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In a circle of radius 21 cm, an arc subtends an angle of ${60}^{\circ }$ at the centre. The length of the arc is

(a) 21 cm (b) 22 cm (c) 18.16 cm (d) 23.5 cm

50 bells B1, B2, B3,.......B50 start ringing together. The bells ring after every 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.....50 sec respectively. Bells numbered as prime numbers ring at intervals. This interval will be the same as___

Find the value of CD?

The median class for the following data is

$$\begin{array}{cccccc}\text{Marks}& \text{Below 10}& \text{Below 20}& \text{Below 30}& \text{Below 40}& \text{Below 50}\\ \text{No. of students}& 5& 10& 23& 31& 40\end{array}$$

In the given figure, O is the centre of the circle. PA and PB are tangents. Show that AOBP is a cyclic quadrilateral.

Solving for x and y by substitution method :



$\frac{m}{x}+\frac{n^2}{y}=1+n\frac{m^2}{x}-\frac{n^2}{y}=m-n,(x\ne 0,y\ne 0)$



x and y are :

$27x^2-10x+1=0$

The distance between the points $(x_1,-y_1)\text{and}(-x_2,y_2)$ is ___ units.

Using trigonometric tables, find the value of $tan{62}^{\circ }{54}^{\prime }$.

Prove that the following are irrationals:

A circle is inscribed in an equilateral triangle of side $a$. The area (in sq. units) of any square inscribed in this circle is

Match the two columns;

$\begin{array}{cc}Column-I& Column-II\\ \text{(A) C is a point on the minor arc AB of the circle with centre O.}& \left(p\right){60}^{\circ }\\ \text{Given}\angle \text{ACB = x. Calculate}\angle \text{x if ACBO is a parallelogram.}& \\ \text{(B) Chord ED is parallel to the diameter AC of the circle.}& \left(q\right){120}^{\circ }\\ \text{Given}\angle CBE={55}^{\circ },\text{calculate}\angle DEC.& \end{array}$

$\begin{array}{cc}\text{(C) In the given figure,O is the centre of the circle.}& \left(r\right){35}^{\circ }\\ \text{If}\angle \text{ACB}={60}^{\circ }\text{find}\angle OAB.& \end{array}$



$\begin{array}{cc}\text{(D) In the given figure, O is the centre of a circle.}& \left(s\right){30}^{\circ }\\ \angle AOB={40}^{\circ }\text{and}\angle BDC={100}^{\circ }.\text{Find}\angle OBC& .\end{array}$

Choose the Correct option;

Solve the following pairs of equations by reducing them to a pair of linear equations:

1. 6

Find the value of y?

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

Find the sum of first $24$ terms of an AP whose $n^{th}$ term is given by $a_n=3+2n$.

Calculate the area of the shaded region if the diameter of the semicircle is 14 cm.

In each of the arithmetic sequences below, some numbers are missing. Their positions are marked with a. Find these numbers.

If $T_n=78$, where $T_n$ denotes the $n^{th}$ term the following AP:
3, 8, 13, 18, . . . then n = ___

The following table gives production yield per hectare of wheat of 100 farms of a village.

Change the distribution to a more than type distribution and draw ogive.

Find the value of $x$ in the diagram below.

If the diagonal of the given square is 4 cm, find its perimeter and area.

Question 7

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is 1:2:3.

How many irrational numbers exist between two rational numbers?

Find the X and Y intercepts of:
(a) x + 3y = 12
(b) 3x + 5y = 15 [4 MARKS]

For which commodities did a price increase immediately follow a price decline only one is this period?

The sum of the first p terms of an A.P is q and the sum of the first q terms is p. The sum of the first (p + q) terms is