If {(a, 8 ),(6, b)}represents an identity function, then the value of a and b are respectively

(a)

(8,6)

(b)

(8,8)

(c)

(6,8)

(d)

(6,6)

\((x-\frac { 1 }{ x } )={ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } \) then f(x) =

(a)

x² + 2

(b)

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

(c)

x²- 2

(d)

\({ x }^{ 2 }-\frac { 1 }{ { x }^{ 2 } } \)

If \(f(x)=\frac { x+1 }{ x-2 } ,g(x)=\frac { 1+2x }{ x-1 } \) then fog(x) is ___________

(a)

Constant function

(b)

Quadratic function

(c)

Cubic function

(d)

Identify function

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

Given a₁ = -1, \(a=\frac { { a }_{ n } }{ n+2 } \), then a₄ is ____________

(a)

\(-\frac { 1 }{ 20 } \)

(b)

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

(c)

\(-\frac { 1 }{ 840 } \)

(d)

\(-\frac { 1 }{ 120 } \)

If p, q, r, x, y, z are in A.P, then 5p + 3, 5r + 3, 5x + 3, 5y + 3, 5z + 3 form ____________

(a)

a G.P

(b)

an A.P

(c)

a constant sequence

(d)

neither an A.P nor a G.P

The solution of (2x - 1)² = 9 is equal to

(a)

-1

(b)

2

(c)

-1, 2

(d)

None of these

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

The parabola y = -3x² is ___________

(a)

Open upward

(b)

Open downward

(c)

Open rightward

(d)

Open leftward

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°

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

If slope of the line PQ is \(\frac { 1 }{ \sqrt { 3 } } \) then slope of the perpendicular bisector of PQ is

(a)

\(\sqrt { 3 } \)

(b)

\(-\sqrt { 3 } \)

(c)

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

(d)

0

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

If sin \(\theta \) = cos \(\theta \), then 2 tan² \(\theta \) + sin² \(\theta \) -1 is equal to 

(a)

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

(b)

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

(c)

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

(d)

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

The angle of depression of the top and bottom of 20 m tall building from the top of a multistoried building are 30° and 60° respectively. The height of the multistoried building and the distance between two buildings (in metres) is

(a)

20, 10\(\sqrt { 3 } \)

(b)

30, 5\(\sqrt { 3 } \)

(c)

20, 10

(d)

30, 10\(\sqrt { 3 } \)

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

(a)

0

(b)

1

(c)

2

(d)

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

9 sec²A  - 9tan²A = ___________

(a)

1

(b)

9

(c)

8

(d)

0

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

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

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)

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