Q. The formula to find the total surface area of a Rs.$5$ coin is ..............

1. $\pi r^{2}h$
2. $\pi r(r+h)$
3. $2\pi r(h+r)$
4. $\pi r^{3}h$

Q. When the length of the shadow of a pole is equal to the height of the pole, the angle of elevation of the Sun has measure of ................

1. ${30}^o$
2. ${75}^o$
3. ${60}^o$
4. ${45}^o$

Q. The product of the zeroes of polynomial $x^2-4x+3$ is ...............

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

Q. In a two digit number, the digit at the units place is $x$ and the digit at tens place is $y$. If $y=5$, then the number is ...............

1. $5x$
2. $50x+5$
3. $x+50$
4. $30x+5$

Q. If $\alpha ,\beta ,\gamma$ are the zeros of a polynomial $P\left(x\right)=a{x}^3+b{x}^2+cx+d(a\ne 0)$ then
$\frac{1}{\alpha }+\frac{1}{\beta }+\frac{1}{\gamma }=$..............

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

Q. With the help of match-sticks, Zalak prepared a pattern as shown below. When $97$ matchsticks are used, the serial number of the figure will be ...........

1. Figure 32
2. Figure 95
3. Figure 49
4. Figure 48

Q. The area of a minor sector of $\odot (P,30)$ is $300{cm}^2$. The length of the corresponding arc in ................. $cm$.

1. $20$
2. $10$
3. $30$
4. $40$

Q. If the area and the circumference of circle are numerically equal, then the radius the circle is _______.

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

Q. For $A(1,2)$ and $B(3,-2)$, the coordinates of the midpoint of $AB$ are is ..........

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

Q. In a given A.P., $T_{25}-T_{20}=15$. $\therefore$ $d=$............. for the A.P.

1. $5$
2. $3$
3. $25$
4. $120$

Q. If $7{\cos }^2\theta +3{\sin }^2\theta =4$, then $\cot \theta =$

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

Q. The volume of a cylinder is $550{cm}^3$. If its radius is $5cm$, then its height is ................ $cm$.

1. $9$
2. $12$
3. $14$
4. $7$

Q. If $\sin 7\theta =\cos 2\theta$ for acute angles $7\theta$ and $2\theta$, then $\theta =$

1. $10$
2. $90$
3. $20$
4. $30$

Q. The chord of a $\odot (0,5)$ touches $\odot (0,3)$. The length of the chord is ...............

1. $6$
2. $8$
3. $7$
4. $2$

Q. The foot of the perpendicular drawn from $P(-3,2)$ to the y-axis is $M$. The coordinates of $M$ are ................

1. $(0,2)$
2. $(3,0)$
3. $(\frac{3}{2},-1)$
4. $(-3,2)$

Q. In the following figure $△ABC$ is an equilateral triangle and $AC=x$ $cm$. $\overline{AD}$ is median on $\overline{BC},D\in \overline{BC}$. If $AD=y$ $cm$, then $y=..................cm$

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

Q. The perimeter of an equilateral triangle is $6$. The length of an altitude drawn on any of its sides is ..............

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

Q. A shown in the following figure, the area of square $ABCD$ is $16{cm}^2$ and the area of square CIPO is $9{cm}^2$. If $\overline{BC}\perp \overline{CO}$ then the length of $\overline{BO}=................cm$

1. $7$
2. $25$
3. $625$
4. $5$

Q. $\frac{{\sin }^4\theta -{\cos }^4\theta }{{\sin }^2\theta -{\cos }^2\theta }=$

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

Q. The ratio of the areas of two similar triangles is $25:16$. The ratio of their perimeters is ..............

1. $625:256$
2. $5:6$
3. $25:16$
4. $5:4$

Q. From the natural number of singles of digit, the probability getting an even number is ...............

1. $\frac{5}{10}$
2. $\frac{4}{9}$
3. $\frac{5}{9}$
4. $\frac{1}{9}$

Q. From the top of a building $h$ metre high, the angle of depression of an object on the ground has a measure $\theta$. The distance of the object from the building is

1. $h\cos \theta$ metre
2. $\tan \theta$ metre
3. $h\cot \theta$
4. $h\sin \theta$ metre

Q. If $y=\frac{2}{3}$ is a root of the quadratic equation $3y^2-ky+8=0$, then the value of $k$ is ..................

1. $13$
2. $-14$
3. $14$
4. $-13$

Q. In any A.P., $S_n-2S_{n-1}+S_{n-2}=.....(n>2)$

1. $a+d$
2. $2d$
3. $d$
4. $a$

Q. 3 years ago, the sum of the ages of a father and his son was $40$ yeas. After 2 years, the sum of their ages will be ............

1. $46$ years
2. $40$ years
3. $50$ years
4. $60$ years

Q. In $△ABC$, correspondence $ABC\leftrightarrow BAC$ is similarity. From the following ........... is true.

1. $\angle C\cong \angle A$
2. $\angle A\cong \angle B$
3. $\angle B\cong \angle C$
4. $\angle A\cong \angle B\cong \angle C$

Q. On walking ............... metres on a slope at an angle of measure 30 with the ground, one can reach the height '$a$' metres from the ground.

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

Q. If the ratio of the areas of two circles is $1:4$, then the ratio of their circumferences is ...................

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

Q. If $\text{cosec}A=\frac{4}{3}$ and $A+B=90$, then $\sec B=$.....

1. $\frac{16}{9}$
2. $\frac{4}{3}$
3. $\frac{3}{4}$
4. $\frac{7}{3}$

Q. From the equations given below, a root of one equation is $3$. The equation is ......................

1. $x^2+x-6=0$
2. $x^2-x-6=0$
3. $x^2+x+6=0$
4. $x^2-x+6=0$