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The diameter of a shot put is 9 cm. Calculate the volume of the shot-put.

Mr Sharma has 60 shares of N.V. Rs 100 and sells them when they are at a premium of 60 %. He invests the proceeds in shares of nominal value Rs 50, quoted at 4% discount, and paying 18% dividend annually. Calculate :

(i) the sale proceeds;

(ii) the number of shares he buys; and

(iii) his annual dividend from the shares.

A number consists of two digits whose sum is 10.If 18 is subtracted from the number,its digits are reversed.Find the number.

A metal sheet of breadth 10 cm is used to make a cone of radius 14 cm and slant height 20 cm. Then length of sheet if 25% of sheet is wasted is .

If an arithmetic sequence has a common difference 10 and its $6^{th}$ term is 52, then find its ${15}^{th}$ term.

Find the length of the tangent drawn from a point whose distance from the center of a circle is 25 cm. Given that the radius of the circle is 7 cm. [3 MARKS]

In Triangle ABC , D is the mid-point of side BC. Find the length of side AB.

The marks obtained by the students of a class , in a exam which was out of 50 mark given below

$\begin{array}{cc}\text{Marks}& \text{Number of students}\\ 5& 1\\ 7& 2\\ 11& 2\\ 16& 3\\ 21& 5\\ 24& 6\\ 28& 3\\ 32& 5\\ 34& 8\\ 39& 6\\ 43& 4\\ 45& 2\\ 49& 3\end{array}$



(i) Find the mean for the ungrouped data.



(ii) Represent the same data as grouped data, with class interval of width = 10

For what value of k,(-4) is a zero of the polynomial x^2-x-(2k+2)

The price of a table and chair together is 1500 rupees. The price of the table is four times that of the chair. What is the price of each?

Two coincident lines are of equal length. One of them is moved clockwise with respect to the other such that they share a common end point until they coincide again. Let A be the area swept by the line and let B be the area swept when this line makes any angle $\theta (\theta <360)$ with fixed line. Then A:B is:

What will be the remainder when $4x^4-3x^3+2x^2-x$ is divided by $x+1$?

What values of $x$ satisfy the given equation

$x^2-3x-10=0$ ?

Find the value of y?

x + y = 1 and -x + y = -3

ABC is an isosceles triangle in which AB = AC, circumscribed about a circle. Show that BC is bisected at the point of contact. [1 MARK]

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If 3π/4 < x < π, then √(2cot x + 1/sin^2 x) is equal to____

Pick a common word among the pictures given below.

How many designs were sent to the Government for approval?

Prepare a trading account of M/s Anjali from the following information Mated to 31st March, 2016.

$\begin{array}{cc}\text{Opening stock}& 60,000\\ \text{Purchases}& 3,00,000\\ \text{Sales}& 7,50,000\\ \text{Purchases return}& 18,000\\ \text{Sales return}& 30,000\\ \text{Carriage on purchases}& 12,000\\ \text{Carriage on sales}& 15,000\\ \text{Factory rent}& 18,000\\ \text{Office rent}& 18,000\\ \text{Dock and clearing charges}& 48,000\\ \text{Freight and octroi}& 6,500\\ \text{Coal, gas and water}& 10,000\end{array}$

If (x – p) and (x – q) are the factors of the polynomial P(x) = $x^2$ + ax + b =0, then P(x) can be written as:

The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find the 26th term.

If the sum of the squares of the zeroes of the quadratic polynomial, $f\left(x\right)=x^2-px+70$ is 149, then the value of p is

Find the coordinates of the points which divide the line segment joining the points (-4, 0) and (0, 6) in four equal parts.

In the given figure, ABCD is a quadrilateral such that $DA\perp AB$ and $CB\perp AB$, x = y and EF || AD such that EF bisects $\angle DEC$, which is equal to 90 degrees. Then $C{D}^2$ is equal to

Find the numbers such that the square of number is 15 lesser than twice the number.

A container in shape of a cylinder can store 7 litres of water. If the curved surface area of the cylinder is $1000c{m}^2$. What is the height of the cylinder?

Construct a tangent to a circle of radius $4cm$ from a point on the concentric circle of radius $6cm$ and measure its length. Also, verify the measurement by actual calculation.