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1. 1280

Factorising and dividing $a^2+7a+10$ by $(a+5)$ gives:

Karan spends ₹ 5000 on food which is $\frac{5}{8}$th of his income. Karan's income is ₹:

Question 93 (iii)

The following expression is the area of a rectangle. Find the possible length and breadth of the rectangle.

$x^2-7x+10$

Coefficient of 'b' in the expression $6b^2$ is ___.

A shop keeper purchases an article for Rs 3,500 and pays transport charge of Rs 100. He incurred a loss of 12% in selling this. Find the selling price of the article.

Question 1 (ii)

What could be the possible ‘one’s’ digit of the square root of following number:

99856

Construct a triangle ABC in which AB + AC = 5.6 cm, BC = 4.5 cm and ∠B = 45°.

In the following series, find the next term.
$0,1,1,2,3,5,8,13,$ __

A rhombus-shaped sheet with a perimeter of 40cm and one diagonal of 12cm, is painted on both sides at the rate of ₹ 5 per $c{m}^2$. Find the cost of painting.

1. 11

Most of the sailboats have two sails, the jib and the mainsail. Assume that the sails are triangles. Find the total area of each sail of the sailboats to the nearest tenth.

A certain mixture contains gases according to the following proportions. Name the first two gases obtained after they are arranged in the decreasing order of their content.

Observe the pattern given below:

1, 4, 9, 16, 25, ...

The algebraic expression for $n^{th}$ term of the pattern is

Find $x$ :

$\frac{x}{2}-\frac{1}{5}=\frac{x}{3}+\frac{1}{4}$

Find the value of x.

$3x+\frac{9}{3}=5x+\frac{5}{9}$

Ramya borrowed a loan from a bank for buying a computer. After 4 years she paid Rs 26,640 and settled the accounts. If the rate of interest is 12% per annum, what was the sum she borrowed?

Draw a number line and answer the following:

Which number will we reach if we move 4 numbers to the right of –2?

Question 71

The class size of the class interval 60 - 68 is 8.

Find $\angle ABD$ in the parallelogram ABCD.

Question 4
The choices of the fruits of 42 students in a class are as follows:
A, O, B, M, A, G, B, G, A, G, B, M, A, G,
M, A, B, G, M, B, A, O, M, O, G, B, O, M,
G, A, A, B, M, O, M, G, B, A, M, O, M, O,
Where A, B, G, M and O, stands for the fruits Apple Banana, Grapes, mango and Orange, respectively.
Which two fruits are liked by equal number of students ?
(a) A and M (b) M and B (c) B and O (d) B and G

Directions:- Study the following information carefully to answer the question given below.

Vikas, Uday and Tushar are seated around a regular hexagonal table facing the centre. Amar, Bimla and Chetan are also seated around the same table but one of them is facing outside. Vikas is second to the left of Chetan. Uday is second to the right of Amar. Bimla is the third to the left of Tushar. Amar is seated next to Vikas.

Which of the following is true regarding the sitting arrangement?

Question 3

Draw a histogram of the following distribution.



$\begin{array}{cc}\text{Height(in cm)}& \text{Number of students}\\ 150-153& 7\\ 153-156& 8\\ 156-159& 14\\ 159-162& 10\\ 162-165& 6\\ 165-168& 5\\ \text{Total}& 145\end{array}$

Solve each of the following equations and also verify your solution :

$\frac{3x}{4}-\frac{(x-1)}{2}=\frac{(x-2)}{3}$

If $a+b+c=0$ then prove

$a^4+b^4+c{}^4=2(a{}^{2}b{}^2+b{}^{2}c{}^2+c{}^2{a}^2)$

The amount on ₹ 10,800 for 3 years at $12\frac{1}{2}\%$ per annum, compounded annually is

Question 6

Find the value of the following letters.



$AB$

$\underset{–}{\times 5}$

$\underset{–}{CAB}$

If I have a quadrilateral PQRS, how many triangles are there in the quadrilateral in which I must have one of the diagonals as a side.

What is the minimum number of parameters needed to construct a square?