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Compute the lengths of all sides of the quadrilateral below:

Represent $\frac{-9}{5}$ on the number line. [2 MARKS]

A right angled triangle of sides $3cm$, $4cm$ and $5cm$ is rotated about the side $3cm$ then, the volume of the cone formed is .

In $△ABC,AD,BE$ and $CF$ are medians, and $G$ is centroid. If $AD=15cm$, find $AG$.

The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius $3cm$ and height $10.5cm.$ The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition? [Assume $\pi =\frac{22}{7}$]

If P(E)= 0.55 what is the value of P(not E)

Find the roots of the equation $x-5=0$.

Consider two triangles shown.







Which of these is true?

Find the value of the following, using suitable properties:

a) 406$\times$516

b) 8 $\times$291$\times$125
[3 MARKS]

Question 10

A circle has radius $\sqrt{2}$ cm. It is divided into two segments by a chord of length 2 cm. Prove that the angle subtended by the chord at a point in the major segment is ${45}^{\circ }$.

ABC is the right angled triangle with $\angle ABC={90}^{\circ }$. The centre of the circle passing through ABC lies on _______.

The denominator of a fraction is 5 more than its numerator. If the numerator is decreased by 1 and the denominator is increased by 2, the resulting fraction is $\frac{1}{5}$Find the original fraction.

If triangle ABC is right angled at B and

$sinA=\frac{3}{5}$, then find the value of cos A.

The $\frac{p}{q}$ form of $0.\overline{18}$ is ______ (where p and q are integers and $q\ne 0$) .

If $2^{x-1}=2^5=2^{a-4}$, then find the value of $x$ and $a$.

In the figure, O is the centre of the circle.

Find $\angle BAC$.

If the radius of a circle is doubled, then the area ___.

The sum of $\frac{-35}{11}$ and $\frac{12}{55}$ is ____________

The vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are of same length and taken pairwise, they form equal angles. If $\overrightarrow{a}=\hat{i}+\hat{j}$ and $\overrightarrow{b}=\hat{j}+\hat{k},$ then the components of $\overrightarrow{c}$ can be

Where would the number $\sqrt{2}$ lie on the number line?

If the point (2k – 3, k + 2) lies on the line 2x + 3y + 15 = 0, find the value of k.

A bus stop is barricaded from the remaining part of the road by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is Rs.12 per $m^2$, what will be the cost of painting these cones? (Use $\pi =3.14and\sqrt{1.04}=1.02)$

In triangles ABC and PQR, AB = AC, $\angle$C = $\angle$P and $\angle$B = $\angle$Q. The two triangles are ___.

Cards were drawn from a regular deck of 52 for a 100 times, replacing it each time after drawing. The data about the number is as follows.

$\begin{array}{cc}\text{Number}& \text{Frequency}\\ \text{A}& 10\\ 2& 8\\ 3& 5\\ 4& 6\\ 5& 8\\ 6& 5\\ 7& 10\\ 8& 11\\ 9& 8\\ 10& 7\\ \text{J}& 6\\ \text{Q}& 7\\ \text{K}& 9\end{array}$

(i) Find the probability of drawing a face card ;

(ii) Find the probability of drawing a number card with a prime number on it . [2MARKS]

If the degree measures of the angles of quadrilateral are 4x, 7x, 9x and 10x, what is the sum of the measures of the smallest angle and largest angle ?

Observe the given bar graph and choose the correct option for: the year in which the difference of the values of export and import is minimum.

A point P is 13 cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12cm. Find the radius of the circle.

Which geometric instrument is necessary for one of the methods in Triangle Construction 1 but not the other?