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

Question # 1

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 # 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 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 # 4

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 # 5

If a,b = 0 then

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

Question # 6

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

√13 A
√7 B
1/√13 C
√29 D

Question # 7

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

√7 A
√41 B
√19 C
√(2&7) D

Question # 8

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 # 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

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 # 11

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 # 12

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 # 13

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 # 14

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 # 15

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

√21 A
√97 B
√39 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

Vector i =

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

Question # 18

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

4 A
6 B
5 C
3 D

Question # 19

O (0,0)is called:

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

Question # 20

The magnitude of vector a 2i-7j is

√23 A
√43 B
3 C
√53 D

Question # 21

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 # 22

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

1 A
√3 B
√2 C
7 D

Question # 23

If u = xi + yj, then|u|

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

Question # 24

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

0 A
1 B
-1 C
3 D

Question # 25

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

5 A
5i B
-5 C
√5 D

Question # 26

The modulus of 12-5i is:

7 A
13 B
√7 C
119 D

Question # 27

Vector additon is:

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

Question # 28

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

√3 A
1 B
√2 C
∞ D

Question # 29

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

1 A
2 B
-1 C
-3 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 = [1,4,3] and B= [2,-1,5] athen the mid point M of AB is:	A. [1,1,1.5] B. [2,2,1.5] C. [1.5,1.5,4] D. None of these
2	The vector k = [0,0,1] is called unit vector along:	A. x -axis B. y - axis C. z- axis D. None of these
3	If u = 2ai + i - k and v = i +ai + 4k are perpendicular then a =	A. 4 B. 1/2 C. 3 D. 4/3
4	If u = xi + yj, then\|u\|	A. x² + y² B. (x² +y²)² C. x²-y² D. √(x²+y²)
5	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
6	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
7	If a=5j + 2j,b=2i -3j, then\|a+2b\|=	A. √21 B. √97 C. √39 D. None of these
8	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
9	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
10	I f a =5i + 2j, then\|a\| =	A. √13 B. √7 C. 1/√13 D. √29

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

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

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

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

If a,b = 0 then

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

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

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:

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:

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

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

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

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

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

Vector i =

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

O (0,0)is called:

The magnitude of vector a 2i-7j is

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

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

If u = xi + yj, then|u|

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

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

The modulus of 12-5i is:

Vector additon is:

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

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

a ______quantity is one that possesses both magnitude and direction.

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