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

Question # 1

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 # 2

Vector i =

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

Question # 3

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

√7 A
√41 B
√19 C
√(2&7) D

Question # 4

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

4 A
6 B
5 C
3 D

Question # 5

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 # 6

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

1 A
2 B
-1 C
-3 D

Question # 7

If a,b = 0 then

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

Question # 8

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

3 A
√35 B
√17 C
√35 D

Question # 9

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 # 10

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 # 11

The modulus of 12-5i is:

7 A
13 B
√7 C
119 D

Question # 12

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

√13 A
√7 B
1/√13 C
√29 D

Question # 13

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 # 14

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

1 A
√3 B
√2 C
7 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

a ______quantity is one that possesses both magnitude and direction.

Scalar A
Vector B
Segment C
None of these D

Question # 17

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

0 A
1 B
-1 C
3 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 additon is:

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

Question # 20

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

√3 A
1 B
√2 C
∞ D

Question # 21

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

5 A
5i B
-5 C
√5 D

Question # 22

The magnitude of vector a 2i-7j is

√23 A
√43 B
3 C
√53 D

Question # 23

If aand bare two vectors then a+b =

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

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 # 26

If u = xi + yj, then|u|

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

Question # 27

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 # 28

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 # 29

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 # 30

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

Sr.#	Question	Answer
1	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
2	O (0,0)is called:	A. Position vector B. Free vector C. Unite vector D. Null vector
3	Vector i =	A. [1,0] B. [0,1,0] C. [0,0,1] 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 m and n be two scalars, then (m+n) g =	A. 0 B. m+n C. m▁a+n▁a D. ma - m▁a
6	I f a =5i + 2j, then\|a\| =	A. √13 B. √7 C. 1/√13 D. √29
7	Vector additon is:	A. Commutative B. Associative C. Commutative and Associative D. None of these
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	The magnitude of vector a 2i-7j is	A. √23 B. √43 C. 3 D. √53
10	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

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

Vector i =

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

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

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

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

If a,b = 0 then

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

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 modulus of 12-5i is:

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

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

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

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

a ______quantity is one that possesses both magnitude and direction.

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 =

Vector additon is:

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

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

The magnitude of vector a 2i-7j is

If aand bare two vectors then a+b =

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

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

If u = xi + yj, then|u|

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

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

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

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

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