Q. If A is an event in a random experiment such that P(A) : P($\overline{A}$) = 5 : 11, then find P (A) and P ($\overline{A}$).

Q. State the Pythagoras theorem.

Q. Find the value of n if ${}^n{P}_4=5{(}^n{P}_3)$.

Q. Prove that $5\sqrt{3}$ is an irrational number.

Q. The volume of a right circular cylinder whose circular base area is $154sq.cm$ and height $10cm$ is

1. $2210c.c.$
2. $15400c.c.$
3. $770c.c.$
4. $1540c.c.$

Q. Write the general form of a quadratic polynomial.

Q. Given A $=\{1,2,3,4\}$, B $=\{3,4,5,6\}$ and C $=\{6,7\}$. Verify that (A $\cap$ B) $\cap$ C = A $\cap$ (B $\cap$ C).

Q. The sum and product of the roots of the equation $x^2+2x+1=0$ are respectively,

1. $2$ and $-1$
2. $-2$ and $-1$
3. $-2$ and $1$
4. $1$ and $2$

Q. Write the relation between standard deviation of a set of scores and its variance.

Q. In a sequence if $T_n=n^2+4$ then find $T_2$.

Q. Draw a circle of radius 3.5 cm and construct a chord of length 6 cm in it. Measure and write the distance between the centre and the chord.

Q. What are like surds and unlike surds? Identify and write the set of like surds in the following groups:
a) { $\sqrt{8},\sqrt{12},\sqrt{20},\sqrt{54}$ }
b) { $\sqrt{50},\sqrt[3]{354},\sqrt[4]{432}$ }
c) {$\sqrt{8},\sqrt{18},\sqrt{32},\sqrt{50}$}.

Q. Rationalise the denominator and simplify:
$\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$

Q. Area of an equilateral triangle is given by $A=\frac{\sqrt{3}{a}^2}{4}$ where A is the area and $a$ is the side. Find the perimeter of the triangle if $A=16\sqrt{3}$ sq.cm.

Q. Find the co-ordinates of the mid-point of the line joining the points $(2,3)$ and $(4,7)$.

Q. Show that the roots of the equation $x^2-2x+3=0$ are imaginary.

Q. If $\tan \theta =\frac{1}{\sqrt{3}}$ and $\cos \theta =\frac{\sqrt{3}}{2}$ then the value of $\sin \theta$ is

1. $\sqrt{3}$
2. $\frac{1}{2}$
3. $\frac{2}{\sqrt{3}}$
4. $\frac{3}{2}$

Q. Draw a plan of a level ground using the information given below:
[Scale:20 metres = 1 cm]

	To D (in metres)
80 to E	150 100 80 30	70 to C 40 to B
	From A

Q. Find the slope of the line joining the points $(4,-8)$ and $(5,-2)$.

Q. $(7\times 11\times 13+13)$ is a/an

1. Composite number
2. Prime number
3. Irrational number
4. Imaginary number.

Q. A fair coin is tossed once. Find the probability that head occurs.

Q. In $△$XYZ, P is any point on XY and PQ $\perp$ XZ. If XP $=4$ cm, XY $=16$ cm and XZ $=24$ cm, find XQ.

Q. Lateral surface area of the frustum of a cone is

1. $\pi (r_1+r_2)h$
2. $\pi (r_2-r_1)h$
3. $\pi (r_1-r_2)l$
4. $\pi (r_1+r_2)l$

Q. The sum of an infinite geometric series whose first term is a and common ratio is r is given by

1. $S_{\infty }=\frac{a}{1-r}$
2. $S_{\infty }=\frac{1-r}{a}$
3. $S_{\infty }=\frac{1}{r-a}$
4. $S_{\infty }=\frac{1}{a-r}$

Q. Show that $\frac{1-ta{n}^{2}A}{1+ta{n}^{2}A}=2co{s}^{2}A-1$

Q. Arithmetic mean between two numbers is 5 and Geometric mean between them is 4. Find the Harmonic mean between the numbers.
And in a harmonic progression third term and fifth terms are respectively 1 and $\frac{1}{-5}$. Find the tenth term.

Q. If a polynomial $p\left(x\right)=x^2-4$ is divided by a linear polynomial $(x-2)$ then the remainder is

1. $2$
2. $0$
3. $-2$
4. $-8$

Q. A polynomial p(x) is divided by (2x - 1). The quotient and remainder obtained are $(7x^2+x+5)$ and 4 respectively. Find p(x).
OR
Find the quotient and remainder using synthetic division.
$(3x^3-2x^2+7x-5)÷(x+3)$.

Q. In a circle the angle between a radius and a tangent at non-centre end of the radius is

1. ${90}^o$
2. ${180}^o$
3. ${45}^o$
4. ${360}^o$

Q. If $U=\{1,2,3,4,5,6\}$ and $A=\{2,3,4,5\}$ then find $A^{\prime }$.