If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is

(a)

3

(b)

2

(c)

4

(d)

8

If g = {(1,1), (2,3), (3,5), (4,7)} is a function given by g(x) = αx + β then the values of α and β are

(a)

(-1,2)

(b)

(2,-1)

(c)

(-1,-2)

(d)

(1,2)

The sum of the exponents of the prime factors in the prime factorization of 1729 is

(a)

1

(b)

2

(c)

3

(d)

4

If 6 times of 6^th term of an A.P. is equal to 7 times the 7^th term, then the 13^th term of the A.P. is

(a)

0

(b)

6

(c)

7

(d)

13

The value of (1³ + 2³ + 3³ +...+15³) - (1 + 2 + 3 +...+ 15)is 

(a)

14400

(b)

14200

(c)

14280

(d)

14520

\(\frac {3y - 3}{y} \div \frac {7y - 7}{3y^{2}}\) is

(a)

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

(b)

\(\frac {9y^{2}}{(21y - 21)}\)

(c)

\(\frac {21y^2 - 42y + 21}{3y^{2}}\)

(d)

\(\frac {7(y^{2} - 2y + 1)}{y^{2}}\)

The solution of (2x - 1)² = 9 is equal to

(a)

-1

(b)

2

(c)

-1, 2

(d)

None of these

The number of points of intersection of the quadratic polynomial x² + 4x + 4 with the X axis is

(a)

0

(b)

1

(c)

0 or 1

(d)

2

If A = \(\left( \begin{matrix} 1 & 2 & 3 \\ 3 & 2 & 1 \end{matrix} \right) \), B = \(\left( \begin{matrix} 1 & 0 \\ 2 & -1 \\ 0 & 2 \end{matrix} \right) \) and C = \(\left( \begin{matrix} 0 & 1 \\ -2 & 5 \end{matrix} \right) \), Which of the following statements are correct?
(i) AB + C =  \(\left( \begin{matrix} 5 & 5 \\ 5 & 5 \end{matrix} \right) \)
(ii) BC = \(\left( \begin{matrix} 0 & 1 \\ 2 & -3 \\ -4 & 10 \end{matrix} \right) \)
(iii) BA + C = \(\left( \begin{matrix} 2 & 5 \\ 3 & 0 \end{matrix} \right) \)
(iv) (AB)C = \(\left( \begin{matrix} -8 & 20 \\ -8 & 13 \end{matrix} \right) \) 

(a)

(i) and (ii) only

(b)

(ii) and (iii) only

(c)

(iii) and (iv) only

(d)

all of these

In the adjacent figure \(\angle BAC\) = 90^o and AD\(\bot \)BC then 

(a)

BD.CD = BC²

(b)

AB.AC = BC²

(c)

BD.CD = AD²

(d)

AB.AC = AD²

The area of triangle formed by the points (−5, 0), (0, −5) and (5, 0) is

(a)

0 sq. units

(b)

25 sq. units

(c)

5 sq. units

(d)

none of these

The slope of the line which is perpendicular to a line joining the points (0, 0) and (– 8, 8) is

(a)

–1

(b)

1

(c)

\(\frac13\)

(d)

-8

A straight line has equation 8y = 4x + 21. Which of the following is true

(a)

The slope is 0.5 and the y intercept is 2.6

(b)

The slope is 5 and the y intercept is 1.6

(c)

The slope is 0.5 and the y intercept is 1.6

(d)

The slope is 5 and the y intercept is 2.6

(2, 1) is the point of intersection of two lines.

(a)

x - y - 3 = 0; 3x - y - 7 = 0

(b)

x + y = 3; 3x + y = 7

(c)

3x + y = 3; x + y = 7

(d)

x + 3y - 3 = 0; x - y - 7 = 0

If sin \(\theta \) = cos \(\theta \), then 2 tan² \(\theta \) + sin² \(\theta \) -1 is equal to 

(a)

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

(b)

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

(c)

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

(d)

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

The electric pole subtends an angle of 30° at a point on the same level as its foot. At a second point ‘b’ metres above the first, the depression of the foot of the pole is 60°. The height of the pole (in metres) is equal to

(a)

\(\sqrt { 3 } \) b

(b)

\(\frac { b }{ 3 } \)

(c)

\(\frac { b }{ 2 } \)

(d)

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

If two solid hemispheres of same base radius r units are joined together along their bases, then curved surface area of this new solid is

(a)

4\(\pi\)r² sq.units

(b)

6\(\pi\)r² sq.units

(c)

3\(\pi\)r² sq.units

(d)

8\(\pi\)r² sq.units

In a hollow cylinder, the sum of the external and internal radii is 14 cm and the width is 4 cm. If its height is 20 cm, the volume of the material in it is

(a)

5600\(\pi\) cm³

(b)

1120\(\pi\) cm³

(c)

56\(\pi\) cm³

(d)

3600\(\pi\) cm³

The ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height is

(a)

1:2:3

(b)

2:1:3

(c)

1:3:2

(d)

3:1:2

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