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

Question # 1

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 # 2

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 # 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

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 # 5

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 # 6

a ______quantity is one that possesses both magnitude and direction.

Scalar A
Vector B
Segment C
None of these D

Question # 7

The modulus of 12-5i is:

7 A
13 B
√7 C
119 D

Question # 8

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 # 9

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 # 10

If aand bare two vectors then a+b =

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

Question # 11

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 # 12

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

4 A
6 B
5 C
3 D

Question # 13

If a,b = 0 then

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

Question # 14

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

√3 A
1 B
√2 C
∞ 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

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 # 17

O (0,0)is called:

Position vector A
Free vector B
Unite vector C
Null vector 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 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 # 20

Vector i =

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

Question # 21

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

√13 A
√7 B
1/√13 C
√29 D

Question # 22

Vector additon is:

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

Question # 23

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 # 24

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

5 A
5i B
-5 C
√5 D

Question # 25

If u = xi + yj, then|u|

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

Question # 26

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

0 A
1 B
-1 C
3 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=5j + 2j,b=2i -3j, then|a+2b|=

√21 A
√97 B
√39 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

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

3 A
√35 B
√17 C
√35 D

Sr.#	Question	Answer
1	If a,b = 0 then	A. a \|b B. a\|\|b C. a = b D. None
2	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
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 m and n be two scalars, then (m+n) g =	A. 0 B. m+n C. m▁a+n▁a D. ma - m▁a
5	O (0,0)is called:	A. Position vector B. Free vector C. Unite vector D. Null vector
6	The modulus of 12-5i is:	A. 7 B. 13 C. √7 D. 119
7	I f a =5i + 2j, then\|a\| =	A. √13 B. √7 C. 1/√13 D. √29
8	If the sum of two unit vectors is a unit vector the the magnitude of their difference is	A. √2 B. √3 C. 1 D. None of these
9	The vector k = [0,0,1] is called unit vector along:	A. x -axis B. y - axis C. z- axis D. None of these
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 positive real number which is the measure of the length of a vector is called the

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

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

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

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.

The modulus of 12-5i is:

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

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

If aand bare two vectors then a+b =

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

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

If a,b = 0 then

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

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

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

O (0,0)is called:

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:

Vector i =

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

Vector additon is:

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

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

If u = xi + yj, then|u|

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

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

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

The magnitude of vector a 2i-7j is

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

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