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Raghu had to make a cylindrical aluminium tube. What is the area of the aluminium sheet he needs to make the tube, if the tube has length of 1m and base radius of 3.5cm? (Take π = $\frac{22}{7}$)

If two matrices $A$ and $B$ are such that, $AB=A$ and $BA=B.$ Then $A^3+B^3$ is equal to

Meena needs to serve mango juice to her guests in cylindrical tumblers of radius 7 cm up to a height of 10 cm. If she wants to serve 25 guests, how much juice does she need to prepare?

Prove that a cyclic parallelogram is a rectangle.

The volumes of two spheres are in the ratio 64:27 and the sum of their radii is 7 cm. What is the difference in their total surface areas?

Two lines AB and CD intersect each other at a point O such that ∠AOC:∠AOD=5:7. Find all the angles.

$In\Delta ABC,\text{BC = AB and}\angle B={80}^{\circ }.Then,\angle A=?\left(a\right){50}^{\circ }\left(b\right){40}^{\circ }\left(c\right){100}^{\circ }\left(d\right){80}^{\circ }$

Identify the non-linear points from the given options.

In a right triangle ABC right angled at B, the square of hypotenuse is equal to twice the product of the perpendicular sides. Find the measure of $\angle A.$

Choose the correct Tally chart that represents the following data.

The following shows the marks obtained by 20 students of a class in a math test (out of 10 marks)

4, 7 , 8, 10, 10, 9 , 3 , 5 , 7 , 8

8 ,4, 9, 3, 10, 8, 9 , 5, 7, 8

Question 2

Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

In the given figure, $\angle ADB=\angle ADC={90}^{\circ }.$ Also if $\angle BAD=\angle DAC$ then values of x and y are:

In a quadrilateral ABCD, the bisectors of C and D meet at E. What is the value of $2\left(\angle CED\right)$?

Expand $(x-2{)}^2$ using suitable identity.

The roots of the equation $(x+5)(x-5)=0$ are

1. 10

Prove that :

(i) ${\left(\frac{x^a}{x^b}\right)}^{a^2+ab+b^2}\times {\left(\frac{x^b}{x^c}\right)}^{b^2+ab+c^2}\times {\left(\frac{x^c}{x^a}\right)}^{c^2+ca+a^2}=1$

(ii) ${\left(\frac{x^a}{x^b}\right)}^c\times {\left(\frac{x^b}{x^c}\right)}^a\times {\left(\frac{x^c}{x^a}\right)}^b=1$

The coordinates of the origin O are _____.

Draw ΔABC, with AB = 5 cm and BC = 7 cm and ∠ABC = 60°. Draw a triangle of the same area with one side as AB and the angle at B equal to 30°

In the figure below, lines AB and CD intersect at O. If $\angle AOC$ + $\angle BOE$ = ${70}^{\circ }$ and $\angle BOD={40}^{\circ }$, find $3\times \angle BOE$ in degrees.

1. 90

Consider the following figure. If AB = 2BD, PD = AC and 2AP = AD.

What is the ratio BC:BD?

Question 115(vi)

Express the following in standard form:

Express 5 tonnes in g.

Question 6 (i)

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

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If $\angle DBC={70}^{\circ },\angle BAC\text{is}{30}^{\circ }$ and AB = BC, find $\angle ECD$.

If BC is a diameter of a circle with centre O and OD is perpendicular to the chord AB of a circle, show that CA = 2 OD. [2 MARKS]

The cotangent of an angle in a right-angled triangle is defined as

What are the next two figures in the pattern shown below?