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

O (0,0)is called:

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

Question # 3

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 # 4

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

√13 A
√7 B
1/√13 C
√29 D

Question # 5

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 # 6

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

3 A
√35 B
√17 C
√35 D

Question # 7

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

√3 A
1 B
√2 C
∞ D

Question # 8

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

0 A
1 B
-1 C
3 D

Question # 9

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 # 10

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 # 11

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

√21 A
√97 B
√39 C
None of these D

Question # 12

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 # 13

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 # 14

Vector additon is:

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

Question # 15

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

4 A
6 B
5 C
3 D

Question # 16

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

5 A
5i B
-5 C
√5 D

Question # 17

If u = xi + yj, then|u|

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

Question # 18

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

√7 A
√41 B
√19 C
√(2&7) D

Question # 19

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 # 20

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

1 A
√3 B
√2 C
7 D

Question # 21

Vector i =

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

Question # 22

If a,b = 0 then

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

Question # 23

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 # 24

The modulus of 12-5i is:

7 A
13 B
√7 C
119 D

Question # 25

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 # 26

If aand bare two vectors then a+b =

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

Question # 27

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

1 A
2 B
-1 C
-3 D

Question # 28

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 # 29

a ______quantity is one that possesses both magnitude and direction.

Scalar A
Vector B
Segment C
None of these D

Question # 30

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

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	If\|a\| =\|b\|=\|a + b\|=1, then\|a+ b\| = 5, then\|a-b\| =	A. 4 B. 6 C. 5 D. 3
3	The vector i = [1,0] is called unit vector along:	A. x-axis B. y - axis C. z- axis D. Botha a and y-axis
4	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
5	The vector k = [0,0,1] is called unit vector along:	A. x -axis B. y - axis C. z- axis D. None of these
6	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
7	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
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	a ______quantity is one that possesses both magnitude and direction.	A. Scalar B. Vector C. Segment D. None of these
10	The magnitude of vector a 2i-7j is	A. √23 B. √43 C. 3 D. √53

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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

O (0,0)is called:

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

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

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

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

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

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

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

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

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

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

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

Vector additon is:

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

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

If u = xi + yj, then|u|

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

Vector i =

If a,b = 0 then

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 =

If aand bare two vectors then a+b =

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

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

a ______quantity is one that possesses both magnitude and direction.

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

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