Q. The probability that you will get $101$ marks in the paper which is in your hand is ___________.

Q. If $a+\sqrt{b}=\sqrt{c}$ where $a\in Q$ and $\sqrt{b}$ and $\sqrt{c}$ are surds, then __________.

1. $a=0$ and $b=c$
2. $a=c$ and $b=0$
3. $a=b$ and $b=c$
4. $a=0$ and $b=0$

Q. $\sqrt{10+\sqrt{64}}=\sqrt{a+2\sqrt{b}}$ then for $a$ and $b$ __________.

1. $a=10$ and $b=64$
2. $a=64$ and $b=10$
3. $a=10$ and $b=16$
4. $a=8$ and $b=2$

Q. The graph of $p\left(x\right)=x^2+4x+5$ is drawn below. From this real zeros is/are __________.

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

Q. If $\alpha ,\beta$ and $\gamma$ are the zeros of cubic polynomial $p\left(x\right)=x^3+5x^2+6x$ then $\alpha \beta \gamma =$ ________.

1. $-7$
2. $7$
3. $6$
4. $0$

Q. $a=3,b=5,c=7,d=11$. Then standard cubic polynomial is _________ from given values of $a,b,c$ and $d$.

1. $3x^3+5x^2-7x-11$
2. $3x^3-5x^2+7x+11$
3. $3x^3+5x^2-7x+11$
4. $3x^3+5x^2+7x+11$

Q. If $\alpha ,\beta$ and $\gamma$ are the zeros of cubic polynomial $p\left(x\right)=a{x}^3+b{x}^2+cx+d,a\ne 0$ then sum of zeroes $\alpha +\beta +\gamma =$ _________.

1. $\frac{c}{a}$
2. $\frac{-b}{a}$
3. $\frac{b}{a}$
4. $\frac{c}{-a}$

Q. Two lines are shown in the following graph
From the above graph, what is true for their solution set from the alternative given below ?

1. Their solution set is infinite set
2. Number of solutions cannot be known without knowing the mathematical equations of lines
3. Pair of equations has unique solution
4. They have no solution

Q. In a two-digit number, the digit in ones place is $x$ and the digit in tens place is $y$. Then double of that number is ___________.

1. $10x+2y$
2. $20y+2x$
3. $2y+20x$
4. $2x+10y$

Q. The perimeter of a rectangle given in the figure is $36\text{cm}$. Then its area is __________.

1. $12{\text{cm}}^2$
2. $24{\text{cm}}^2$
3. $72{\text{cm}}^2$
4. $36{\text{cm}}^2$

Q. A quadratic equation has two equal roots, if __________.

1. $D<0$
2. $D>0$
3. $D=0$
4. $D$ is non-zero perfect square

Q. The formula to find the third term of a given equation $x^2-8x+15=0$ to make it perfect square is _________ .

1. $\pm 2\sqrt{\text{First term}}\times \sqrt{\text{Last term}}$
2. $\frac{({\text{Middle term)}}^2}{64\times \text{First term}}$
3. $\frac{({\text{Middle term)}}^2}{64\times \text{Last term}}$
4. $\frac{({\text{Last term)}}^2}{64\times \text{First term}}$

Q. The product of the roots of equation $x^2-3x=10$ is __________.

1. $-10$
2. $-15$
3. $-30$
4. $-5$

Q. If $17x+29y=63$ and $29x+17y=75$ then $(y-x{)}^2=$ __________.

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

Q. In the following figure, the number of dots upto a given row is the number of triangles. The dots form a triangle. Then the number of triangles upto ${12}^{th}$ row is __________.

1. $78$
2. $68$
3. $12$
4. $24$

Q. Here, an A.P., $-11,-15,-19,-23$ , ------ is given. Then common difference is __________.

1. $-4$
2. $18$
3. $-18$
4. $-7$

Q. If $S_m=n$ and $S_n=m$ then $S_{m+n}=$ __________.

1. $-(m+n)$
2. $0$
3. $m+n$
4. $2m-2n$

Q. In the following figure, $BD:DC=3:4$ and $AB=7.5$ then $AC=$ ___________.

1. $5$
2. $10$
3. $-10$
4. $7.5$

Q. In $\Delta PQR$ , corresponding $PQR\leftrightarrow RQP$ is a similarity. Then _________ of the following is true.

1. $\angle P\cong \angle Q$
2. $\angle P\cong \angle R$
3. $\angle Q\cong \angle R$
4. $\angle P\cong \angle Q\cong \angle R$

Q. The line segment adjacent to $\overline{AB}$ in the following figure is __________.

1. $\overline{BD}$
2. $\overline{CD}$
3. $\overline{AC}$
4. $\overline{AD}$

Q. In $△ABC,AB=BC=AC=4$. Then its length of altitude is ___________.

1. $6$
2. $4$
3. $3\sqrt{3}$
4. $2\sqrt{3}$

Q. In $△ABC,m\angle A:m\angle B:m\angle C=1:2:3$. If $AB=15$ then $BC=$ _________.

1. $\frac{15\sqrt{3}}{2}$
2. $17$
3. $8$
4. $7.5$

Q. The coordinates of the midpoint of a line segment whose end points are $P(x_1,y_1)$ and $Q(x_2,y_2)$ are __________.

1. $[\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}]$
2. $[\frac{x_1+y_2}{2},\frac{x_2+y_2}{2}]$
3. $[\frac{y_1+y_2}{2},\frac{x_1+y_1}{2}]$
4. $[\frac{x_1+x_2+y_1+y_2}{2},\frac{x_1-x_2-y_1-y_2}{2}]$

Q. If $P$ in the interior of $△ABC$ then $APB+BPC=$ __________.

1. $ABC-BPC$
2. $BPC-ABC$
3. $ABC-CPA$
4. $ABC+BPC$

Q. Circumcircle of $△ABC$ is given in figure. If $m\angle PAC=30$ then $m\angle APC=$ __________.

1. ${120}^o$
2. ${60}^o$
3. ${90}^o$
4. ${40}^o$

Q. The coordinates of the point which divides $\overline{AB}$ joining $A(x_1,y_1)$ and $B(x_2,y_2)$ in the ratio $\lambda :1$ __________.

1. $[\frac{\lambda x_1+x_2}{\lambda +1},\frac{\lambda y_1+y_2}{\lambda +1}]$
2. $[\frac{\lambda x_2+x_1}{\lambda -2},\frac{\lambda y_2+y_1}{\lambda +1}]$
3. $[\frac{\lambda x_2+x_1}{\lambda +1},\frac{\lambda y_2+y_1}{\lambda +1}]$
4. $[\frac{\lambda x_2+x_1}{\lambda -1},\frac{\lambda y_2+y_1}{\lambda -1}]$

Q. If $\sin \theta =\frac{1}{2}$ then $\frac{{\theta }^2}{15}=$ _________.

1. ${30}^o$
2. ${60}^o$
3. ${90}^o$
4. ${45}^o$

Q. The ratio of the height of tower and length of its shadow is $1:\sqrt{3}$. Then the angle of elevation of sun is __________.

1. ${30}^o$
2. ${45}^o$
3. ${60}^o$
4. ${90}^o$

Q. $\sin \theta :\cos \theta =1:\sqrt{3}$ $\therefore \theta =$ __________.

1. ${30}^o$
2. ${45}^o$
3. ${60}^o$
4. ${90}^o$

Q. If ${\sec }^2\theta -{\text{cosec}}^2\theta =0$ then $\theta =$ _________.

1. ${90}^o$
2. ${45}^o$
3. ${60}^o$
4. ${30}^o$