Q. The volume of a cone having radius 2 cm and height 6 cm is .............. cm${}^3$

1. $14\pi$
2. $12\pi$
3. $8\pi$
4. $16\pi$

Q. In right angle triangle, the side opposite to the angle having measure 30 is ................. to the hypotenuse

1. half
2. three times
3. double
4. fourth part

Q. The decimal expansion of $\frac{1}{32}$ is

1. 0.15625
2. 0.03125
3. 0.3125
4. 0.00625

Q. The curved surface area of a sphere is 1256 cm${}^2$. Find the radius of the sphere. $(\pi =3.14)$

1. 10 cm
2. 100 cm
3. 1 cm
4. 314 cm

Q. In a circle having radius r, an arc of a circle subtends an angle $\theta$ at the centre, then the length of arc l = ...............

1. $2\pi r$
2. $\frac{\pi r\theta }{180}$
3. $\pi r^2$
4. $\frac{\pi r^2\theta }{360}$

Q. A chord of $⨀$(0, 10) touches $⨀$(0, 6). Therefore the length of the chord is ................

1. 10
2. 8
3. 16
4. 6

Q. $co{t}^2-cose{c}^2\theta =$ ............... $(0<\theta <90)$

1. -1
2. 1
3. 0
4. Not defined

Q. Find the probability that one will get 75 marks in the question paper of 100 marks.

1. $\frac{75}{100}$
2. $\frac{1}{100}$
3. $\frac{1}{101}$
4. $\frac{75}{101}$

Q. If the radius of a circle increased by 20% then the corresponding increase in the area of circle is ................

1. 40%
2. 20%
3. 21%
4. 44%

Q. A(2, -2), B(4, 3) and C(-3, 11) are the vertices of $\Delta$ABC. If G is centroid of triangle, then the co-ordinate of G is:

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

Q. Following is the information about the number of students studying in a high school. If one student of the school is to be elected as a representative, find out the probability of the elected student to be a boy of Std. IX.

Std.	Boys	Girls	Total
IX	220	110	330
X	110	110	220
Total	330	220	550

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

Q. $\Delta ABC,AB=5,BC=12$ and $AC=13$, then the radius of the circle touching all the three sides is ______.

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

Q. Here is a graph of "Less than type" and "more than type" give is drawn.
It shows the information about the yearly salary (In lakhs Rs.) of officers in a factory.
Boundary points (Annual Salary)
Both the curves intersect $(20.5,15)$. Find the median of the information.

1. $35.5$ lakhs
2. $20.5$ lakhs
3. $15$ lakhs
4. $17.75$ lakhs

Q. The volume of sphere is $\frac{4}{3}\pi c{m}^3$. Then the radius is ................. m.

1. 0.02
2. 2
3. 0.01
4. 1

Q. An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his/her eyes has measure 45. What is the height of the tower?

1. 28.5 m
2. 27 m
3. 30 m
4. 1.5 m

Q. $1-2{\sin }^2{30}^{\circ }=$ ______.

1. $cosec{60}^{\circ }$
2. $sin{60}^{\circ }$
3. $tan{60}^{\circ }$
4. $cos{60}^{\circ }$

Q. The co-ordinates of the foot perpendicular from P(-3, 1) to X axis are .................

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

Q. The wickets taken by a bowler in a one-day cricket match are $4,5,6,3,4,0,3,2,3,5.$ The mode of the data is ...............

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

Q. For some data $M+\overline{X}=22$ and $M-\overline{X}=2$, then $Z=$ .............

1. $14$
2. $15$
3. $16$
4. $12$

Q. If $15{\tan }^2\theta +4{\sec }^2\theta =23$ then ${\tan }^2\theta =$..............

1. $\frac{27}{15}$
2. $45$
3. $\frac{19}{11}$
4. $1$

Q. In figure the shaded region indicates.

1. Major segment
2. Minor sector
3. Major sector
4. Minor segment

Q. D, E and F are respectively mid points of sides $\overline{AB},\overline{BC}$ and $\overline{CA}$ of $\Delta ABC$. Which of the following correspondence between $\Delta ABC$ and $\Delta DEF$ of similarity.

1. $ABC\sim EFD$
2. $ABC\sim FED$
3. $ABC\sim EDF$
4. $ABC\sim DEF$

Q. A(1, 2) and (3, -2) are the end points of $\overline{AB}$. Then the midpoints of $\overline{AB}$.

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

Q. An observer from the top of the light house, the angle of depression of two ships $P$ and $Q$ anchored in the sea to the same side are found to have measure $35$ and $50$ respectively. Then from the light house ...............

1. The distance of $P$ is more than $Q$.
2. The distance of $Q$ is more than $P$.
3. $P$ and $Q$ are at equal distance.
4. The relation about the distance of $P$ and $Q$ cannot be determined.

Q. If n is positive even integer, then $n(n+1)(n+2)$ is ................

1. a prime number
2. divisible by 24
3. divisible by 16
4. divisible by 20

Q.

If ${\sin }^{2}45-{\sin }^{2}60=x{\cos }^{2}45$ then $x=$ ..............

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

Q. The length of the minor arc ACB of a circle $⨀$(0, r) is 1/6 part of its circumference. Then the measure of angle of minor arc ACB subtending at the centre is ................

1. 90
2. 60
3. 30
4. 120

Q. The degree of polynomial $(x+1)(x^2-x-x^4+1)$ is .................

1. 4
2. 5
3. 1
4. 3

Q. If $\alpha$ and $\beta$ are the zeroes of polynomial $P\left(x\right)=x^2-3x+2k$, and $\alpha +\beta =\alpha .\beta$, then the value of k is ...............

1. 3
2. 1
3. 3/2
4. -3

Q. Answer the following question from the given figure.
Here the solid is composed of cube, cylinder and cone.
Here,
The curved surface area of cone is P.
The curved surface area of cylinder is Q.
The area of the base of cone and cylinder is R and the Total surface area of cube is S.
Then, find the total surface area of solid.

1. P + Q - 2R + S
2. P + Q + 2R + S
3. P + Q + R + S
4. P + Q - R + S