If n(A x B) = 6 and A = {1,3} then n(B) is

(a)

1

(b)

2

(c)

3

(d)

6

Let n(A) = m and n(B) = n then the total number of non-empty relations that can be defined from A to B is

(a)

mⁿ

(b)

n^m

(c)

2^mn-1

(d)

2^mn

Using Euclid’s division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are

(a)

0, 1, 8

(b)

1, 4, 8

(c)

0, 1, 3

(d)

0, 1, 3

If A = 2⁶⁵ and B = 2⁶⁴ + 2⁶³ + 2⁶² +...+ 2⁰ Which of the following is true?

(a)

B is 2⁶⁴ more than A

(b)

A and B are equal

(c)

B is larger than A by 1

(d)

A is larger than B by 1

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

(a)

4x²

(b)

16x²

(c)

8x²

(d)

-8x²

Transpose of a column matrix is

(a)

unit matrix

(b)

diagonal matrix

(c)

column matrix

(d)

row matrix

Find the matrix X if 2X + \(\left( \begin{matrix} 1 & 3 \\ 5 & 7 \end{matrix} \right) =\left( \begin{matrix} 5 & 7 \\ 9 & 5 \end{matrix} \right) \)

(a)

\(\left(\begin{array}{cc} -2 & -2 \\ 2 & -1 \end{array}\right)\)

(b)

\(\left(\begin{array}{cc} 2 & 2 \\ 2 & -1 \end{array}\right)\)

(c)

\(\left(\begin{array}{ll} 1 & 2 \\ 2 & 2 \end{array}\right)\)

(d)

\(\left(\begin{array}{ll} 2 & 1 \\ 2 & 2 \end{array}\right)\)

In ∆LMN, \(\angle\)L = 60^o, \(\angle\)M = 50^o. If ∆LMN ~ ∆PQR then the value of \(\angle\)R is

(a)

40^o

(b)

70°

(c)

30°

(d)

110°

A tangent is perpendicular to the radius at the

(a)

centre

(b)

point of contact

(c)

infinity

(d)

chord

If (5, 7), (3, p) and (6, 6) are collinear, then the value of p is

(a)

3

(b)

6

(c)

9

(d)

12

When proving that a quadrilateral is a parallelogram by using slopes you must find

(a)

The slopes of two sides

(b)

The slopes of two pair of opposite sides

(c)

The lengths of all sides

(d)

Both the lengths and slopes of two sides

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)

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

The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is

(a)

60\(\pi\) cm²

(b)

68\(\pi\) cm²

(c)

120\(\pi\) cm²

(d)

136\(\pi\) cm²

If the radius of the base of a right circular cylinder is halved keeping the same height, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

(a)

1:2

(b)

1:4

(c)

1:6

(d)

1:8

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 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

The mean of 100 observations is 40 and their standard deviation is 3. The sum of squares of all observations is

(a)

40000

(b)

160900

(c)

160000

(d)

30000

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

A purse contains 10 notes of Rs. 2000, 15 notes of Rs. 500, and 25 notes of Rs. 200. One note is drawn at random. What is the probability that the note is either a Rs. 500 note or Rs. 200 note?

(a)

\(\frac{1}{5}\)

(b)

\(\frac{3}{10}\)

(c)

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

(d)

\(\frac{4}{5}\)