Q. If $f\left(x\right)=x^2-4$, find $f\left(4\right)$.

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

Q. Rationalise the denominator and simplify:
$\frac{\sqrt{6}+\sqrt{3}}{\sqrt{6}-\sqrt{3}}$

Q. In the given figure, find the values of $\cos \theta$ and $\tan \theta$

Q. Express $210$ as the product of prime factors.

Q. Find the number of sides of a polygon having $35$ diagonals.

Q. In a class of $100$ students, $55$ students have passed in physics and $67$ students have passed in Mathematics. Find the number of students passed in Physics only.

Q. The harmonic mean between $2$ and $4$ is

1. $\frac{8}{3}$
2. $\frac{6}{8}$
3. $\frac{3}{8}$
4. $\frac{8}{6}$

Q. In how many ways $4$-digits numbers can be formed using the digits $1,2,3,7,8,9$ without repetition? How many of these are even numbers?

Q. What must be added to the polynomial $P\left(x\right)=x^4+2x^3-2x^2+x-1$. So that the resulting polynomial is exactly divisible by $x^2+2x-3$?

1. $x+2$
2. $x-2$
3. $x-1$
4. $x+1$

Q. Two dice are thrown simultaneously. Find the probability of getting
(a) same number on both faces and
(b) both faces having multiples of five.

Q. Find the product of $\sqrt{2}$ and $\sqrt[3]{35}$.

Q. The slope of the line joining the point $(3,2)$ and $(4,5)$ is

1. $3$
2. $1$
3. $7$
4. $\frac{3}{7}$

Q. Solve the equation by using formula: $x^2-4x+2=0$.

Q. In the figure, $BC$ is the diameter. What is the measure of $x$?

Q. A conical flask is full of water. The flask has base radius $3cm$ and height $15cm$. The water is poured into cylindrical glass tube of uniform inner radius $1.5cm$ placed vertically and closed at lower end. Find the height of water in the glass tube.

Q. The value of ${\tan }^2{60}^{\circ }$ is

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

Q. Calculate variance for the following data: $2,4,6,8$ and $10$.

Q. The distance between the points $(2,3)$ and $(6,6)$ is

1. $5$ units
2. $3$ units
3. $7$ units
4. $4$ units

Q. Solve the given equation by the method of Completion of Squares: $x^2+4x+4=0$?

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

Q. Mean and standard deviation of runs scored by a cricket player are $80$ and $4$ respectively. Find the coefficient of variation.

Q. The given pie-chart shows annual agriculture yield of certain place. If the total production is $8100$ tons, then the yield of Ragi in tons is

1. $225$
2. $2250$
3. $22.5$
4. $2.250$

Q. $A$ and $B$ are the two subsets of Universal Set $U$ such that $n\left(U\right)=700,n\left(A\right)=200,n\left(B\right)=300$ and $n(A\cap B)=100$. Find $n(A^{\prime }\cap B^{\prime })$

Q. Draw a plan of a level ground using the given information:

	Metre To $D$
To $E$ $60$	$150$ $100$ $80$ $40$	$80$ to $C$ $40$ to $B$
	from $A$

Q. The probability of winning a game is $\frac{5}{6}$. Then the probability of losing it is.

1. $-\frac{5}{6}$
2. $\frac{5}{6}$
3. $-\frac{1}{6}$
4. $\frac{1}{6}$

Q. If $A=\{1,2,3,4\}$ and $B=\left\{1\right\}$, find $A\setminus B$.

Q. Find the perimeter of a triangle whose vertices have the coordinates $(3,10),(5,2)$ and $(14,12)$.

Q. In $△ABC,XY\parallel BC,\frac{AY}{CY}=\frac{1}{2}$ and $AX=4$. Find $BX$.

Q. Draw a circle of radius $3cm$ and construct two tangents to it from an external point $8cm$ away from its centre.

Q. Find the value of $a$ if $(x-5)$ is a factor of $(x^3-3x^2+ax-10)$.