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Draw a pair of tangents to a circle of any convenient radius, which are inclined to the line joining the centre of the circle and intersect at a point forming an angle of 45 degree with the line.

Given the linear equation 2x + 3y - 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:

(i) intersecting lines

(ii) parallel lines

(iii) coincident lines.

For a symmetrical distribution, which is correct

Find the volume of the square pyramid, if one of the triangular faces is given below.

The houses on one side of a road are numbered using consecutive even numbers. The sum of the numbers of all the houses in that row is 170. If there are at least 6 houses in that row and a is the number of the sixth house, then

1. 0.4

For any positive integers n, prove that $n^3-n$ is divisible by 6.

Find the factors of $x^2+8x+16$ by splitting the middle term.

Find the distance of point P from the centre of circle given the radius is 5 cm & length of tangent PA is 12 cm

Solve each of the following systems of eqautions by the method of cross-multiplication:

$\frac{5}{x+y}-\frac{2}{x-y}=-1$

$\frac{15}{x+y}+\frac{7}{x-y}=10$

If the sum of first 10 natural numbers is $S_1$ and that of first 10 whole numbers is $S_2$ . Then $S_1-S_2$ is

In the following data, find the values of $p$ and $q$ Also, find the median class and modal class.

$\begin{array}{ccc}\text{Class}& \text{Frequency(f)}& \text{Cumulative~frequency(cf)}\\ 100-200& 11& 11\\ 200-300& 12& p\\ 300-400& 10& 13\\ 400-500& q& 46\\ 500-600& 20& 66\\ 600-700& 14& 80\end{array}$

If 9th term of an AP is 15 and the common difference is 2, the 1st term of the AP is

Find the sum of each of the following APs:
(i) 2, 7, 12, 17,... to 19 terms.
(ii) 9, 7, 5, 3, ... to 14 terms.
(iii) -37, -33, -29, ... to 12 terms.
(iv) $\frac{1}{15},\frac{1}{12},\frac{1}{10},...to11$
(v) 0.6, 1.7, 2.8, ... to 100 terms.

If the sum of the ages of a father and his son in years is 65 and twice the difference of their ages in years is 50, then the age of the father is

How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?

$[Assume\pi =\frac{22}{7}]$

The 13th term of an AP is 4 times its 3rd term. If its 5th term is 16, find the sum of its first 10 terms.

$If△ABC\sim △DEFsuchthatAB=6cmandDE=7cm.Findtheratioofareasof△ABCand△DEF.$

Mahi uses a coin in which both the faces are the same i.e. tails. What is the probability that Mahi will win the toss, if she always calls heads?

Find the volume of the figure.

ABCD is a cylic quadrilateral in which BC is parallel to AD, angle ADC = ${110}^o$ and angle BAC = ${50}^o$. Find angle DAC and angle DCA.

(i) How many terms of the sequence $18,16,14,...$ should be taken so that their sum is zero?
(ii) How many terms are there in the A.P. whose first and fifth terms are $-14$ and $2$ respectively and the sum of the terms is $40$?
(iii) How many terms of the A.P. $9,17,25,...$ must be taken so that their sum is $636$?
(iv) How many terms of the A.P. $63,60,57,...$ must be taken so that their sum is $693$?
(v) How many terms of the A.P. $27,24,\mathrm{21...}$ should be taken so that their sum is zero?

A card is chosen at random from a standard deck of $52$ playing cards. What is the probability (in percent) of choosing a card that is not a club?

Question 10
A solid piece of iron in the form of a cuboid of dimensions $49cm\times 33cm\times 24cm$, is moulded to form a solid sphere. Then, radius of the sphere is
(A) 21 cm
(B) 23 cm
(C) 25 cm
(D) 19 cm