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Question 92 (vii)

Factorise the following using the identity $a^2-b^2=(a+b)(a-b).$

$25a{x}^2-25a$

Construct a triangle XYZ in which XY = 5 cm, YZ = 5.5 cm and ∠XYZ = 100°.

Question 1(iii)
Evaluate:

${\left(\frac{1}{2}\right)}^{-5}$

A die is thrown. Find the probability of getting :

(i) a prime number (ii) 2 or 4 (iii) a multiple of 2 or 3

Which among the following are the possible ordered pair which can satisfy the given linear equation in two variable $5x+2y=3$?

In the given figure, if $\angle AOC={130}^{\circ },$ then the value of $\angle ABC$ = _______.

In the given figure, P is the midpoint of AB. If $\angle PAC=\angle PBD,$ then which of the following are true?

In a colony, the number of rooms in an apartment is equal to the number of apartments. If the total number of rooms in the colony is 2401, what is the number of apartments?

If $x\text{and}y$ are directly related, then, find $l,m\text{and}n$.

A teacher wrote a large number on a board and asked the students to tell about the divisors of the number one by one.

The 1st said, divisible by 2, the 2nd said by 3, the 3rd said by 4 and so on the 30th said the number is divisible by 31.

The teacher then commented that exactly 2 students were wrong, who spoke consecutively.

Which 2 students were wrong? Explain your answer with appropriate justification.

How do you write 75% as a fraction?

Question 126 (a) (iv)

Architects design many types of buildings. They draw plans for houses, such as the plant shown in the following figure.

An architect wants to install a decorative moulding around the ceilings in the rooms. The decorative moulding costs Rs. 500/ meter.

Find how much moulding will be needed for bedroom 1

Rajan deposited 10000 rupees in a bank, which gives 6% simple interest. Write and equation connecting the number of years of deposit and the total interest. Is the total interest proportional to the number of years? What if interest is compounded?

If the original size of an image is $540\times 680$, which of the following image sizes cannot be achieved to ensure that there is no deformation in the picture?

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

$\frac{7y+2}{5}=\frac{6y-5}{11}$

Measure of one of the angles of a parallelogram is twice the measure of its adjacent angle. Then angles of the parallelogram are

Scientific notation can be written in the general form as $a\times {10}^n$, where $n$ is an integer. Find the range of $a$.

Four alternative options are given for each of the following statements.

Select the correct option.

The principal that yields a simple interest of Rs 1,280 at 16% per annum for 8 months is:

A. Rs 10,000

B. Rs, 12,000

C. Rs 12,800

D. Rs 14,000

In the adjoining figure the value of x is:

(a) What are three conditions you need in order to say that the given two angles are adjacent angles? [3 MARKS]

(b) In the given figure, $\angle 1$ and $\angle 2$ are supplementary angles. If $\angle 1$ is decreased, what changes should take place in $\angle 2$ so that both the angles still remain supplementary?

Mr. Aakash has a saving bank account in Bank of India. His passbook has the following entries.

Calculate the interest due to him at the end of September (2008) at the rate of 4% p.a.

At what rate per cent per annum compound interest will Rs. 4000 amount to Rs. 5324 in 3 years

Laxmi is a cashier in a bank.She has currency notes of denominations rs100,rs 50and rs10,respectively.The ratio of the number of these notes is 2:3:5 .The total cash with laxmi is 4,00,000 . How many notes of of each denominations she have.

A rectangle WXYZ can be constructed if the length of

Construct a triangle ABC in which AB = 5 cm, BC = 4.7 cm and AC = 4.3 cm.

Identify the integer(s) whose square root lies between $2$ and $3.$

Match the following expressions with their respective common factors.

What will be the cost of the product in rupees after adding 10% sales tax on Rs 400?

Which of the following conditions can be used for the construction of quadrilaterals?

Use the formula and expand the following:

Factorise $(a^2+1)b^2-b^4-a^2$.

Which of the following quadrilaterals is not a parallelogram ?

The number of apples sold by a shop is given in the table below:

$$\begin{array}{cc}\text{Day}& \text{No. of apples sold}\\ \text{Monday}& 60\\ \text{Tuesday}& 35\\ \text{Wednesday}& 50\\ \text{Thursday}& 55\end{array}$$

If the picture of an apple represents 10 apples, then identify the correct pictograph for the above data.

Geeta borrowed Rs. 15,000 for 18 months at a certain rate of interest compounded semi-annually. If at the end of six months it amounted to Rs. 15,600; calculate :

(i) the rate of interest per annum.

(ii) the total amount of money that Geeta must pay at the end of 18 months in order to clear the account.

ABC is a right-angled triangle and O is the mid point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you).

Question 57

The number of workers and the time to complete a job is a case of direct proportion.

ABCD is a parallelogram. DK is perpendicular to BA produced at K and DM is perpendicular to BC produced at M. Find the measure of $\angle KDM.$

If AB || CD and XY is transversal which meets AB at M and CD at N also $\angle AMX={62}^{\circ }$, then $\angle DNY=$.