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Question 77

State whether the following statement is true or false:

Cube of an even number is odd.

Factorise:
$1+2x+x^2$

$Solve:4yz(z^2+6z-16)÷2y(z+8)$

Evaluate :
(i) 55% of 160 + 24% of 50 - 36% of 150
(ii) 9.3% of 500 - 4.8% of 250 - 2.5% of 240

Question 95

Solve the following:

Express $\frac{16}{81}and\frac{-16}{81}$ as powers of rational number.

Find the square root of :

(i) $\frac{1764}{2809}$ (ii) $\frac{507}{4107}$

(iii) $\sqrt{108\times 2028}$ (iv) $0.01+\sqrt{0.0064}$

If the side of a square is "a”, the area and perimeter can be found by using the formulae,

Expand $(1+x+x^2{)}^3$ using binomial expansion.

A person sells an article for Rs. 550, gaining $\frac{1}{10}$ of its C.P. Find gain percent.

Range = Largest value - ______ value

Data arranged in an unorganised manner is called

Adrienne has free passes to a music concert and can take $2$ friends along, but she has $5$ friends who could go with her. In how many ways can she select $2$ friends out of $5$?

Question 2
A number of the form $\frac{p}{q}$ is said to be a rational number, if
(a) p and q are integers.
(b) p and q are integers and q ≠ 0
(c) p and q are integers and p ≠ 0
(d) p and q are integers and p ≠ 0 also q ≠ 0.

Which one of the following expansions is correct?

Are the triangles below congruent? Give the reason.

A sells a radio to B at a loss of 20%, B sells it to C at a loss of 30% and C sells it to D at a loss of 10%. If A pays ₹ 2000, then the Cost Price for D is :

The organisers Orphan essay competition decide the winner in the competition gets the price of rupees hundred and the participant who does not win gets a price of rupees 25 the total prize money distributed is rupees 3000 find the number of winner if the total number of participants 63

Question 83

Solve the following:

Kaustabh had 60 flowers. He offered some flowers in temple and found that the ratio of the number of remaining flowers to that of flowers in the beginning is 3:5. Find the number of flowers offered by him in the temple.

Compute the value of ${\left(6\frac{1}{2}\right)}^2-{\left(4\frac{1}{2}\right)}^2$

1. 486

$1+\frac{1}{5}+\frac{1.3}{5.10}+\frac{\mathrm{1.3.5}}{\mathrm{5.10.15}}$ + .... is equal to :

The kind of graph the following figure represents is a __ graph

Rahim, a mechanical engineer, wants to fit some pipes into a rectangular door of dimension 96 X 60 square cm. If on fixing 5 pipes, at equal distances, along the longer side of the door, the gap between each pipe is 19.2 cm, how many pipes should be fixed in the same manner so that the spacing between the pipes is 8 cm?

If 26136 x k is a perfect cube, then the smallest value of k is

The dimensions of a room are l = 8 m, b = 5 m, h = 4 m. Find the cost of distempering its four walls at the rate of Rs 40/m².

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

Find a relation between $a$ and $b$ such that the point $(a,b)$ is equidistant from the points $(1,1)$ and $(7,9).$

If a – b = 4 and ab = 21, find the value of a³ - b³.

15% increase in price of an article, which is Rs 1620, is the increase of Rs ___

The value of $[4^{-1}+3^{-1}+6^{-2}{]}^{-1}$ is ___.