Q. Find the equation of a line making an angle of ${60}^{\circ }$ with the positive direction of $X$-axis and having a $y$-intercept $3$ units

Q. Find the area of the triangles (in sq. units) formed by the points $(-2,3),(7,5)$ and $(3,-5)$.

Q. The Mean and Median of a Uni-modal grouped data are $36.5$ and $38.5$ respectively. Find the Mode of the data.

Q. Prove that $\frac{\tan \theta +\sec \theta -1}{\tan \theta -\sec \theta +1}=\frac{1+\sin \theta }{\cos \theta }$

Q. List the essential components of a Computer

Q. Sum of the Binomial coefficients of the expansion of ${(\frac{x}{y}+\frac{y}{x})}^4$ is

1. $6$
2. $16$
3. $4$
4. $32$

Q. Find the ratio in which $P(3,0)$ divides the joint of $A(1,a)$ and $B(7,-4)$. And also find the value of $a$.

Q. If $f\left(x\right)=x^2+4x-12$, what are the zeros of $f$?

1. $\{-3,-2\}$
2. $\{-6,2\}$
3. $\{3,2\}$
4. $\{6,2\}$

Q. The point which satisfies the inequation $3x+y>6$ is .........

1. $(2,1)$
2. $(-1,0)$
3. $(1,3)$
4. $(-2,1)$

Q. Find the matrix $X$, given that $X+2I=\left[\begin{array}{cc}3& -1\\ 1& 2\end{array}\right]$

Q. State the converse of Pythagorean Theorem.

Q. Find the mean for the following distribution table, using Deviation method.

Class Interval	$0-9$	$10-19$	$20-29$	$30-39$	$40-49$	$50-50$	$60-60$
Frequency	$8$	$10$	$22$	$26$	$18$	$9$	$7$

Q. Find the equation of the line which passes through the point $(1,-6)$ and whose product of the intercepts on the co-ordinate axes is one

Q. Solve the following equations using Matrix Inversion method.
$2x-3y+6=0$ and $6x+y+8=0$

Q. If $n\left(A\right)=6,n\left(B\right)=8$ and $n(A\cup B)=12$, then $n(A\cap B)=$

1. $2$
2. $6$
3. $12$
4. $8$

Q. Construct a triangle $ABC$, in which $BC=7cm,\angle A={70}^{\circ }$ and foot of the perpendicular $D$ on $BC$ from $A$ is $4.5cm$ away from $B$

Q. ${\left(x^{\frac{2}{3}}\right)}^p=x^2$, then find $p$.

Q. In what ratio, does $P(4,6)$ divide the join of $A(-2,3)$ and $B(6,7)$

Q. Write the conditions that are required for "Two polygons to be similar to each other".

Q. If the roots of an equation $p{x}^2+qx+r=0$ are equal, then

1. $q^2=4pr$
2. $p^2=4qr$
3. $q^2=pr$
4. $p=qr$

Q. If $A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ and $I=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$, then show that $A^2-(a+d)A=(bc-ad)I$

Q. Find the value of ${\sin }^2{30}^{\circ }+{\cos }^2{60}^{\circ }$

Q. $\sim [p\wedge (\sim q\left)\right]=$

1. $\sim p\wedge \sim q$
2. $\sim p\vee \sim q$
3. $\sim p\vee q$
4. $\sim p\wedge q$

Q. The upper part of a tree, broken by wind in two parts, makes an angle of ${30}^{\circ }$ with the ground. The top of the tree touches the ground at a distance of $20\text{m}$ from the foot of the tree. Find the height of the tree before it was broken

Q. The sum of $15$ observations of a data is $420$. Find the Mean

Q. In what ratio, does $P(4,6)$ divide the join of $A(-2,3)$ and $B(6,7)$

1. $1:2$
2. $4:1$
3. $3:1$
4. $2:1$

Q. Show that $\sqrt{\frac{1+\cos \theta }{1-\cos \theta }}=\text{cosec}\theta +\cot \theta$

Q. If $A=\left[\begin{array}{cc}1& 4\\ 2& 1\end{array}\right],B=\left[\begin{array}{cc}-3& 2\\ 4& 0\end{array}\right],C=\left[\begin{array}{cc}1& 0\\ 0& 2\end{array}\right]$; find $A^2+BC$

Q. If $(a+b,1)=(5,a-b)$, then the value of $2a+3b=$?

1. $6$
2. $12$
3. $8$
4. $5$

Q. If $x^2-5x+4<0$, then $x$ lies between

1. $1$ and $5$
2. $2$ and $5$
3. $2$ and $3$
4. $1$ and $4$