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

Let f(x) = x² - x, then f(x- 1) - (x + 1) is ___________

(a)

4x

(b)

2-2x

(c)

2-4x

(d)

4x-2

If f(x) + f(1 - x) = 2 then \(f\left( \frac { 1 }{ 2 } \right) \) is ___________

(a)

5

(b)

-1

(c)

-9

(d)

1

Given F₁ = 1, F₂ = 3 and F_n = F_n-1 + F_n-2 then F₅ is

(a)

3

(b)

5

(c)

8

(d)

11

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

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

If the roots of the equation q²x² + p²x + r² = 0 are the squares of the roots of the equation qx² + px + r = 0, then q, p, r are in __________.

(a)

A.P

(b)

G.P

(c)

Both A.P and G.P

(d)

none of these

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)

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

The product of the sum and product of roots of equation (a²-b²)x²-(a+b)²x+(a³-b³) = 0 is ___________

(a)

\(\frac { { a }^{ 2 }+ab+{ b }^{ 2 } }{ (a-b) } \)

(b)

\(\frac { a-b }{ a+b } \)

(c)

\(\frac { a-b }{ a+b } \)

(d)

\(\frac { a-b }{ { a }^{ 2 }+ab+{ b }^{ 2 } } \)

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

(a)

one

(b)

two

(c)

infinite

(d)

zero

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 theri corresponding sides

(c)

The ratio of theri corresponding attitudes

(d)

The square of the ratio of their corresponding sides

The slope of the line which is perpendicular to a line joining the points (0, 0) and (– 8, 8) is

(a)

–1

(b)

1

(c)

\(\frac13\)

(d)

-8

The four vertices of a quardrilateral 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

If 5x = sec\(\theta \) and \(\frac { 5 }{ x } \) = tan\(\theta \), then x² - \(\frac { 1 }{ { x }^{ 2 } } \) is equal to 

(a)

25

(b)

\(\frac { 1 }{ 25 } \)

(c)

5

(d)

1

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

If cos (∝ - β) =, then sin (∝ - β)  can be reduced to ___________

(a)

cos β

(b)

cos 2β

(c)

sin ∝

(d)

sin 2∝

If a sin (90 - θ) of (90^o - θ) = cos(90^o - θ)tan equal to ___________

(a)

0

(b)

1

(c)

-1

(d)

2

The value of \(\cfrac { 3 }{ cot^{ 2 }\theta } -\cfrac { 3 }{ { cos }^{ 2 }\theta } \) is equal to ___________

(a)

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

(b)

3

(c)

0

(d)

-3

If the radius of the base of a cone is tripled and the height is doubled then the volume is

(a)

made 6 times

(b)

made 18 times

(c)

made 12 times

(d)

unchanged

A solid is hemispherical at the bottom and conical above. If the curved surface areas of the two parts are equal, then the ratio of its radius and the height of its conical part is ___________

(a)

1:3

(b)

\(1:\sqrt { 3 } \)

(c)

1:1

(d)

\(\sqrt { 3 } :1\)

Which of the following is not a measure of dispersion?

(a)

Range

(b)

Standard deviation

(c)

Arithmetic mean

(d)

Variance

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)

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

The standard deviation is the ____ of variance 

(a)

cube

(b)

square

(c)

square root

(d)

cube root

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)

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