Let A = {1, 2, 3, 4} and B = {4, 8, 9, 10}. A function f: A ⟶ B given by f = {(1, 4), (2, 8), (3, 9), (4,10)} is a

(a)

Many-one function

(b)

Identity function

(c)

One-to-one function

(d)

Into function

Let f(x) = x² - x, then f(x- 1) - (x + 1) is ___________

(a)

4x

(b)

2-2x

(c)

2-4x

(d)

4x-2

If f is identify function, then the value of f(1) - 2f(2) + f(3) is: 

(a)

-1

(b)

-3

(c)

1

(d)

0

The first term of an arithmetic progression is unity and the common difference is 4. Which of the following will be a term of this A.P.

(a)

4551

(b)

10091

(c)

7881

(d)

13531

A square is drawn by joinintg the mid points of the sides of a given square in the same way and this process continues indefinitely. If the side of the first square is 4 cm, then the sum of the area of all the squares is ____________

(a)

8 cm²

(b)

16 cm²

(c)

32 cm² 

(d)

64 cm²

\(\frac { x }{ { x }^{ 2 }-25 } -\frac { 8 }{ { x }^{ 2 }+6x+5 } \) gives

(a)

\(\frac { { x }^{ 2 }-7x+40 }{ \left( x-5 \right) \left( x+5 \right) } \)

(b)

\(\frac { { x }^{ 2 }+7x+40 }{ \left( x-5 \right) \left( x+5 \right) \left( x+1 \right) } \)

(c)

\(\frac { { x }^{ 2 }-7x+40 }{ \left( { x }^{ 2 }-25 \right) \left( x+1 \right) } \)

(d)

\(\frac { { x }^{ 2 }+10 }{ \left( { x }^{ 2 }-25 \right) \left( x+1 \right) } \)

Which of the following can be calculated from the given matrices A  = \(\left( \begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix} \right) \), B = \(\left( \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix} \right) \),
(i) A²
(ii) B²
(iii) AB
(iv) BA

(a)

(i) and (ii) only

(b)

(ii) and (iii) only

(c)

(ii) and (iv) only

(d)

all of these

\(\frac { { x }^{ 2 }+7x12 }{ { x }^{ 2 }+8x+15 } \times \frac { { x }^{ 2 }+5x }{ { x }^{ 2 }+6x+8 } =\_ \_ \_ \_ \_ \_ \_ \_ \_ \)

(a)

x+2

(b)

\(\frac { x }{ x+2 } \)

(c)

\(\frac { 35{ x }^{ 2 }+60x }{ { 48x }^{ 2 }+120 } \)

(d)

\(\frac { 1 }{ x+2 } \)

If \(A=\left[ \begin{matrix} y & 0 \\ 3 & 4 \end{matrix} \right] \) and \(I=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right] \) then A² = 16 I for ___________

(a)

y = 4

(b)

y = 5

(c)

y = -4

(d)

y = 16

In a \(\triangle\)ABC, AD is the bisector \(\angle\)BAC. If AB = 8 cm, BD = 6 cm and DC = 3 cm. The length of the side AC is

(a)

6 cm

(b)

4 cm

(c)

3 cm

(d)

8 cm

In a triangle, the internal bisector of an angle bisects the opposite side. Find the nature of the triangle.

(a)

right angle

(b)

equilateral

(c)

scalene

(d)

isosceles

The slope of the line joining (12, 3), (4, a) is \(\frac 18\). The value of ‘a’ is

(a)

1

(b)

4

(c)

-5

(d)

2

If the mid-point of the line segment joining \(A\left( \frac { x }{ 2 } ,\frac { y+1 }{ 2 } \right) \) and B(x + 1, y-3) is C(5, -2) then find the values of x, y ____________

(a)

(6, -1)

(b)

(-6, 1)

(c)

(-2, 1)

(d)

(3, 5)

The angle of elevation of a cloud from a point h metres above a lake is b. The angle of depression of its reflection in the lake is 45^o. The height of location of the cloud from the lake is ___________

(a)

\(\frac { h(1+tan\beta ) }{ 1-tan\beta } \)

(b)

\(\frac { h(1-tan\beta ) }{ 1+tan\beta } \)

(c)

h tan(45^o- β)

(d)

None of these

tan \(\theta \) cosec²\(\theta \) - tan\(\theta \) is equal to 

(a)

sec\(\theta \)

(b)

\(cot^{ 2 }\theta \)

(c)

sin\( \theta \)

(d)

\(cot\theta \)

Two persons are standing ‘x’ metres apart from each other and the height of the first person is double that of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the shorter person (in metres) is

(a)

\(\sqrt { 2 } \) x

(b)

\(\frac { x }{ 2\sqrt { 2 } } \)

(c)

\(\frac { x }{ \sqrt { 2 } } \)

(d)

2x

Given that sin ∝ = \(\frac{1}{2}\) and cos β = \(\frac{1}{2}\), then the value of (∝ + β) is ___________

(a)

0^o

(b)

30^o

(c)

60^o

(d)

90^o

(cosec²θ - cot²θ) (1 - cos²θ) is equal to ___________

(a)

cosec θ

(b)

cos²θ

(c)

sec²θ

(d)

sin²θ

A frustum of a right circular cone is of height 16 cm with radii of its ends as 8 cm and 20 cm. Then, the volume of the frustum is

(a)

3328\(\pi\) cm³

(b)

3228\(\pi\) cm³

(c)

3240\(\pi\) cm³

(d)

3340\(\pi\) cm³

The radio of base of a one 5 cm and to height 12 cm. The slant height of the cone ___________

(a)

12 cm

(b)

17 cm

(c)

7 cm

(d)

60 cm

The material of a cone is converted into the shape of a cylinder of equal radius. If the height of the cylinder is 5 cm, then height of the cone is ___________

(a)

10 cm

(b)

15 cm

(c)

18 cm

(d)

24 cm

The sum of all deviations of the data from its mean is

(a)

Always positive

(b)

always negative

(c)

zero

(d)

non-zero integer

IF the probability of the non-happening of a event is q, then the probability of happening of that event is 

(a)

1-q

(b)

q

(c)

q/2

(d)

∝q

If the co-efficient of variation and standard deviation of a data are 35% and 7.7 respectively then the mean is ___________

(a)

20

(b)

30

(c)

25

(d)

22

A nuber x is chosen at random drom -4, -3, -2, -1, 0, 1, 2, 3, 4. The probability that \(\left| x \right| \le 3\) is ___________

(a)

\(\frac { 3 }{ 9 } \)

(b)

\(\frac { 4 }{ 9 } \)

(c)

\(\frac { 1 }{ 9 } \)

(d)

\(\frac { 7 }{ 9 } \)