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

Vector i =

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

Question # 3

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 # 4

The magnitude of vector a 2i-7j is

√23 A
√43 B
3 C
√53 D

Question # 5

If u = xi + yj, then|u|

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

Question # 6

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 # 7

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

1 A
√3 B
√2 C
7 D

Question # 8

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 # 9

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

√7 A
√41 B
√19 C
√(2&7) 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

The modulus of 12-5i is:

7 A
13 B
√7 C
119 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

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 # 14

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

0 A
1 B
-1 C
3 D

Question # 15

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 # 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

If aand bare two vectors then a+b =

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

Question # 18

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 # 19

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

3 A
√35 B
√17 C
√35 D

Question # 20

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

√13 A
√7 B
1/√13 C
√29 D

Question # 21

If a,b = 0 then

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

Question # 22

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 # 23

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 # 24

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 # 25

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

1 A
2 B
-1 C
-3 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

O (0,0)is called:

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

Question # 28

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

5 A
5i B
-5 C
√5 D

Question # 29

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

√3 A
1 B
√2 C
∞ D

Question # 30

a ______quantity is one that possesses both magnitude and direction.

Scalar A
Vector B
Segment C
None of these D

Sr.#	Question	Answer
1	If\|a\| =\|b\|=\|a + b\|=1, then\|a+ b\| = 5, then\|a-b\| =	A. 4 B. 6 C. 5 D. 3
2	Vector additon is:	A. Commutative B. Associative C. Commutative and Associative D. None of these
3	If a=5j + 2j,b=2i -3j, then\|a+2b\|=	A. √21 B. √97 C. √39 D. None of these
4	The vector k = [0,0,1] is called unit vector along:	A. x -axis B. y - axis C. z- axis D. None of these
5	If a,b = 0 then	A. a \|b B. a\|\|b C. a = b D. None
6	If u = xi + yj, then\|u\|	A. x² + y² B. (x² +y²)² C. x²-y² D. √(x²+y²)
7	If c = 2i+j+k and d= -1 + 4j +2k, then [c-d]=	A. √7 B. √41 C. √19 D. √(2&7)
8	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
9	O (0,0)is called:	A. Position vector B. Free vector C. Unite vector D. Null vector
10	If aand bare two vectors then a+b =	A. b + a B. b - a C. ab D. a^ b

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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:

Vector i =

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

The magnitude of vector a 2i-7j is

If u = xi + yj, then|u|

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

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

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

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

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

The modulus of 12-5i is:

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:

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

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

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

If aand bare two vectors then a+b =

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

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

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

If a,b = 0 then

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 =

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

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

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

O (0,0)is called:

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

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

a ______quantity is one that possesses both magnitude and direction.

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