Explore topic-wise InterviewSolutions in .

Mode of the data

15, 14, 19, 20, 14, 15, 19, 14, 15, 20, 14, 19, 15, 15, 17 is

Evaluate $\int ({\sin }^2(\frac{\pi }{4}+x)-{\sin }^2(\frac{\pi }{4}-x))dx$

(where $C$ is constant of integration)

CD and GH are respectively the bisectors of ∠ACB and ∠EGF such that D and H lie on sides AB and FE of ΔABC and ΔEFG respectively. If ΔABC ∼ ΔFEG, Show that:

(i)

(ii) ΔDCB ∼ ΔHGE

(iii) ΔDCA ∼ ΔHGF

Draw a circle of radius 3 cm. Extend its diameter and mark two points P and Q each at a distance of 7 cm from the centre. From the points P and Q, draw tangents to the circle and find their approximate lengths.

The radius of the base of a right circular cone is r. It is cut by a plane parallel to the base at a height h from the base.

The slant height of the frustum is $\sqrt{h^2+\frac{4}{9}{r}^2}$ . Show that the volume of the frustum is $\frac{13}{27}\pi r^{2}h$

Question 2 (vi)

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

4, 1

Find the area of a rectangle, if the length of the rectangle is x and the breadth is twice the length the area of the rectangle?

If $-9+(-10)=x$, then the value of $x$ is

Five years hence, the age of jacob will be three times that of his son. Five years ago, Jacob's age was seven times that of his son. What are their present ages?

ABCD is a flower bed If OA = 21m and OC = 14m. Find the area of the bed in $m^2$.

Evaluate each of the following

(${Cot}^2)$ ${30}^{\circ }$ + 2(${Cos}^2)$ ${60}^{\circ }$ – 34 (${Sec}^2)$ ${45}^{\circ }$ - 4 (${Sec}^2)$ ${30}^{\circ }$

The volume of a right circular cone is $110m^3$ and diameter is $2\sqrt{15}m$. Calculate
i) Height of the cone
ii) Slant height
iii) Curved Surface area [4 MARKS]

If $x-3y=p,ax+2y=q$ and $ax+y=r$ form a right angled triangle, then

If the ratio of volume to total surface area of a solid sphere is 8 : 1, then radius of the sphere is ___.

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that a red ball, find the number of blue balls in the bag.

Given that $a_1{a}_2,\cdots ,a_{2004}$ are distinct positive real numbers then $\frac{a_1}{a_2}+\frac{a_2}{a_3}+\cdots +\frac{a_{2003}}{a_{2004}}+\frac{a_{2004}}{a_1}$ is

Water in a canal 1.5 m wide and 6 m deep is flowing with a speed of 10 km/hr. How much area will it irrigate in 30 minutes if 8 cm of standing water is desired

Consider an arithmetic sequence whose m^{​​​​​​th} term is 'n' and n^​​th term is 'm'

a) Find the common difference of the sequence

b) Prove that ( m+n+p) ^th term of the sequence is '-p'

The following table summarises the marks received by students for a Physics examination out of 50 :

$\begin{array}{cc}\text{Class interval}& \text{Frequency}\\ 0-9& 2\\ 10-19& 31\\ 20-29& 73\\ 30-39& 85\\ 40-49& 29\end{array}$

Estimate the Median mark.

If A = {1, 3, 5, ..... ,17}, B ={2, 4, 6, ..... ,18} and N, the set of natural numbers is the universal set, then $(A^{\prime }\cup [(A\cup B)\cap B^{\prime }\left]\right)$ is