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Write each of the following in exponential form:

$\left(i\right){\left(\frac{3}{2}\right)}^{-1}\times {\left(\frac{3}{2}\right)}^{-1}\times {\left(\frac{3}{2}\right)}^{-1}\times {\left(\frac{3}{2}\right)}^{-1}\left(ii\right){\left(\frac{2}{5}\right)}^{-2}\times {\left(\frac{2}{5}\right)}^{-2}\times {\left(\frac{2}{5}\right)}^{-2}$

If the diagonals of a rhombus get doubled, then the area of the rhombus becomes ___ its original area.

Question 92 (iii)

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

$4x^2-49y^2$

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

$\frac{5x}{3}-\frac{(x-1)}{4}=\frac{(x-3)}{5}$

Given the side length as 10m and base length as 9m and height as 5m of a parallelogram. Find the area and its perimeter. [2 MARKS]

1. 120

By using the formula, find the amount and compound interest on:

$Rs.62500$ for $2$ years $6$ months at $12\%$ per annum compounded annually.

Age of a man was ${\frac{2}{5}}^{th}$ of the age of the tree in his housing complex. The tree was 90 years old. If the man's age multiplied by a number $x$ equals 180, then find $x$.

Question 56

If x varies inversely as y and when x = 6, y = 8, then x = 8, the value of y is 10.

What is the probability of getting a prime number when a die is rolled?

In the II Quadrant, x is __ and y is positive.

Find the value of the given expression:

$\frac{1}{4-\sqrt{15}}-\frac{1}{\sqrt{15}-\sqrt{14}}+\frac{1}{\sqrt{14}-\sqrt{13}}-\frac{1}{\sqrt{13}-\sqrt{12}}+\frac{1}{\sqrt{12}-\sqrt{11}}-\frac{1}{\sqrt{11}-\sqrt{10}}+\frac{1}{\sqrt{10}-3}$

Question 32

A glass jar contains 6 red, 5 green, 4 blue and 5 yellow marbles of same size. Hari takes out a marble of red colour. What is the probability that the chosen marble is of red colour?



(a) $\frac{7}{10}$

(b) $\frac{3}{10}$

(c) $\frac{4}{5}$

(d) $\frac{2}{5}$

Question 103

Three cubes each of side 10 cm are joined end to end. Find the surface area of the resultant figure.

Find the angles x and y respectively.

Formula to find the perimeter of square is:

Which of the following points lies on the y-axis?

A square yard has area 1764 m². From a corner of this yard, an-other square part of area 784 m² is taken out for public utility. The remaining portion is divided in to 5 equal square parts. What is the perimeter of each of these equal parts?

What would be the equation of a line having slope $9$ and passing through the point $(4,5)?$

Rahul's dad was seeing the plan for their new house, the outline of the house is shown in the figure,

Rahul's Dad asked him to find the value of "$x$" if the perimeter of the outline is 101 m.

$x$ is equal to

In the diagram below, there are four circles, each with an angle formed in the center and a point on the remaining part of the circle. How many circles do you think justifies the statement : "The Angles subtended by an arc in the same segment of a circle are equal."?

What is the square root of 49?

Prove that the base angles of an isosceles trapezium are equal.

Ordinate of a point is negative in which quadrants?

If Fig. PQRS is a quadrilateral and T and U are respectively points on PS and RS such that PQ = RQ.
Also, $\angle$ PQT = $\angle$ RQU and $\angle$ TQS = $\angle$ UQS. Then

For a science exhibition, tickets for children cost 2 rupees and for adults, 5 rupees. 100 tickets were sold for one show, and 290 rupees was got. How many children were there for this show?

If a, b, c are rational numbers such that a² + b² + c² − ab − bc − ca = 0, prove that a = b = c.

Question 46

State whether the following statement is true (T) or false (F).

If x is an even number, then the next even number is 2(x+1).

Question 153(ii)

In a repeater machine with 0 as an exponent, the base machine is applied 0 times.

What do you think the value of $6^o$ is ?

You have seen that a hook up of repeater machines with the same base can be replaced by a single repeater machine. Similarly, when you multiply exponential expressions with the same base, you can replace them with a single expression.

Asif Raza thought about how he could rewrite the expression $2^{2}0\times 2^5$.



Asif Raza's idea is one of the product laws of exponents, which can be expressed like this

Multiplying Expressions with the same base $a^b\times a^c=a^{b+c}$

Actually, this law can be used with more than two expressions. As long as the bases are the same, to find the product you can add the exponents and use the same base.

e.g. $3^2\times 3^3\times 3^{10}=3^{2+3+10}=3^{15}$

Simplification of $\frac{(p+a)}{5}=3p$ yields

If two cardboard boxes occupy 500 cubic centimetres space, then how much space is required to keep 200 such boxes?

Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. Then, the probability that the ticket has a number which is a multiple of 3 and 7 is

Question 2(iii)

Find the product:

$(a^2+b)(a+b^2)$

Question 2

If the median of the distribution given below is 28.5, find the values of x and y.

$\begin{array}{cc}Classinterval& Frequency\\ 0-10& 5\\ 10-20& x\\ 20-30& 20\\ 30-40& 15\\ 40-50& y\\ 50-60& 5\\ Total& 60\end{array}$

Compute the following in your head:

(i) 67² − 33²

(ii) 123² − 122²

(iii)

(iv) 0.27² − 0.23²