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

Question # 1

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 # 2

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 # 3

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

1 A
2 B
-1 C
-3 D

Question # 4

If a,b = 0 then

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

Question # 5

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

5 A
5i B
-5 C
√5 D

Question # 6

If u = xi + yj, then|u|

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

Question # 7

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

√3 A
1 B
√2 C
∞ D

Question # 8

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 # 9

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

0 A
1 B
-1 C
3 D

Question # 10

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

√7 A
√41 B
√19 C
√(2&7) D

Question # 11

a ______quantity is one that possesses both magnitude and direction.

Scalar A
Vector B
Segment C
None of these D

Question # 12

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

3 A
√35 B
√17 C
√35 D

Question # 13

Vector additon is:

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

Question # 14

The magnitude of vector a 2i-7j is

√23 A
√43 B
3 C
√53 D

Question # 15

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 # 16

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

√21 A
√97 B
√39 C
None of these D

Question # 17

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 # 18

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 # 19

Vector i =

[1,0] A
[0,1,0] B
[0,0,1] C
None of these 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 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 # 22

If aand bare two vectors then a+b =

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

Question # 23

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

4 A
6 B
5 C
3 D

Question # 24

The modulus of 12-5i is:

7 A
13 B
√7 C
119 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 vector k = [0,0,1] is called unit vector along:

x -axis A
y - axis B
z- axis C
None of these D

Question # 27

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 # 28

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 # 29

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 # 30

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

1 A
√3 B
√2 C
7 D

Sr.#	Question	Answer
1	If u =2i +pi + 5k and v = 3i + i +pk are perpendicular , then p=	A. 1 B. 2 C. -1 D. -3
2	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
3	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
4	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
5	If u = 2ai + i - k and v = i +ai + 4k are perpendicular then a =	A. 4 B. 1/2 C. 3 D. 4/3
6	If\|a\| =\|b\|=\|a + b\|=1, then\|a+ b\| = 5, then\|a-b\| =	A. 4 B. 6 C. 5 D. 3
7	If a,b = 0 then	A. a \|b B. a\|\|b C. a = b D. None
8	The vector k = [0,0,1] is called unit vector along:	A. x -axis B. y - axis C. z- axis D. None of these
9	If\|a\| =\|b\| = \|a+b\|=1, then\|a-b\| is equal to:	A. 1 B. √3 C. √2 D. 7
10	a ______quantity is one that possesses both magnitude and direction.	A. Scalar B. Vector C. Segment 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

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

If a,b = 0 then

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

If u = xi + yj, then|u|

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

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

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

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

a ______quantity is one that possesses both magnitude and direction.

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

Vector additon is:

The magnitude of vector a 2i-7j is

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

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

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

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

Vector i =

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

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

If aand bare two vectors then a+b =

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

The modulus of 12-5i is:

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

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

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

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

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:

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