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Identify the quadratic surd(s).

The volume of the two cubes are in the ratio 64:27. Find the ratio of their surface area.

108 can be written as:

A quadrilateral ABCD can be constructed given

Write an equivalent expression for the following problem:

$5^5$x $5^2$

A man sold 2 watches at ₹450 each. He sold one at a loss of 15% and the other at a profit of 15%. His profit or loss is :

Which of the following is a linear expression in one variable?

In 10 days, the earth picks up = $2.6\times {10}^8$ pounds of dust from the atmosphere. How much dust will it pick up in 45 days.

Simplify: ${(3pq+3qr)}^2-18p{q}^{2}r$

In triangle ABC, if DE is parallel to BC, then which of the following is stated by Basic Proportionality Theorem?

If two quantities a and b are in direct variation, then the ratio $\frac{a}{b}$ is always:

The height of a circular cylinder is 2 cm and radius of its base is 7 cm. Then, the total surface area of the cylinder will be (in centimetre square) ___

In a rhombus PQRS, if PQ = 3x − 7 and QR = x + 3, find PS.

Which of the following are algebraic expressions?

Find the smallest number by which 28812 must be divided so that the quotient becomes a perfect square.

If sum of the number 985 and two other numbers obtaind by arranging the digits of 985 in cyclic order is divided by 111 , 22 and 37 respectively.

Find the quotient in each case.

Factorize the given expression:

$9(2x-3y{)}^2-12(2x-3y\left)\right(2x+3y)+4(2x+3y{)}^2$

Find the next two terms of the sequence: $4,13,8,17,12,21,...$

Arrange in ascending order

Construct a right angle triangle ABC in which ∠B = 90°, BC = 4 cm and AC = 5 cm.

Factorise : $x^2-x-72$

Prove the following identities :

$\left(i\right)(a+b{)}^2=a^2+b^2+2ab$

$\left(ii\right)(a-b{)}^2=a^2+b^2-2ab$ [2 MARKS]

Evaluate :

$\frac{a^{2n+1}\times a^{(2n+1)(2n-1)}}{a^{n(4n-1)}\times (a^2{)}^{2n+3}}$

What is the expansion for the identity ${(a–b)}^2$?

Is it possible to construct a square if only one of its diagonals is given?

The recipe of a cake includes the following steps:



$\text{Step A:}1\frac{1}{4}\text{cups of flour is mixed with}2\frac{5}{8}$

$\text{cups of chocolate.}$



$\text{Step B: Add}\frac{1}{8}\text{cups of sugar to the flour and}$

$\text{chocolate mixture.}$



Calculate the total amount of the mixture after both the steps.

If $y=\frac{2x+1}{2x-1}$, we can express x in terms of y as$x=a\left(\frac{y+1}{y-1}\right).Find\frac{1}{a}$

Given an example of a number which is divisible by:
(i) 2 but not by 4.
(ii) 3 but not by 6.
(ii) 4 but not by 8.
(iv) both 4 and 8 but not by 32.

If Zero is divided by $\frac{7}{2}$, the resulting number is a:

Construct a quadrilateral ABCD given that AB = 4 cm, BC = 3 cm, $\angle A={75}^{\circ },\angle B={80}^{\circ }$ and $\angle C={120}^{\circ }$.

$\text{Evaluate (using factors) :}{301}^2\times 300-{300}^3.$

Let’s find out

(i) (−2) × (−5)

(ii) (−5) × (−5)

(iii) (−1) × (−1)

(iv)

(v)

(vi) (−2) × (−5)

(vii) (−12) ÷ (−4)

(viii) (−12) ÷ (−12)

(ix)

(x)

(xi)

(xii) −2.5 × − 0.2

Find the amount and the compound interest on $Rs.10,000$ for $1\frac{1}{2}$ years at $10\%$ per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?