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If the coefficients of $x^7$ in ${(x^2+\frac{1}{bx})}^{11}$ and $x^{-7}$ in ${(x-\frac{1}{b{x}^2})}^{11},b\ne 0,$ are equal, then the value of $b$ is equal to

Anita and Divya are preparing for their exam. Anita says $3\times 2\frac{1}{5}=\frac{33}{5}$. But, Divya says $3\times 2\frac{1}{5}=\frac{30}{5}$.
Who is right? ___

Select the rational numbers which lie between $\frac{2}{5}$ and $\frac{3}{10}$. Use the LCM method.

In which of the following quadrilaterals, a diagonal is not an angle bisector?

Question 3 (v)
Identify which of the following pairs of angles are complementary and which are supplementary:
${45}^{\circ },{45}^{\circ }$

Question 96

Solve the following question:

Using prime factorization, find the square roots of

a) 11025

b) 4761

Find the value of the unknown x in the following diagrams:

If 3 of your friends eat one slice each from a medium-sized pizza containing 6 equal slices, then what fraction of the pizza is eaten by your friends?

The figure shows two paths drawn inside a rectangular field 60 m long and 30 m wide. If the width of each path is 5 m, then find the perimeter of the shaded portion.

The measure of y in the given figure is .

Question 159(vi)

Find a single repeater machine that will do the same work as each hook-up.

If a box is 20 m long, 10 m wide, and 8 m tall, how many cubic metres of water can it hold?

Danny has some apples. Rajesh has 9 apples more than Danny. Manoj says that he has 11 more apples than the number of apples Danny and Rajesh have together. How many apples does Manoj have?

A die is thrown 1000 times with the following frequency for the outcomes 1, 2, 3, 4, 5 and 6 as given below :

$$\begin{array}{ccccccc}\text{Outcome}& 1& 2& 3& 4& 5& 6\\ \text{frequency}& 179& 150& 157& 149& 175& 190\end{array}$$

(i) Find the probability of getting a 4 or a 6
(ii) Find the probability of getting a multiple of 3 [ 2 MARKS]

On the day of the result, Ted got his report card. His sister, who studied in another school, also got her report card surprisingly. And she was jumping around saying she has scored a better total than Ted.

Which parameter would be easier to decide about who has done better?

Question : 8

For any two integers $xandy$, which of the following suggests that operation of addition is commutative ?

(a)$x+y=y+x$

(b)$x+y>x$

(c)$x-y=y-x$

(d) $xy=yx$

Find the HCF of $81$ and $237$ and express it as a linear combination of $81$ and $237$. What does inear combination mean?

Solve the following problems.

What is the rate of interest, if Rs. 1,200 amounts to Rs. 1,500 in 2 years?

1. 8

If a die is thrown 50 times and six appears 8 times, then the probability of getting a six is _______.

Fill in the blanks with suitable signs = or ≠.

The figure below is made up of 3 squares of sides 5 cm. What is the perimeter of the figure?

Arun
bought a car for Rs 3,50,000. The next year, the price went upto

Rs
3,70,000. What was the percentage of price increase?

Verify

18×(7×(-3) =18×7+18×(-3)

Is LHS =RHS

Consider a building with $20$ stairs above ground level and $20$ stairs below ground level. Considering the ground level as zero, if you are standing at the $6^{\text{th}}$ step below the ground level, how will you represent it?​

The idea of perimeter plays an important for ____.

Point A represents which of the following rational numbers?

Change the
following statements using expressions into statements in ordinary
language.

(For example, Given Salim scores r runs in a cricket match,
Nalin scores

(r
+ 15) runs. In ordinary language − Nalin scores 15 runs more
than Salim.)

(a) A note
book costs Rs p. A book costs Rs 3 p.

(b) Tony
puts q marbles on the table. He has 8 q marbles in his
box.

(c) Our
class has n students. The school has 20 n students.

(d) Jaggu is z years old. His uncle is 4 z years old
and his aunt is (4z − 3) years old.

(e) In an
arrangement of dots there are r rows. Each row contains 5
dots.

In the given figure, what is the value of 't' ?

Which of the following are factors of $11984670$

Find the perimeter of a square with side 8 cm.

Which of the following is/are a polynomial?