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

Let f(x) = \(\sqrt { 1+x^{ 2 } } \) then

(a)

f(xy) = f(x).f(y)

(b)

f(xy) ≥ f(x).f(y)

(c)

f(xy) ≤ f(x).f(y)

(d)

None of these

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

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)

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

A system of three linear equations in three variables is inconsistent if their planes

(a)

intersect only at a point

(b)

intersect in a line

(c)

coincides with each other

(d)

do not intersect

y² + \(\frac {1}{y^{2}}\) is not equal to

(a)

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

(b)

\({ \left( y+\frac { 1 }{ y } \right) }^{ 2 }\)

(c)

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

(d)

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

Graph of a linear equation is a ____________

(a)

straight line

(b)

circle

(c)

parabola

(d)

hyperbola

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 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

In figure CP and CQ are tangents to a circle with centre at O. ARB is another tangent touching the circle at R. If CP = 11 cm and BC = 7 cm, then the length of BR is

(a)

6 cm

(b)

5 cm

(c)

8 cm

(d)

4 cm

The slope of the line joining (12, 3), (4, a) is \(\frac 18\). The value of ‘a’ is

(a)

1

(b)

4

(c)

-5

(d)

2

(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\(\theta \) = 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

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 cylinder whose radius is \(\frac{1}{3}\)of its height is

(a)

\(\frac { 9\pi { h }^{ 2 } }{ 8 } \) sq.units

(b)

24\(\pi\)h² sq.units

(c)

\(\frac { 8\pi { h }^{ 2 } }{ 9 } \) sq.units

(d)

\(\frac { 56\pi { h }^{ 2 } }{ 9 } \) sq.units

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 volume (in cm³) of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is

(a)

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

(b)

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

(c)

\(5\pi\)

(d)

\(\frac{20}{3}\pi\)

If the standard deviation of x, y, z is p then the standard deviation of 3x + 5, 3y + 5, 3z + 5 is

(a)

3p + 5

(b)

3p

(c)

p + 5

(d)

9p + 15

The probability a red marble selected at random from a jar containing p red, q blue and r green marbles is

(a)

\(\frac { q }{ p+q+r } \)

(b)

\(\frac { p }{ p+q+r } \)

(c)

\(\frac { p+q }{ p+q+r } \)

(d)

\(\frac { p+r }{ p+q+r } \)

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)

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