If f: A ⟶ B is a bijective function and if n(B) = 7, then n(A) is equal to

(a)

7

(b)

49

(c)

1

(d)

14

If f(x) = mx + n, when m and n are integers f(-2) = 7, and f(3) = 2 then m and n are equal to ___________

(a)

-1, -5

(b)

1, -9

(c)

-1, 5

(d)

1, 9

If \(f(x)=\frac { x+1 }{ x-2 } ,g(x)=\frac { 1+2x }{ x-1 } \) then fog(x) is ___________

(a)

Constant function

(b)

Quadratic function

(c)

Cubic function

(d)

Identify function

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

The first term of an A.P. whose 8^th and 12^th terms are 39 and 59 respectively is ____________

(a)

5

(b)

6

(c)

4

(d)

3

The solution of the system x + y − 3z = −6, −7y + 7z = 7, 3z = 9 is

(a)

x = 1, y = 2, z = 3

(b)

x = −1, y = 2, z = 3

(c)

x = −1, y = −2, z = 3

(d)

x = 1, y = -2, z = 3

Graph of a linear equation is a ____________

(a)

straight line

(b)

circle

(c)

parabola

(d)

hyperbola

Graphically an infinite number of solutions represents ___________

(a)

three planes with no point in common

(b)

three planes intersecting at a single point

(c)

three planes intersecting in a line or coinciding with one another

(d)

None

Choose the correct answer
(i) Every scalar matrix is an identity matrix
(ii) Every identity matrix is a scalar matrix
(iii) Every diagonal matrix is an identity matrix
(iv) Every null matrix is a scalar matrix

(a)

(i) and (iii) only

(b)

(iii) only

(c)

(iv) only

(d)

(ii) and (iv) only

If in \(\triangle\)ABC, DE || BC, AB = 3.6 cm, AC = 2.4 cm and AD = 2.1 cm then the length of AE is

(a)

1.4 cm

(b)

1.8 cm

(c)

1.2 cm

(d)

1.05 cm

The height of an equilateral triangle of side a is

(a)

\(\frac { a }{ 2 } cm\)

(b)

\(\sqrt { 3a } \)

(c)

\(\frac { \sqrt { 3 } }{ 2 } a\)

(d)

\(\frac { \sqrt { 3 } }{ 4 } a\)

The point of intersection of 3x − y = 4 and x + y = 8 is

(a)

(5, 3)

(b)

(2, 4)

(c)

(3, 5)

(d)

(4, 4)

Find the equation of the line passing the point which is parallel to the y axis (5, 3) is ____________

(a)

y = 5

(b)

y = 3

(c)

x = 5

(d)

x = 3

If sin \(\theta \) + cos\(\theta \) = a and sec \(\theta \) + cosec \(\theta \) = b, then the value of b(a² - 1) is equal to 

(a)

2a

(b)

3a

(c)

0

(d)

2ab

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

If cos A = \(\frac{4}{5}\), then the value of tan A is ___________

(a)

\(\frac{3}{5}\)

(b)

\(\frac{3}{4}\)

(c)

\(\frac{4}{3}\)

(d)

\(\frac{5}{3}\)

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

(a)

cosec θ

(b)

cos²θ

(c)

sec²θ

(d)

sin²θ

The angle of depression of a boat from a \(50\sqrt { 3 } \) m high bridge is 30^o. The horizontal distance of the boat from the bridge is ___________

(a)

150 m

(b)

\(150\sqrt { 3 } \)

(c)

60m

(d)

\(60\sqrt { 3 } \)

The total surface area of a hemi-sphere is how much times the square of its radius.

(a)

\(\pi\)

(b)

4\(\pi\)

(c)

3\(\pi\)

(d)

2\(\pi\)

The height and radius of the cone of which the frustum is a part are h₁ units and r₁ units respectively. Height of the frustum is h₂ units and radius of the smaller base is r₂ units. If h₂ : h₁ = 1:2 then r₂ : r₁ is

(a)

1:3

(b)

1:2

(c)

2:1

(d)

3:1

The volume of a frustum if a cone of height L and ends-radio and r₁ and r₂ is ___________

(a)

\(\frac{1}{3}\)πh1(r₁²+r₂²+r₁r₂)

(b)

\(\frac{1}{3}\)πh(r₁²+r₂²-r₁r₂)

(c)

πh(r₁²+r₂²+r₁r₂)

(d)

πh(r₁²+r₂²-r₁r₂)

Kamalam went to play a lucky draw contest 135 tickets of the lucky draw were sold. If the probability of Kamalam winning is \(\frac { 1 }{ 9 } \), then the number of tickets bought by kamalam is ____________

(a)

5

(b)

10

(c)

15

(d)

20

The standard deviation of a data is 3. If each value is multiplied by 5 then the new variance is

(a)

3

(b)

15

(c)

5

(d)

225

If a letter is chosen at random from the English alphabets {a, b,...,z}, then the probability that the letter chosen precedes x

(a)

\(\frac{12}{13}\)

(b)

\(\frac{1}{13}\)

(c)

\(\frac{23}{26}\)

(d)

\(\frac{3}{26}\)

The range of first 10 prime number is ___________

(a)

9

(b)

20

(c)

27

(d)

5

If the probability of non-happening of an event is, then probability of happening of the event is ___________

(a)

1-q

(b)

q

(c)

\(\frac { q }{ 2 } \)

(d)

2q