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Two taps can fill a cistern in 10 hours in 8 hours respectively a third tapthat can empty it in 15 hours how long will it take to fill the empty cistern ifall of them are opened together?

$(4\times {10}^3+3\times 1+1\times {10}^{-1}+6\times {10}^0)=$_

A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.
$[Assume\pi =\frac{22}{7}]$

Bisectors of the angles $B$ and $C$ of an isosceles triangle with $AB=AC$ intersect each other at $O.$ Show that external angle adjacent to $\angle ABC$ is equal to $\angle BOC$.

A large circular farm is next to a river. A farmer can fence the farm with iron wire of length 18.84 m. How much area will be enclosed by the fence (in $m^2)$?

You asked your mom to give a 2 digit number. She said 19. Then you asked your mom to give a 3 digit number and she said 109. Now, you both had to multiply 19 × 109.

The easiest method to find the answer using brackets would be:

Meenakshi cycles to her school at an average speed of 12 km/hr and takes 20 minutes to reach her school. If she wants to reach her school in 12 minutes, her average speed should be:

which of the following about ratio are true ?

a)Ratio is a fraction

b) Ratio has no unit .

c) Ratio can be formed between two quantities which have different units .

d) We can find a ratio in simplest form

If 8 pens cost ₹ 84 , how much does 14 pens cost ?

Question 27
Factorise the following:

$\left(i\right)9x^2–12x+3$

$\left(ii\right)9x^2–12x+4$

Rashi went on shopping with her mother. There she saw a toy whose actual cost was Rs 200. If the shopkeeper sells it at a loss of 15%, find the price at which it is sold. [4 MARKS]

(a) Show with an example that two triangles can't be congruent using AAA criterion.

(b) Which congruence criterion will you use in the following?

Given: AC = DF

AB = DE

BC = EF

So, ΔABC ≅ ΔDEF

[3 MARKS]

$2\frac{1}{3}+3\frac{1}{3}$ is same as

Question 91

State whether the statement is True or False.

Two right angles are congruent.

(a) The ratio of 20 minutes to 2 hrs.
(b) Find $x$ if $5:4::125:x$
[2 MARKS]

If CD is a median of $\Delta$ABC, then

Simplify $(x+3)(x+5)$.

The ___ always passes through the centre of the circle.

Solve the equation $\frac{3}{x+1}=\frac{6}{5x-1}$.

The graph shown below gives the monthly sale of various Apple products. What kind of graph is it?

Which of the following powers do not have negative exponents?

Evaluate $\frac{-1}{2}$ + $\frac{3}{4}$ + $\frac{2}{3}$

Find the interest on ₹4500 at 5% interest rate deposited in the bank for 2 years.

Which of the following represents congruent figure?

Solve and sort the result in ascending order. : (smallest on top)

If 2 : 9 :: x : 18 then find the value of x.

A fraction, whose numerator or denominator or both are not integers, is called a ___ fraction.

The value of $(3^0-2^0)\times 5^2$ is:

$\text{Solve for x:}$

$\frac{x}{3}+\frac{7}{2}=\frac{3}{2}$

If you add -6 to 7 and then subtract -8 from the result, what will be the answer?

In the given figure, QTSR is a parallelogram. PQR is a straight line and QU = UT. Which of the following statements are correct?

Identify the region which represents the power $2^2.$

What should be added to $6xy+3y^2+7x^2+2zx$ to get $2x^2+3xy$?

A right triangle with the lengths of perpendicular sides 5 cm and 6 cm is constructed. Then, the length of the third side is

Rectify the following errors.

(a) Credit sales to Mohan Rs. 7,000 were recorded as Rs. 7,200.

(b) Credit purchase from Rohan Rs. 9,000 were recorded as Rs. 9,900.

(c) Goods returned to Rakesh Rs. 4,000 were recorded as Rs. 4,040.

(d) Goods returned from Mahesh Rs. 1,000 were recorded as Rs. 1,600.

Convert $4\frac{3}{8}$ to decimal.

Amar buys a car for ₹5,00,000. The car's value decreases by 10 % after every year's use. What will be the value of car after 2 years?

In power notation, $\frac{81}{16}$ can be expressed as ___.

Tina buys 5 TitTat chocolates which cost ₹x each, 3 Crunch chocolates which cost ₹y each and 10 Marymilk chocolates which cost ₹z each. Later she returns 4 Marymilk but buys 3 more Crunch.

What is the expression that represents the final amount (in ₹)?

Question 18

Fill in the blanks to make the statement true.

In the formula, area of circle $=\pi r^2,$ the numerical constant of the expression $\pi r^2$ is ___

What is the number of lines of symmetry in an equilateral triangle?

If one angle of a triangle is equal to the sum of the other two angles which are equal, then the triangle is a/an _________ .