A = {a, b, p}, B = {2, 3}, C = {p, q, r, s} then n[(A U C) x B] is

(a)

8

(b)

20

(c)

12

(d)

16

If f(x) = 2x² and g(x) = \(\frac{1}{3x}\), then f o g is

(a)

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

(b)

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

(c)

\(\\ \frac { 2 }{ 9x^{ 2 } } \)

(d)

\(\\ \frac { 1 }{ 6x^{ 2 } } \)

The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

(a)

2025

(b)

5220

(c)

5025

(d)

2520

In an A.P., the first term is 1 and the common difference is 4. How many terms of the A.P. must be taken for their sum to be equal to 120?

(a)

6

(b)

7

(c)

8

(d)

9

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

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

The values of a and b if 4x⁴ - 24x³ + 76x² + ax + b is a perfect square are

(a)

100, 120

(b)

10, 12

(c)

-120, 100

(d)

12, 10

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)

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

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

If in triangles ABC and EDF,\(\cfrac { AB }{ DE } =\cfrac { BC }{ FD } \) then they will be similar, when

(a)

\(\angle B=\angle E\)

(b)

\(\angle A=\angle D\)

(c)

\(\angle B=\angle D\)

(d)

\(\angle A=\angle F\)

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

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

(a)

one

(b)

two

(c)

infinite

(d)

zero

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)

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

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

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 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

A page is selected at random from a book. The probability that the digit at units place of the page number chosen is less than 7 is

(a)

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

(b)

\(\frac{7}{10}\)

(c)

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

(d)

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

The probability of getting a job for a person is \(\frac{x}{3}\). If the probability of not getting the job is \(\frac{2}{3}\)  then the value of x is

(a)

2

(b)

1

(c)

3

(d)

1.5