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If $x+x^{-1}=10$ and $x\ne 0$ then evaluate $x^2+x^{-2}$.

If $a-b=3andab=10;$ find $a^3-b^3$

Question 3

Assuming land to be uniformly fertile, the area of land and the yield on it vary
(a) directly with each other
(b) inversely with each other
(c) Neither directly nor inversely with each other
(d) Sometimes directly and sometimes inversely with each other

If $(a+b)=7$ and $ab=12$, then .

What is the value of $1,{111}^2$?

Ramesh invests Rs.12800 for three years at the rate of $10\%$ per annum compound interest. Find the sum due to Ramesh at the end of the first year.

Examine
the table. (Each figure is divided into triangles and the sum of the
angles deduced from that.)

What can
you say about the angle sum of a convex polygon with number of sides?

(a) 7

(b) 8

(c) 10

(d) n

Is 140xyz and140yzx are the same, if yes then why?

Write three sets of pythagorean triplets such that each set has numbers less than 30.

Using ruler and compasses only, construct a parallelogram ABCD, in which : AB = 6 cm, AD = 3 cm and $\angle DAB={60}^{\circ }$. In the same figure draw the bisector of angle DAB and let it meet DC at point P. Measure angle APB.

the diogonals of a rhombus are of measurement 12 CM and 16cm. Find the length of side of the rhombus.

In the binomial expansion of ${(x+\frac{1}{x})}^{10}$, the coefficient of $7^{\text{th}}$ term from the end is

Jane's father brought a square-shaped white marble tile and placed in the dining area of the house. Jane wanted to see it closely, so she picked it up. But before she could place it back on the table, it slipped from her hand and broke into four pieces.

Find the actual image of the marble tile before it was broken.

If you are given AB = 5cm, BC =6cm, CD = 7cm, DA = 6cm and $\angle$ABC=${60}^{\circ }$. Can you draw the quadrilateral?

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Question 56

State whether the following statement is true or false:

The cube of 0.4 is 0.064.

Find the smallest perfect square divisible by 3,4 5 and 6.

Students in Mrs. Smeera's class were surveyed about snacks and asked to choose one snack they liked most from a list. The bar graph below summarizes the data collected from this survey.



Assuming that one student likes only one of the given snacks, ___ percentage of students liked mixture.

नसीरूद्दीन और जमाल साहब बनठन कर घूमने के लिए निकले।

(क) तुम बनठन कर कहाँ-कहाँ जाते हो?

(ख) तुम किस-किस तरह से बनते-ठनते हो?

The triangle ABC is given below :

The areas of AOB and AOC are in the ratio 14 : 20

If the area of the smaller triangle is $24c{m}^2$ less than the area of larger triangle, find the total area of the triangle ABC.

Construct a $△$ ABC in which AC = 5 cm, and $\angle BAC={60}^{\circ }$ and AB – BC = 1.2 cm.

Two coincident lines are of equal length. One of them is moved clockwise with respect to the other such that they share a common end point until they coincide again. Let A be the area swept by the line and let B be the area swept when this line makes any angle $\theta (\theta <360)$ with fixed line. Then A:B is:

Draw a straight line AB = 6.5 cm. Draw another line which is parallel to AB at a distance of 2.8 cm from it.

Check whether the statement is valid or not. The square of a natural number other than 1 is either a multiple of 3 or exceeds a multiple of 3 by 1

There are 216 workers in a factory out of which 75 are laborers. What would be the central angle of the sector representing laborers in a pie chart?

In the following figure, if OQ is angle bisector of $\angle POA$, then $\angle POQ$ will be equal to ___ degree.

1. 45

A/an _______ is the collection of one or more outcomes in the sample space of an experiment.

A rectangular piece of paper of dimensions 22 cm by 12 cm is rolled along its length to form a cylinder. The volume of the cylinder so formed is _____.