Explore topic-wise InterviewSolutions in .

A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, each of diameter 3.5 cm and height 3 cm. Find the number of cones so formed.

The number of $6$ letter words with or without meaning that can be made from the letters of the word $MONDAY$, assuming that no letter is repeated is

If the 5th term of an A.P. is 31 and 25th term is 140 more than the 5th term, find the A.P.

The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition.

$\begin{array}{cc}\text{Scores}& \text{No. of shooters}\\ 0-10& 10\\ 10-20& 12\\ 20-30& 15\\ 30-40& 8\\ 40-50& 20\\ 50-60& 24\\ 60-70& 7\\ 70-80& 11\\ 80-90& 30\\ 90-100& 18\end{array}$

Use a graph sheet to draw an ogive for the distribution.

Using the graph estimate the Median.

The following table shows the marks scored by 80 students in an examination:
$\begin{array}{ccccccccc}\text{Marks}& \text{Less}& \text{Less}& \text{Less}& \text{Less}& \text{Less}& \text{Less}& \text{Less}& \text{Less}\\ & \text{than 5}& \text{than 10}& \text{than 15}& \text{than 20}& \text{than 25}& \text{than 30}& \text{than 35}& \text{than 40}\\ \text{Number of}& & & & & & & & \\ \text{students}& 3& 10& 25& 49& 65& 73& 78& 80\end{array}$
Calculate the mean marks correct to 2 decimal places.

A girl goes to her friend's house, which is at a distance of 12 km. She covers half of the distance at a speed of x km/hr and the remaining distance at a speed of (x + 2) km/hr. If she takes 2 hrs 30 minutes to cover the whole distance, find `x`.

In a given $\Delta$ ABC, AB =20 cm, $\angle A={30}^{\circ }$ as shown in figure. If the area of the triangle is $100c{m}^2$, then the length of AC is equal to

Construct rhombus ABCD with sides of length 4 cm and diagonal AC of length 5 cm. Find the point R on AD such that RB = RC. Then the length of AR is

How many sub-shells are possible for n = 4?

A is elder to B by 2 years. A’s father F is twice as old as A and B is twice as old as his sister S. If the ages of the father and sister differ by 40 years, find the age of A.

Solve the following systems of equations:

$\frac{x}{2}+y=0.8$

$\frac{7}{x+\frac{y}{2}}=10$

If D is a point on the side AB of $\Delta ABC$ such that AD : DB =3.2 and E is a point on BC such that DE || AC. Find the ratio of areas of $\Delta ABC$ and $\Delta BDE$.

Find the product of roots of the quadratic equation $2x^2+24x+36=0$

Construct a $\angle$ABC = 30${}^{\circ }$ . Mark a point D on BC such that BD = 6 cm. Find the radius of the circle to touch AB at B and also pass through D.

Show that the line segment joining the points of contact of two parallel tangents passes through the centre.

If P(3 , 4) & Q( , -7) find ‘’ if PQ is || to Y – axis.

Which of the following expressions is a polynomial in one variable?

In the given figure, PQ is a chord of length 8 cm of a circle with centre O and radius 5 cm. If the tangents to the circle at the points P and Q intersect at 'T', then the length of PT is

LCM of 60, 45 is

$3tan\theta$ + $cot\theta$ = 5 $cosec\theta$. Find the value of $\theta$,

0 < $\theta$ ≤ 90.

Question 2 (i)

E and F are points on the sides PQ and PR respectively of a $\Delta PQR$. For the following case, state whether EF || QR.

(i) PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm

What is the common difference of an AP in which $a_{27}-a_7=84$

1. 6

Question 1 (v)

Find the roots of the quadratic equations by using the quadratic formula in the following question.

$x^2+2\sqrt{2}x-6=0$

Question 8

A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is ${60}^{\circ }$ and from the same point the angle of elevation of the top of the pedestal is ${45}^{\circ }$. Find the height of the pedestal.

A solid sphere of radius 10.5 cm is cut into 2 halves. Find the total surface area of both the hemispheres.