Q. Select the correct option.
If one of the zeroes of the quadratic polynomial $x^2+3x+k$ is $2$, then the value of $k$ is

1. $10$
2. $-10$
3. $-7$
4. $-2$

Q. Select the correct option.
The total number of factors of a prime number is

1. $1$
2. $0$
3. $2$
4. $3$

Q. Select the correct option. The quadratic polynomial, the sum of whose zeroes is −5 and their product is 6, is

1. $x^2+5x+6$
2. $x^2-5x+6$
3. $x^2-5x-6$
4. $-x^2+5x+6$

Q. Select the correct option.
The value of $k$ for which the system of equations $x+y-4=0$ and $2x+ky=3$, has no solution, is

1. $-2$
2. $\ne 2$
3. $3$
4. $2$

Q. Select the correct option.
The HCF and the LCM of $12,21,15$ respectively are

1. $3,140$
2. $12,420$
3. $3,420$
4. $420,3$

Q. Select the correct option.
The value of $x$ for which $2x,(x+10)$ and $(3x+2)$ are the three consecutive terms of an AP, is

1. $6$
2. $-6$
3. $18$
4. $-18$

Q. Select the correct option.
The first term of an $AP$ is $p$ and the common difference is $q$, then its ${10}^{th}$ term is

1. $q+9p$
2. $p-9q$
3. $p+9q$
4. $2p+9q$

Q. Select the correct option.
The distance between the points $(a\cos \theta +b\sin \theta ,0)$ and $(0,a\sin \theta -b\cos \theta )$, is

1. $a^2+b^2$
2. $a^2-b^2$
3. $\sqrt{a^2+b^2}$
4. $\sqrt{a^2-b^2}$

Q. Select the correct option.
If the point $P(k,0)$ divides the line segment joining the points $A(2,-2)$ and $B(-7,4)$ in the ratio $1:2$, then the value of k is

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

Q. Select the correct option.
The value of $p$, for which the points $A(3,1),B(5,p)$ and $C(7,-5)$ are collinear, is

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

Q. Fill in the blank.
In fig., $\Delta ABC$ is circumscribing a circle, the length of $BC$ is ________ cm.

Q. Divide the polynomial $f\left(x\right)=3x^2-x^3-3x+5$ by the polynomial $g\left(x\right)=x-1-x^2$ and verify the division algorithm.

Q. In $DE||AC$ and $DC||AP$. Prove that $\frac{BE}{EC}=\frac{BC}{CP}$

Q. Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are given by $2y-x=8,5y-x=14$ and $y-2x=1$.

Q. Fill in the blank.
Given $\Delta ABC\sim \Delta PQR$, if $\frac{AB}{PQ}=\frac{1}{3},$ then $\frac{ar\left(\Delta ABC\right)}{ar\left(\Delta PQR\right)}=$______ .

Q. If $4$ is a zero of the cubic polynomial $x^3-3x^2-10x+24$, find its other two zeros.

Q. Fill in the blank.
$ABC$ is an equilateral triangle of side $2a$, then length of one of its altitude is ______ .

Q. The rod $AC$ of a TV disc antenna is fixed at right angles to the wall $AB$ and a rod $CD$ is supporting the disc as shown in Fig. 1. If $AC=1.5m$ long and $CD=3m$, Find
(i) $\tan \theta$
(ii) $\sec \theta +cosec\theta$

Q. Fill in the blank.
$\frac{\cos {80}^{\circ }}{\sin {10}^{\circ }}+\cos {59}^{\circ }cosec{31}^{\circ }=$ ______

Q. Fill in the blank.
The value of $({\sin }^2\theta +\frac{1}{1+{\tan }^2\theta })=$______ .

Q. A piece of wire $22$ cm long is bent into the form of an arc of a circle subtending an angle of ${60}^0$ at its center. Find the radius of the circle $[Use\pi =\frac{22}{7}]$

Q. Fill in the blank.
The value of $(1+{\tan }^2\theta )(1-\sin \theta )(1+\sin \theta )=$ ______ .

Q. Find the area of triangle $PQR$ formed by the points $P(-5,7),Q(-4,-5)$ and $R(4,5)$

Q. If a number $x$ is chosen at random from the numbers $-3,-2,-1,0,1,2,3$. What is probability that $x^2\le 4$?

Q. The ratio of the length of a vertical rod and the length of its shadow is $1:\sqrt{3}$ . Find the angle of elevation of the sun at that moment ?

Q. Find the mean of the following distribution:

Class:	$3-5$	$5-7$	$7-9$	$9-11$	$11-13$
Frequency:	$5$	$10$	$10$	$7$	$8$

Q. Two cones have their heights in the ratio $1:3$ and radii in the ratio $3:1$. What is the ratio of their volumes ?

Q. If the point $C(-1,2)$ divides internally the line segment joining $A(2,5)$ and $B(x,y)$ in the ratio
3 : 4. find the coordinates of $B$.

Q. Find the mode of the following data:

Class:	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$	$100-120$	$120-140$
Frequency:	$6$	$8$	$10$	$12$	$6$	$5$	$3$

Q. A letter of English alphabet is chosen at random. What is the probability that the chosen letter is a consonant.