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Prove that root 3 is an irrational number .Hence prove that 3(2 root 3) is an irrational number.

a mem travels 600km to his home partly by train and bus he takes 8 hours, if he travel 120km by the train and rest by bus. further it take 20min longer if he travel 200km by the bus find the speeds of the train and the bus

Find the least number that is divisible by the first 5 even numbers

If the replacement set is the set of whole number (W) the solution set of $4x-2<2x+10$ will be

A mapping is selected at random from the set of all the mappings of the set A = {1, 2, …….., n} into itself. The probability that the mapping selected is an injection is:

ABCD is a cyclic quadrilateral whose side AD is a diameter of the circle through A, B, C and D. If $\angle ABC={110}^{\circ }$, find $\angle BDAC$.

If a line passing through $(2,4)$ divides the segment between the axes in the ratio 3:4 internally, then the equation of the line is

If three vertices of a parallelogram are on a circle and fourth vertex is at the centre, then find the value of x.

Prove that: tantheata+sintheata/tantheata-sintheata=sectheata+1/sectheata-1

$Theratioofsurfaceareasof1cubeofvolume64c{m}^{3}and64cubesofvolume1c{m}^{3}is$

The theoretical formula for probability is based on the assumption that all outcomes are __

Sum of first n terms of an A.P is $2n^2$. Find its $n^{th}$ term.

The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window. At certain instant the angles of elevation of a balloon from these windows are observed to be ${60}^{\circ }$ and ${30}^{\circ }$ respectively. Find the height of the balloon above the ground.

What is the area of the shaded region, if the shaded part is twice that of the corner triangle? (side of square = 6 cm)

In Fig. ABC is a right angled triangle in which $\angle A={90}^{\circ }$, AB = 21 cm and AC = 28 cm. Semi - circles are described on AB, BC and AC as diameters. Find the area if the shaded region.

(i) A box contains 80 discs, which are numbered from 1 to 80. If one disc is drawn at random from the box, find the probability that it bears a perfect square number.
(ii) A box contains 90 discs which are numbered 1 to 90. If one disc is drawn at random from the box, find the probability that it bears (a) a two- digit number (b) a number divisible by 5

During conversion of a solid from one shape to another, the volume of the new shape will

(a) decrease (b) increase

(c) remain unaltered (d) be doubled

In the equation $ax+by+c=0$, if $y=\frac{(cx+d)}{b}$ then $x=$

If a square is inscribed in a circle, find the ratio of the areas of the circle and the square.

If triangle ABC is an isosceles triangle in which AB = AC = 13 cm, then find the value of $\frac{\text{area of}\Delta ADC}{\text{area of}\Delta EFB}.$ (upto two decimal places)

1. 0.52

If the ratio of the radius of a cone and a cylinder of equal volume is 3:5, then find the ratio of their heights.

does the point (3,1) lie on 5x+ 4y = 17?

Mayank made a birdbath for his garden in the shape of a cylinder with a hemispherical depression at one end (see Fig.). The height of the cylinder is $1.45m$ and its radius is $30cm$. Find the total surface area of the birdbath. (Take $\pi$ = $\frac{22}{7}$)

In the assumed mean method, if A is the assumed mean, then deviation $d_i$ is :

Question 132

In a test, +3 marks are given for every correct answer and - 1 mark is given for every incorrect answer. Sona attempted all the questions and scored +20 marks, though she got 10 correct answers.
How many incorrect answers has she attempted?
How many questions were given in the test?

Question 89

A carpenter had a board which measured $3m\times 2m$. She cut out a rectangular piece of $250cm\times 90cm$. What is the ratio of the area of a cut-out piece and the remaining piece?

4, 3, 2, 1

What order are the above numbers arranged in?

___ (ascending/descending)

If L.C.M. (150, 100) = 300, then find H.C.F. (150, 100).

Compute the mode from the following data:
$\begin{array}{cccccccc}\text{Size}& 45-55& 55-65& 65-75& 75-85& 85-95& 95-105& 105-115\\ \text{Frequency}& 7& 12& 17& 30& 32& 6& 10\end{array}$

In the given right triangle, the value of $\sin \theta$ is .

A wheel has diameter 84 cm. Find how many complete revolutions must it make to cover 792 m.

Find the slope and the inclination of the line AB if :

(i) A = (-3, -2) and B = (1, 2)

(ii) A = $(0,-\sqrt{3})$ and B = (3, 0)

(iii) A = $(-1,2\sqrt{3})$ and B = $(-2,\sqrt{3})$

In the figure, the graph of a polynomial p(x) is shown. The number of zeroes of p(x) is:

The mean of 6 numbers is 16. With the removal of a number the mean of remaining numbers is 17. The number removed is:

4 kg of fruits are shared equally among 5 children. How many grams of fruits does each child get?

If $y=2^{\frac{1}{{\log }_{x}4}}$. Then

A spiral is made up of successive semicircles, with centers alternatively at A and B, starting with center at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ... as shown in the figure.What is the total length of such a spiral made up of thirteen consecutive semicircles?

Find the equation of the line.

In $\Delta$ ABC, $\frac{AD}{DB}=\frac{AE}{EC}$ and $\angle$ ADE = $\angle$ ACB. Then $\Delta$ ABC is a/an

An A.P., a G.P., and an H.P. have $a$ and $b$ for their first two terms. Their $(n+2{)}^{th}$ terms will be in G.P. if $\frac{b^{2n+2}-a^{2n+2}}{ab(b^{2n}-a^{2n})}$

If α and β are the zeroes of the quadratic polynomial p(x) = x²– x – 2, find a polynomial whose zeroes
are 2α + 1 and 2β + 1.

There are 540 mangoes and 280 apples in a box. The teacher wants to distribute these equally among children (each child gets the same number of apples and a same number of mangoes). What is the maximum number of children among which she can distribute the fruits?