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 \(f(x)=\frac { 1 }{ x } \), and \(g(x)=\frac { 1 }{ { x }^{ 3 } } \) then f o g o(y), is ________

(a)

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

(b)

\(\frac { 1 }{ { y }^{ 6 } } \)

(c)

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

(d)

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

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

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

(a)

2

(b)

1

(c)

0

(d)

3

A boy saves Rs. 1 on the first day Rs. 2 on the second day, Rs. 4 on the third day and so on. How much did the boy will save upto 20 days?

(a)

2¹⁹ + 1

(b)

2¹⁹- 1

(c)

2²⁰- 1

(d)

2²¹- 1

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

Transpose of a column matrix is

(a)

unit matrix

(b)

diagonal matrix

(c)

column matrix

(d)

row matrix

For what set of values \(\frac { { x }^{ 2 }+5x+6 }{ { x }^{ 2 }+8x+15 } \) is undefined ___________

(a)

-3, -5

(b)

-5

(c)

-2, -3, -5

(d)

-2, -3

The parabola y = -3x² is ___________

(a)

Open upward

(b)

Open downward

(c)

Open rightward

(d)

Open leftward

The two tangents from an external points P to a circle with centre at O are PA and PB. If \(\angle APB\) = 70^o then the value of \(\angle AOB\) is

(a)

100°

(b)

110°

(c)

120°

(d)

130°

The ratio of the areas of two similar triangles is equal to ____________

(a)

The ratio of their corresponding sides

(b)

The cube of the ratio of their corresponding sides

(c)

The ratio of their corresponding attitudes

(d)

The square of the ratio of their corresponding sides

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

(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

Find the ratio in which the line segment joining the points (-3, 10) and (6,-8) is internally divided by (-1, 6) ____________

(a)

7:2

(b)

3:4

(c)

2:7

(d)

5:3

Find the equation of the line passing through the point (0, 4) and is parallel to 3x+5y+15 = 0 the line is ___________

(a)

3x+5y+15 = 0

(b)

3x+5y-20 = 0

(c)

2x+7y-20 = 0

(d)

4x+3y-15 = 0

If the ratio of the height of a tower and the length of its shadow is \(\sqrt{3}: 1\), then the angle of elevation of the sun has measure

(a)

45°

(b)

30°

(c)

90°

(d)

60°

If (sin α + cosec α)² + (cos α + sec α)² = k + tan²α + cot²α, then the value of k is equal to

(a)

9

(b)

7

(c)

5

(d)

3

The value of (tan1^o tan2^o tan3^o..... tan89^o) is ___________

(a)

0

(b)

1

(c)

2

(d)

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

The maximum value of sin θ is ___________

(a)

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

(b)

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

(c)

1

(d)

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

A spherical ball of radius r₁ units is melted to make 8 new identical balls each of radius r₂ units. Then r₁:r₂ is

(a)

2:1

(b)

1:2

(c)

4:1

(d)

1:4

The height of a cone is 60 cm. A small cone is cut off at the top by plane parallel to the base and its volume is \(\left[ \frac { 1 }{ 64 } \right] ^{ th }\) the volume of the original cone. Then the height of the smaller cone is ___________

(a)

45 cm

(b)

30 cm

(c)

15 cm

(d)

20 cm

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)

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

The mean of first first 10 odd natural number is ___________

(a)

5

(b)

10

(c)

20

(d)

19

A number x is chosen at random from -4, -3, -2, -1, 0, 1, 2, 3, 4. The probability that \(\left| x \right| \le 3\) is ___________

(a)

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

(b)

\(\frac { 4 }{ 9 } \)

(c)

\(\frac { 1 }{ 9 } \)

(d)

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