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(a) What should be added to x² + xy + y² to obtain 2x² + 3xy?

(b) What should be subtracted from 2a + 8b + 10 to get − 3a + 7b + 16?

In the figure given below, l and m are two parallel lines. Which of the following statement is true?

Question 4

The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.

Draw an angle of ${80}^{\circ }$ using a protractor and divide it into four equal parts, using ruler and compass. Check your constuction by measurement.

Find the value of:

(1)

(2)

(3)

(4)

(5)

Question 94

A number is as much greater than 27 as it is less than 73. Find the number.

Simplify:

(i) (ii) (iii)

A person is riding a bicycle at the speed of $17.6$ metre per second. Round this speed up to nearest natural number and find it's prime factorisation.

In the following figure, the area of the total cloth required is $80c{m}^2$ and the area of the yellow cloth required is $60c{m}^2$. If the red colored parts are congruent to each other and the blue cloth is $\frac{1}{{10}^{th}}$ of the yellow cloth, what is the area of the red cloth required?

If AM is a median of triangle ABC, then which of the following relation will always hold good?

Question 80 (i)

Rani bought a new field that is next to one she already owns in the given figure. This field is in the shape of a square of side 70 m. She makes a semi-circular lawn of maximum area in this field.

Find the area of the square field excluding the lawn.

Find the difference between the Rational numbers B and A as shown on the number line.

The monthly expense of Rahul in the month of August was Rs 41,500 and in the month of June was Rs 39,500. If his monthly income is Rs 60,000. In which month did he save more?

The figure below shows a circle divided into 3 equal parts.The shaded region corresponds to ${\frac{2}{3}}^{rd}$ of the circle. The unshaded region corresponds to ${\frac{a}{3}}^{rd}$ of the circle. Then, the value of a is _____.

___

Simplify: $x^2{y}^2{x}^5{y}^3$

In a juice bar, the shopkeeper can extract $14u^7$ milliliters of juice from a single orange. After receiving an order of a certain number of glasses of juice, the shopkeeper extracted juice from $v^2$ number of oranges. In his bar, each glass can hold $2u^{2}v$ ml of juice. Determine how many juice glasses were ordered.

Let x be the number of integer lying between 2999 and 8001 which have atleast two digit equal . Then what is the value of x.

Pavan's car can go 100 km with 50 litres of petrol. How far can the car go with 30 litres of petrol?

Question 4

Next three consecutive numbers in the pattern 11, 8, 5, 2, ___, ___, ___ are

(a) 0, – 3, – 6 (b) – 1, – 5, – 8
(c) – 2, – 5, – 8 (d) – 1, – 4, – 7

1. 311

A man purchased a book for Rs. 600 and sold it for Rs 335. Find the loss amount.

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The coefficient of $a$ in the expression $4a+7b+2$ is

Simplify ${\left(256\right)}^{\frac{-1}{2}}$.

Verify Euler's formula for each of the following polyhedrons:

The sides of a triangle are $6$ cm, $8$ cm and $10$ cm. Then the largest angle of the triangle is -

You are given the measurement of the two legs of a right angled triangle. What else do you need in order to draw a triangle?

Question 9

If k + 7 = 16, then the value of 8k - 72 is

(a) 0

(b) 1

(c) 112

(d) 56

Find the Range of the following scores.

(a) 18, 23, 19, 25, 22, 14, 21, 30

(b) 45, 39, 40, 36, 42, 48, 39