The range of the relation R = {(x, x²) |x is a prime number less than 13} is

(a)

{2,3,5,7}

(b)

{2,3,5,7,11}

(c)

{4,9,25,49,121}

(d)

{1,4,9,25,49,121}

If f is constant function of value \(\frac { 1 }{ 10 } \), the value of f(1) + f(2) + ... + f(100) is _________

(a)

\(\frac { 1 }{ 100 } \)

(b)

100

(c)

\(\frac { 1 }{ 10 } \)

(d)

10

The next term of the sequence \(\frac { 3 }{ 16 } ,\frac { 1 }{ 8 } ,\frac { 1 }{ 12 } ,\frac { 1 }{ 18 } \), ..... is

(a)

\(\frac { 1 }{ 24 } \)

(b)

\(\frac { 1 }{ 27 } \)

(c)

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

(d)

\(\frac { 1 }{ 81 } \)

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

Which of the following should be added to make x⁴ + 64 a perfect square

(a)

4x²

(b)

16x²

(c)

8x²

(d)

-8x²

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

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

The product of the sum and product of roots of equation (a²-b²)x²-(a+b)²x+(a³-b³) = 0 is ___________

(a)

\(\frac { { a }^{ 2 }+ab+{ b }^{ 2 } }{ (a-b) } \)

(b)

\(\frac { a-b }{ a+b } \)

(c)

\(\frac { a-b }{ a+b } \)

(d)

\(\frac { a-b }{ { a }^{ 2 }+ab+{ b }^{ 2 } } \)

How many tangents can be drawn to the circle from an exterior point?

(a)

one

(b)

two

(c)

infinite

(d)

zero

If ABC is a triangle and AD bisects A, AB = 4cm, BD = 6cm, DC = 8cm then the value of AC is ____________

(a)

\(\frac { 16 }{ 3 } cm\)

(b)

\(\frac { 32 }{ 3 } cm\)

(c)

\(\frac { 3 }{ 16 } cm\)

(d)

\(\frac { 1 }{ 2 } cm\)

The equation of a line passing through the origin and perpendicular to the line 7x - 3y + 4 = 0 is

(a)

7x - 3y + 4 = 0

(b)

3x - 7y + 4 = 0

(c)

3x + 7y = 0

(d)

7x - 3y = 0

The four vertices of a quardrilateral are (1, 2), (5, -6), (7, -4) and (k, -2) taken in order. If the area of quadrilateral is zero then find the value of k.

(a)

4

(b)

-2

(c)

6

(d)

3

(1 + tan \(\theta \) + sec\(\theta \)) (1 + cot\(\theta \) - cosec\(\theta \)) is equal to 

(a)

0

(b)

1

(c)

2

(d)

-1

If ∆ABC is right angled at C, then the value of cos (A + B) is ___________

(a)

0

(b)

1

(c)

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

(d)

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

If 4 tan θ = 3, then \(\left( \frac { 4sin\theta -cos\theta }{ 4sin\theta +cos\theta } \right) \) is equal to ___________

(a)

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

(b)

\(\frac{1}{3}\)

(c)

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

(d)

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

If a sin (90 - θ) of (90^o - θ) = cos(90^o - θ)tan equal to ___________

(a)

0

(b)

1

(c)

-1

(d)

2

If x = a sec θ and = b tan θ, then b²x² - a²y² is equal to ___________

(a)

ab 

(b)

a²-b²

(c)

a²+b²

(d)

a²b²

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 ratio of the volumes of two spheres is 8 : 27. If r and R are the radii of sphere respectively, Then (R - r) : r is ___________

(a)

1:2

(b)

1:3

(c)

2:3

(d)

4:9

A solid is hemispherical at the bottom and conical above. If the curved surface areas of the two parts are equal, then the ratio of its radius and the height of its conical part is ___________

(a)

1:3

(b)

\(1:\sqrt { 3 } \)

(c)

1:1

(d)

\(\sqrt { 3 } :1\)

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

If the mean and coefficient of variation of a data are 4 and 87.5% then the standard deviation is

(a)

3.5

(b)

3

(c)

4.5

(d)

2.5

The mean of first first 10 odd natural number is ___________

(a)

5

(b)

10

(c)

20

(d)

19

Th4e batsman A is more consistent than batsman B if ___________

(a)

C.V of A > C.V of B

(b)

C.V of A < C.V of B

(c)

C.V of a =C.V of B

(d)

C.V of A≥C.V of B

A box contains some milk chocalates and some coco chocolates and there are 60 choolates in the box. If the probability of taking a milk chocolate is \(\frac { 2 }{ 3 } \) then the number of coco chocolates is ___________

(a)

40

(b)

50

(c)

20

(d)

30