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Shalini has 1.5L of soda in a bottle. How many glasses can be filled, each of which has a capacity of 50 ml? How many glasses of capacity 60ml each be filled? [3 MARKS]

What is the volume of a cylindrical bottle having base radius 7 cm and height 20 cm.

Seven cubes of same volume having side $5cm$ are joined end to end. Find the Surface area of the resulting cuboid.

If a box of sweets is divided among 24 children, they will get 5 sweets each. If the number of the children is reduced by 4, each child would get___sweets?

For the given pair of linear equations,
$a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$.
The values of x and y are given by:

If 40 bags of cotton costs Rs.2200 then how much would 25 bags of cotton cost?

1. 300

If A and B are two points on the circle, then the line joining A and B is called as the ____.

Solve the following pairs of equations:
$\frac{1}{x}+\frac{3}{y}=1$
$\frac{6}{x}-\frac{12}{y}=2$
(Where $x\ne 0,y\ne 0)$

Find the values of $x$ and $y$ that satisfy both the given equations.
$y-2x=4$ and $y-3x=2$

P and Q are the mid-points of sides AB and BC of triangle ABC respectively and R is the mid-point of AP, then ar ($△$PRQ) is equal to

In the following figure, both the triangles are congruent where, $AC=2x-y,AB=2x+y$, $RP=2units,PQ=6units$.
What is the value of x and y?

A is of the same age as B and C is of the same age as B.Euclid's which axiom illustrates the relative ages of
A and C?

(a) First axiom

(b) Second axiom

(c) Third axiom

(d) Fourth axiom

In the given figure, SP is bisector of $\angle$ RPT and PQRS is a cyclic quadrilateral. Prove that :

SQ = SR.

1. 8

Find the value of p(2) if p(x) has (x-2) as its factor.

Given that $y=\frac{(cx+d)}{b}$;

where $b\ne 0\&(a+c)\ne 0$,

then, what is the value of x, if $ax+by+c=0$?

PQR is a triangle in which PQ = PR and S is any point on the side PQ. Through S, a line is drawn parallel to QR and intersecting PR at T. Prove that PS = PT.

If $\frac{2^{m+n}}{2^{n-m}}=16,\frac{3^p}{3^n}=81anda=2^{\frac{1}{10}},then\frac{a^{2m+n-p}}{(a^{m-2n+2p}{)}^{-1}}=$

The quadrilateral formed by joining the mid-points of the sides of a quadrilateral
$PQRS$, taken in order, is a rhombus, if

$\text{In the given figure, side BC of}\Delta ABC\text{has been produced to a point D.If}\angle A=3y^{\circ },\angle x^{\circ },\angle C5y^{\circ }and\angle CBD=7y^{\circ }.Then.thevalueofxis$

$\left(a\right){60}^{\circ }\left(b\right){50}^{\circ }\left(c\right){45}^{\circ }\left(d\right){35}^{\circ }$

The ratio of 5 cm to 5 m is:

We get a rhombus by joining the mid-points of the sides of a

If ${9x}^2+{25y}^2=181$ and xy = - 6. Find the value of 3x + 5y

Represent 4$\frac{3}{5}$ in form of decimals.

If $3^{-x}$ = $\frac{1}{81}$, the value of x is ________ .

Kamala borrowed Rs. 26400 from a bank to buy a scooter at a rate of 15% p.a. compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan?

If $\overline{x}$ is the mean of $x_1,x_2\dots ,x_n$ then for $a\ne 0$, the mean of $a{x}_1,a{x}_2\dots ,a{x}_n,\frac{x_1}{a},\frac{x_2}{a},\dots ,\frac{x_n}{a}$ is
(a) $(a+\frac{1}{a})\overline{x}$
(a) $(a+\frac{1}{a})\frac{\overline{x}}{2}$
(c) $(a+\frac{1}{a})\frac{\overline{x}}{n}$
(d) $\frac{(a+\frac{1}{a})\overline{x}}{2n}$

In the given figure, ABCD is a quadrilateral in which AB = AD and BC = DC. Prove that (i) AC bisects $\angle Aand\angle C$, (ii) BE = DE, (iii) $\angle ABC=\angle ADC$.

Which of the following expressions is a polynomial ?
(a) $\sqrt[3]{3y}+4$
(b) $\sqrt{y}-3$
(c) $y$
(d) $\frac{1}{\sqrt{y}}+7$

$△$ABC is a right angled triangle, right angled at B. BD is perpendicular as shown. If AD: DC = 1:2, then $\frac{{AB}^2}{{BC}^2}$ is:

A triangle can have:

The sum of the digits of a two digit number is 5. Now, when the reverse of the number is subtracted from the original one then the difference is 27. What is the original number?

The inclination of the line whose slope is zero is

A kite in the shape of a square with a diagonal 32cm and an isosceles triangles of base 8cm and sides 6cm each is to be made of three different shades as shown in the given figure. How much paper of each shade has been used in it?

Draw the graph of the equation 2x + y = 6. Shade the region bounded by the graph and the coordinate axes. Also, find the area of the shaded region.

Look at several examples of rational number in the form $\frac{p}{q}$ $(q\ne 0)$, where p and q are integers with no common factors other than 1 and having terminating decimal representations. Can you guess what property q must satisfy ?

Question 77

Rectangle MNOP is made up of four congruent rectangles. If the area of one of the rectangles is $8m^2$ and breadth is 2 m, then find the perimeter of MNOP?

Question 3

Find the missing values:

$$\begin{array}{cccc}S.No.& Base& Height& Areaoftheparallelogram\\ a.& 20cm& & 246c{m}^2\\ b.& & 15cm& 154.5c{m}^2\\ c.& & 8.4cm& 48.72c{m}^2\\ d.& 15.6cm& & 16.38c{m}^2\end{array}$$

Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of $14\%$ p.a. and $11\%$ p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?

An irrational number between 2 and 3 is____