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Solve
and check result:

The fraction for the shaded part in step 3, in the given process is

The number of arcs to be made to divide a line segment in the ratio 5:7 using a single ray are ___.

Question 2

Find the values of the letters in the following and give reasons for the steps involved.

$4A\underset{–}{+98}\underset{–}{CB3}$

Factorise:

$(x^2+\frac{1}{x^2})-4(x+\frac{1}{x})+6$

Let $a=\sqrt{7}-\sqrt{6}$ and $b=\sqrt{7}+\sqrt{6}.$ Find the value of $a^3-b^3.$

Match the solid figures with their $2$-D nets.

Question 2 (iii)

Without doing any calculation, find the numbers which are surely not perfect squares:

408

Preeti has solved a question in her exam using the following method. In which step has she gone wrong and what is the correct answer obtained after the calculation?
Question: $(2p{)}^3+3p^3=11p^3+a$. Find the value of a.
step i: $6p^3+3p^3=11p^3+a$
Step ii: $9p^3=11p^3+a$
step iii: $-2p^3=a$

1. 11

What is the usual form of 7.54 $\times$ ${10}^{-3}$?

Question 87

Solve the following:

Find a number whose fifth part increased by 30 is equal to its fourth part decreased by 30.

Diagram of the adjacent picture frame has outer dimensions = 24 cm × 28 cm and inner dimensions 16 cm × 20 cm. Find the area of each section of the frame, if the width of each section is same.

Find two smallest perfect squares whose product is a perfect cube.

Two adjacent sides of a parallelogram are 16 and 24 centimetres long. The height from the longer side is 15 centimetres. What is the height from the shorter side?

Express 32000 as a product of powers of prime factors.

The product of a monomial and a binomial is:

Will n be an integer?

I. 3n is an odd number.

II. 2n is an even number.

Expand $(a-b)(a^2+ab+b^2).$

Question 1

$\left[\right(-3{)}^2{]}^3$ is equal to
(a) $(-3{)}^8$
(b) $(-3{)}^6$
(c) $(-3{)}^5$
(d) $(-3{)}^{23}$

In a polyhedron, ______ is the intersection of two faces.

The two parallel sides and distance between them are in the ratio 3:4:2. If the area of the trapezium is 175cm². Find its height

Factorization:

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

Question 42

Devangi travels 50 m distance in 75 steps, then the distance travelled in 375 steps is___km.

Which among the following is the standard form of the polynomial $2x^5-7x^4+8x^6-3x^9$ ?

Factorise:
$x^2-17x+16$

A relation $R$ is defined as $R=\left\{\right(x,y):x<y\}$. Which among the following options is an ordered pair of $R$?

Solve the given equation
$3x+5=17$

Question 76

Write the name of

a) vertices,

b) edges and

c) faces of the prism, shown in the given figure.

Match the values with the corresponding laws of exponents.

$2y^5+10y^4+6y^3+y^2+5y+3by2y^3+1$