Let f and g be two functions given by
f = {(0,1), (2,0), (3,-4), (4,2), (5,7)}
g = {(0,2), (1,0), (2,4), (-4,2), (7,0)} then the  range of f o g is

(a)

{0,2,3,4,5}

(b)

{–4,1,0,2,7}

(c)

{1,2,3,4,5}

(d)

{0,1,2}

The function t which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined Fahrenheit degree is 95, then the value of  C \(t(C)=\frac { 9c }{ 5 } +32\) is ___________

(a)

37

(b)

39

(c)

35

(d)

36

An A.P. consists of 31 terms. If its 16^th term is m, then the sum of all the terms of this A.P. is

(a)

16 m

(b)

62 m

(c)

31 m

(d)

\(\frac { 31 }{ 2 } \) m

The difference between the remainders when 6002 and 601 are divided by 6 is ____________

(a)

2

(b)

1

(c)

0

(d)

3

Sum of first n terms of the series \(\sqrt { 2 } +\sqrt { 8 } +\sqrt { 18 } +...\) is ____________

(a)

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

(b)

\(\sqrt { n } \)

(c)

\(\frac { n\left( n+1 \right) }{ \sqrt { 2 } } \)

(d)

1

The square root of \(\frac { 256{ x }^{ 8 }{ y }^{ 4 }{ z }^{ 10 } }{ 25{ x }^{ 6 }{ y }^{ 6 }{ z }^{ 6 } } \) is equal to

(a)

\(\frac { 16 }{ 5 } \left| \frac { { x }^{ 2 }{ z }^{ 4 } }{ { y }^{ 2 } } \right| \)

(b)

\(16\left| \frac { { y }^{ 2 } }{ { x }^{ 2 }{ z }^{ 4 } } \right| \)

(c)

\(\frac { 16 }{ 5 } \left| \frac { y }{ x{ z }^{ 2 } } \right| \)

(d)

\(\frac { 16 }{ 5 } \left| \frac { x{ z }^{ 2 } }{ y } \right| \)

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 \(\frac { p }{ q } =a\) then \(\frac { { p }^{ 2 }+{ q }^{ 2 } }{ { p }^{ 2 }-{ q }^{ 2 } } \) ___________

(a)

\(\frac { { a }^{ 2 }+1 }{ { a }^{ 2 }-1 } \)

(b)

\(\frac { 1+{ a }^{ 2 } }{ 1-{ a }^{ 2 } } \)

(c)

\(\frac { 1-{ a }^{ 2 } }{ 1-{ +a }^{ 2 } } \)

(d)

\(\frac { { a }^{ 2 }-1 }{ { a }^{ 2 }+1 } \)

If P and Q are matrices, then which of the following is true?

(a)

PQ ≠ QP

(b)

(P^T)^T ≠ P

(c)

P + Q ≠ Q + P

(d)

All are true

In figure if PR is tangent to the circle at P and O is the centre of the circle, then \(\angle PQR\) is

(a)

120^o

(b)

100°

(c)

110°

(d)

90°

In the given figure if OC = 9 cm and OB = 15 cm then OB + BD is equal to ____________

(a)

23 cm

(b)

24 cm

(c)

27 cm

(d)

30 cm

If A is a point on the Y axis whose ordinate is 8 and B is a point on the X axis whose abscissae is 5 then the equation of the line AB is

(a)

8x + 5y = 40

(b)

8x - 5y = 40

(c)

x = 8

(d)

y = 5

The four vertices of a quadrilateral 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

The y-intercept of the line 3x - 4y + 8 = 0 is ___________

(a)

\(-\frac { 8 }{ 3 } \)

(b)

\(\frac { 8 }{ 3 } \)

(c)

2

(d)

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

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

(a)

0

(b)

1

(c)

2

(d)

-1

If cos9∝ = sin∝ and 9∝ < 90^o, then the value of tan t∝ is

(a)

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

(b)

\({\sqrt{3}}\)

(c)

1

(d)

0

The maximum value of sin θ is ___________

(a)

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

(b)

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

(c)

1

(d)

\(\frac{1}{\sqrt2}\)

(sec A + tan A)(1 - sin A) is equal to ___________

(a)

sec A

(b)

sin A

(c)

cosec A

(d)

cos A

A ladder of length 14m just reaches the top of a wall. If the ladder makes an angle of 60^o with the horizontal, then the height of the wall is ____________

(a)

\(14\sqrt { 3 } \)

(b)

\(28\sqrt { 3 } \)

(c)

\(7\sqrt { 3 } \)

(d)

\(35\sqrt { 3 } \)

The height of a right circular cone whose radius is 5 cm and slant height is 13 cm will be

(a)

12 cm

(b)

10 cm

(c)

13 cm

(d)

5 cm

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)

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

The radius of a wire is decreased to one-third of the original. If volume the same, then the length will be increased _______of the original.

(a)

3 times

(b)

6 times

(c)

9 times

(d)

27 times

Which of the following is incorrect?

(a)

P(A) > 1

(b)

0 ≤ P(A) ≤ 1

(c)

P(ф) = 0

(d)

P(A) + P(\(\bar { A } \)) = 1

The mean of a observation x₁, x₂, x₃, ......... x_n is \(\bar { x } \). If each observation is multiplied by p, there the mean of the new observations is ___________

(a)

\(\frac { \bar { x } }{ p } \)

(b)

p\(\bar { x } \)

(c)

\(\bar { x } \)

(d)

P+\(\bar { x } \)

In a competition containing two events A and B, the probability of winning the events A and B are \(\frac { 1 }{ 3 } \) and \(\frac { 1 }{ 4 } \) respectively and the probability if winning both events is ___________

(a)

\(\frac { 1 }{ 12 } \)

(b)

\(\frac { 5 }{ 12 } \)

(c)

\(\frac { 1 }{ 12 } \)

(d)

\(\frac { 7 }{ 12 } \)