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

If f(x) = mx + n, when m and n are integers f(-2) = 7, and f(3) = 2 then m and n are equal to ___________

(a)

-1, -5

(b)

1, -9

(c)

-1, 5

(d)

1, 9

The first term of an arithmetic progression is unity and the common difference is 4. Which of the following will be a term of this A.P.

(a)

4551

(b)

10091

(c)

7881

(d)

13531

What is the HCF of the least prime and the least composite number?

(a)

1

(b)

2

(c)

3

(d)

4

Sum of infinite terms of G.P is 12 and the first term is 8. What is the fourth term of the G.P?

(a)

\(\frac { 8 }{ 27 } \)

(b)

\(\frac { 4 }{ 27 } \)

(c)

\(\frac { 8 }{ 20 } \)

(d)

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

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

(a)

4x²

(b)

16x²

(c)

8x²

(d)

-8x²

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

The HCF of two polynomials p(x) and q(x) is 2x(x + 2) and LCM is 24x(x + 2)² (x - 2) if p(x) = 8x³ + 32x² + 32x, then q(x) ___________

(a)

4x³-16x

(b)

6x³-24x

(c)

12x³+24x

(d)

12x³-24x

Choose the correct answer
(i) Every scalar matrix is an identity matrix
(ii) Every identity matrix is a scalar matrix
(iii) Every diagonal matrix is an identity matrix
(iv) Every null matrix is a scalar matrix

(a)

(i) and (iii) only

(b)

(iii) only

(c)

(iv) only

(d)

(ii) and (iv) only

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

S and T are points on sides PQ and PR respectively of \(\Delta PQR\) If PS = 3cm, AQ = 6 cm, PT = 5 cm, and TR = 10 cm and then QR

(a)

4 ST

(b)

5 ST

(c)

3 ST

(d)

3 QR

Two concentric circles if radii a and b where a>b are given. The length of the chord of the circle which touches the smaller circle is ____________

(a)

\(\sqrt { { a }^{ 2 }-{ b }^{ 2 } } \)

(b)

\(\sqrt { { a }^{ 2 }-{ b }^{ 2 } } \)

(c)

\(\sqrt { { a }^{ 2 }+{ b }^{ 2 } } \)

(d)

\(2\sqrt { { a }^{ 2 }+{ b }^{ 2 } } \)

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)

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

Find the slope of the line 2y = x + 8 ____________

(a)

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

(b)

1

(c)

8

(d)

2

A tower is 60 m height. Its shadow is x metres shorter when the sun’s altitude is 45° than when it has been 30°, then x is equal to

(a)

41.92 m

(b)

43.92 m

(c)

43 m

(d)

45.6 m

If ∆ABC is right angled at C, then the value of cos (A + B) is ___________

(a)

0

(b)

1

(c)

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

(d)

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

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

(a)

sec A

(b)

sin A

(c)

cosec A

(d)

cos A

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

A cylinder 10 cone and have there are of a equal base and have the same height. what is the ratio of there volumes?

(a)

3:1:2

(b)

3:2:1

(c)

1:2:3

(d)

1:3:2

A spherical steel ball is melted to make 8 new identical balls. Then the radius each new ball is how much times the radius of the original ball?

(a)

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

(b)

\(\frac { 1 }{ 4 } \)

(c)

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

(d)

\(\frac { 1 }{ 8 } \)

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

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)

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

If the co-efficient of variation and standard deviation of a data are 35% and 7.7 respectively then the mean is ___________

(a)

20

(b)

30

(c)

25

(d)

22