 5k and v = 3i + i +pk are perpendicular , then p=	A. 1 B. 2 C. -1 D. -3
10	The modulus of 12-5i is:	A. 7 B. 13 C. √7 D. 119

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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

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

If a,b = 0 then

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

If aand bare two vectors then a+b =

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

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

If u = xi + yj, then|u|

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

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

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

O (0,0)is called:

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

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=

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

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

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:

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

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

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

a ______quantity is one that possesses both magnitude and direction.

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

The modulus of a vector i-i+ k 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:

Vector additon is:

Vector i =

The magnitude of vector a 2i-7j is

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

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