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Answer the following:
(i) A circle is inscribed in a square. A point inside the square is randomly selected. What is the probability that the point is inside the circle as well?

(ii) If, instead, the square was inscribed in the circle, and a point inside the circle was randomly selected, what is the probability that it is inside the square? [4 MARKS]

The frequency polygon below shows marks obtained by students of a class.

From the graph, it can be said that the maximum number of student have scored ____

1. 12

The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

If the curved surface area of a right circular cylinder is 1760 cm² and its radius is 10 cm, then what is its height?

What will be the linear equation for the given graph?

The radii of two spheres are in ratio 1 : 2. Find the ratio of their surface areas.

The value of $(\sqrt{3}+\sqrt{2}{)}^2$ is equal to ____.

Match the following:



$\begin{array}{cc}\text{Quadrilateral}& \text{Properties}\\ \text{1. Trapezium}& \text{A) A parallelogram, where diagonals bisect at right}\text{angles, all sides are equal and none}\text{of the angles are equal to}{90}^{\circ }\\ \text{2. Square}& \text{B) A quadrilateral, where only one pair}\text{of opposite sides is parallel and unequal}\\ \text{3. Rectangle}& \text{C) A parallelogram, where diagonals are equal,}\text{all sides equal and all the angles are}{90}^{\circ }\\ \text{4. Rhombus}& \text{D) A parallelogram, where diagonals and}\text{opposite sides are equal, and all the angles are}{90}^{\circ }\end{array}$

In the figure below, O is the centre of the circle and $\angle QPR=x^{\circ },\angle ORQ=y^{\circ }.$ Which statement is true about $x^{\circ }$ and $y^{\circ }$?

The height h of a cylinder equals the circumference of the cylinder. in terms of h, what is the volume of the cylinder ?

(a) $\frac{h^3}{4\pi }$ (b) $\frac{h^2}{2\pi }$

(c) $\frac{h^3}{2}$ (d) $\pi h^3$

Find the area of the quadrilateral shown below:

Given: Area $\left(\Delta ADC\right)=16c{m}^2$

Question 2 (i)

Write the coordinates of B.

In the given figure, $\angle PQR={68}^{\circ }$ and QS is the bisector of $\angle PQR,$, If QM and QN bisect $\angle PQS$ and $\angle SQR$ respectively. Then $\angle MQN,$ will be

A roof is made by using 20 triangular rocks which are equally divided in 4 different colours.The sides of each piece are 2 m, 5 m and 5 m. What is the area covered by each colour?

Find the roots of the quadratic equation $x^2-3x+2=0$, using factorisation method.

Question 3

P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD in which AC=BD. Prove that PQRS is a rhombus.

Thinking Process

If O is the center of the circle, find the value of $x$ in each of the following figures.
(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

(xi)

(xii)

Locate $\sqrt{10}$ on the number line.

Can 0 be a zero of a polynomial?

Find the following products:



(i) (3x + 2y + 2z) (9x² + 4y² + 4z² − 6xy − 4yz − 6zx)



(ii) (4x − 3y + 2z) (16x² + 9y² + 4z² + 12xy + 6yz − 8zx)



(iii) (2ab − 3b − 2c) (4a² + 9b² +4c² + 6 ab − 6 bc + 4ca)



(iv) (3x − 4y + 5z) (9x² +16y² + 25z² + 12xy −15zx + 20yz)

IF $a^2+b^2+c^2=250$ and $ab+bc+ca=3,$ find a + b +c.

The decimal expansion of pi is: