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Find the measure of an angle which is ${30}^{\circ }$ less than its supplement.

Find the area of the shaded region in the figure given below, if ABCD is a square of side 14 $cm$ and APD and BPC are semicircles.

(Take $\pi =\frac{22}{7}$)

Question 3 (iii)

Prove that $6+\sqrt{2}$ is irrational.

Equation of the circle of radius √2 containing the point (3, 1) and touching the line |x-1|=|y-1|, is

In $△ABC$ if $AB=2AC=2$ and internal and external angular bisector of $\angle A$ intersects side $BC$ at the points $(1,-2)$ and $(-3,4)$ respectively, then

If x = $\frac{1}{2-\sqrt{3}}$ find the value of $x^3-2x^2-7x+5$

ABCD is a parallelogram whose diagonals intersect at O. A line through O intersects AB at P and DC at Q. Then

Variables end after z so how can it be infinite

Factorise:
px-5q+pq-5x

In a triangle $ABC,$ of $2\angle A=3\angle B=6\angle C$ , then the measurement of $\angle B$ is?

In Fig. there are three semicircles, A, B and C having diameter 3 cm each, and another semicircle E having a circle D with diameter 4.5 cm are shown. Calculate the cost of painting the shaded region at the rate of ₹25 per $c{m}^2$.

Volume of water that can be stored in a spherical tank of diameter $42cm$ is.

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

The base radii of two cylinders of same height are in the ratio 3:5. What is the ratio of their volumes?

Draw a line, 10 centimetres long ad divide it in the ratio 3 : 4.

Which of the figure represents the point

(5, 0) on the coordinates plane.

The area of a square is $36c{m}^2$. If the side of the square is equal to the side of an equilateral triangle, then find the area of the triangle.

In a triangle $ABC$, median $AD$ and $CE$ are drawn. If $AD=5,\angle DAC=\frac{\pi }{8}$ and $\angle ACE=\frac{\pi }{4},$ and the area of the triangle $ABC$ is equal to $\Delta$, then $3\Delta$ is equal to:

A circle of diameter 13 cm has two chords of lenght 12cm and 5cm. If both the chords lie on the same semicircle, what is the distance between the chords?

If the radius of a hemisphere is $2x$, then its total surface area is given by:

In a triangle ABC, E is the mid-point of median AD. Show that ar (BED) = ar (ABC)

Question 3 (ii)

Explain how a square is:

(ii) A parallelogram

The area of a triangle whose sides are 8 cm, 10 cm and 14 cm is equal to

In a single throw of dice,the probability of getting a number greater than 6 is___

Question 28

The lowest form of the product $2\frac{3}{7}\times \frac{7}{9}$ is ___

A right circular cone is 3.6 cm high and the radius of its base is 1.6 cm, It is melted and recast into a right circular cone having base radius 1.2 cm. Find its height.

In the given figure, $\angle$ BAD = ${65}^o$, $\angle$ ABD = ${70}^o$ and $\angle$ BDC = ${45}^o$, Find :

(i) $\angle$ BCD

(ii) $\angle$ ACB

Hence, show that AC is a diameter.

Dividing $(a+b{)}^2$+$(a-b{)}^2$ by $a^2$+$b^2$ gives:

A vector which makes equal angles with the vectors $\frac{1}{3}(\hat{i}-2\hat{j}+2\hat{k}),\frac{1}{5}(-4\hat{i}-3\hat{k}),\hat{j}.$ is