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The dimensions of a cinema hall are 100 in, 50 m and 18 m. How man persons can sit in the hall, if each person requires 150 $m^3$ of air ?

Find the degree of the polynomial expression $7x^5+2x^4+6x^8$.

Question 2
Find the values of the letters in the following and give reasons for the steps involved.
$4A\underset{–}{+98}\underset{–}{CB3}$

Find the number whose square is the sum of the cube of the first 5 natural numbers.

Question 2 (v)

The following number is obviously not a perfect square. Give reasons.

64000

Evaluate
(i) (ii)

Question 7

30 children were asked about the number of hours they watched TV programs last week. The results are recorded as under:



$\begin{array}{ccccc}\text{Number of hours}& 0-5& 5-10& 10-15& 15-20\\ \text{Frequency}& 8& 16& 4& 2\end{array}$



Can we say that the number of children who watched TV for 10 or more hour in a week is 22? Justify your answer.

Which of the following polynomials has the highest degree?

Find the squares of the following numbers using the identity $a+b{)}^2=a^2+2ab+b^2$

(i) 405 (ii) 510
(iii) 1001 (iv) 209
(v) 605

Which of the following is a rational number between $\frac{1}{6}$ and $\frac{1}{4}$?

Question 62

Solve the following:

$\frac{x}{2}-\frac{1}{4}(x-\frac{1}{3})=\frac{1}{6}(x+1)+\frac{1}{12}$

In the given figure if $\angle ADC={110}^{\circ },$ then $\angle ABC=$

Find the cube of :

(i) $a+2$

(ii) $2a-1$

(iii) $2a+3b$

(iv) $3b-2a$

(v) $2x+\frac{1}{x}$

(vi) $x-\frac{1}{2}$

If AOB is a diameter of the circle and AC = BC, then $\angle CAB$ is equal to:

Write five rational numbers which are greater than $\frac{-3}{2}$

If $(x^2-y^2)=18$ and $(x-y)=3$, find the value of $x^2+y^2+2xy$.

Which of the following is not a polynomial?

Question 104

A table cover of dimensions 3 m 25 cm x 2 m 30 cm is spread on a table. If 30 cm of the table cover, is hanging all around the table, find the area of the table cover, which is hanging outside the top of the table. Also, find the cost of polishing the top at Rs.16 per square metre.

A room is 6 m long, 4 m broad and 3 m high. Find the cost of laying tiles on its floor and four walls at the cost of Rs. 80/m².

Find the greatest common factors (GCF / HCF) of the following polynomials :

$6x^2{y}^2,9x{y}^3,3x^3{y}^2$

Solve $\frac{2x}{3}-\frac{3x}{7}=\frac{5}{21}$.

The common difference for the arithmetic progression

$3+2\sqrt{2},3+4\sqrt{2},3+6\sqrt{2},3+8\sqrt{2}$ is

5% of apples in a basket were rotten and another 10% were discarded by the fruit vendor. If 1700 apples remain in the basket, then the original number of apples in the basket was ___

What is the factorization of $x^2+7x-8$?

Tick the correct answer in each of the following:

The sum that amounts to Rs 4913 in 3 years at $6\frac{1}{4}\%$ per annum compounded annually, is

(a) Rs 3096 (b) Rs 4076 (c) Rs 4085 (d) Rs 4096

Twelve added to three times a number is equal to three added to four times a number. Find the number.

The inside perimeter of a running track (shown in Fig.) is 400 m.The length of each of the straight portion is 90 m and the ends are semi-circles.If track is everywhere 14 m wide,find the area of the track.Also,find the length of the outer running track.

Can we draw a quadrilateral ABCD with following measurements: AB = 3cm, BC = 5cm, AD = 4cm, CD= 7cm and BD=8cm?