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A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?

$If2x+3y=14and2x-3y=2,\text{find the value of xy.}$

Factorise:

$25(2a-b{)}^2-81b^2$

Expanded form of $243.7=(2\times {10}^2)+(4\times {10}^1)+$ + $(7\times {10}^{-1}$)

Which of the following functions are identical to f(x)?

$f\left(x\right)=\{\begin{array}{cc}x,& 1\le x<2\\ x^2,& 2\le x<3\end{array}$

(1 $\le$ x < 3 )

The perimeter of a rectangular swimming pool is $64m$. If its length and breadth are in the ratio of $5:3$, then find the length of the pool (in metre).

A treasure is split between 5 explorers equally. Each explorer further divides his share of the treasure into 4 equal parts and pays one of those parts as tax. What fraction of the treasure do the 5 explorers together pay as tax ?

If the area and the perimeter of a sector of a circle are $12{\text{cm}}^2$ and $14\text{cm}$ respectively, then possible values of:

The number of apples sold by a shop is given in the table below:

$$\begin{array}{cc}\text{Day}& \text{No. of apples sold}\\ \text{Monday}& 60\\ \text{Tuesday}& 35\\ \text{Wednesday}& 50\\ \text{Thursday}& 55\end{array}$$

If the picture of an apple represents 10 apples, then draw a pictograph for the above data.

Penny gives a box with 3 action figures to each of her four friends. How many action figures does Penny give in total?

What is the remainder when $4x^4-3x^3+2x^2-x$ is divided by x + 1?

The value of x will be

.

If x + (1/x) = 3, find x² + (1/x²) and x³ + (1/x³)

Can the sides of a triangle be in the ratio 1 : 2 : 3?

What will be the ratio of the areas of squares, when the diagonal of one square is twice of the other.

The area of a rhombus and that of a square are equal. The side of the square is 6 cm. If one of the diagonal of the rhombus is 4 cm, then the length of its other diagonal is ______ .

Find and correct the errors in the statement: x + 2x
+ 3x = 5x

Value of n^0 where n not equal to zero is always ___.

$\text{What is the ratio of}5\frac{3}{4}\text{years to 65 months?}$

Question 1

Match the following:

Find the cube of 3x - 2y - 4z

Question 67

State whether the following statement is true or false:

For an integer a, $a^3$ is always greater than $a^2$.

Two water taps together can fill a tank in $9\frac{3}{8}$ hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

If a scooterist drives at the rate of 25 km per hour, he reaches his destination 7 minutes late, and if he drives at the rate of 30 km per hour, he reaches his destination 5 minutes earlier. How far is his destination?

Construct a quadrilateral ABCD in which AB = 3.4 cm, CD = 3 cm, DA = 5.7 cm, AC = 8 cm and BD = 4 cm.

Find the value of $x$ in the equation

$\frac{x}{3}+4=2$

The following data relates to the expenses for a household in Bangalore.

$\begin{array}{cc}\text{Items}& \text{Expenditure(in Rs)}\\ \text{Food}& \text{4000}\\ \text{Clothing}& \text{2000}\\ \text{Rent}& \text{1500}\\ \text{Education}& \text{1500}\\ \text{Miscellaneous}& \text{1000}\end{array}$

The central angle of Clothing will be ___.