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If the hypotenuse of a right angled triangle is $h$ and perpendicular sides are $a$ and $b$, then

The ratio in which the line 2x+y-4=0 divides the line segment joining A(2,-2) and B(3,7) is

If f(x) is a function satisfying f(x + y) = f(x)f(y) for all x, y ∈ N such that f(1) = 3 and $\sum _{x=1}^n$f(x) = 120. Then find the value of n.

Find the HCF of the following polynomials.
P(x) = $(x^4-81)$
Q(x) = $(x^3-27)$

using the formula, sin A=whole root 1-cos A/2, find the value of sin30,it being given that cos60=1-2

If $tan4\theta =cot(\theta -{10}^{\circ })$, where $4\theta$ and$(\theta -{10}^{\circ })$ are acute angles then the value of $\theta$ in degrees is

The length of the complete circle is called __ of the circle.

Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or a non-terminating decimal expansion:
$\frac{7^3}{2^3\times 5^2}$ and $\frac{3\times 7^3}{2^3\times 3}$

1. 7

In a rectangle ABCD, AB = 20 cm, $\angle$ BAC = ${60}^{\circ }$. The length of side BC is :

If the cost of one notebook is Rs 40, then the cost of 19 similar notebooks is ___.

Match the expressions given on the left side with their L.C.M. given on the right side.

The equation of a line AB is 4x - 4y + 9 = 0, the angle made by this line with x -axis is _________.

In below shown figure, $\frac{PS}{SQ}$= $\frac{PT}{TR}$ and$\angle$PST= $\angle$PRQ. Then $\Delta$PQR is a/an __ triangle.

If the image of a point P is P itself, then P is an ___ point.

In an equilateral triangle ABC, match the following ratios to the values.

A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume.
The heap is to be covered by canvas to protect it from the rain. Find the area of the canvas required.
$[Assume\pi =\frac{22}{7}]$

Which of the following statements is correct?

The sums of first n terms of three A.P.s are $S_1,S_2$ and $S_3$. The first term of each). their common differences are 2, 4 and 6 respectively. Prove that $S_1+S_3=2S_2$ .

$2(a^2+b^2)$ =${(a+b)}^2$
Which of the following option will satisfy the above condition?

Solve the following quadratic equation by factorization.
$x-\frac{1}{x}=3,x\ne 0$

A canal is 300 cm wide and 120 cm deep.The water in the canal is flowing with a speed of 20 km/hr. How much area will it irrigate in 20 minutes if 8 cm of standing water is desired?

what is the value of tan $\theta$ in the given triangle?

From a circular piece of cardboard of radius 3 cm, two sectors of ${90}^{\circ }$ have been cut off. Find the perimeter of the remaining portion nearest hundredth centimeters. (Take $\pi =\frac{22}{7}$)

Taxi charges in a city consisting of fixed charges and the remaining depending upon the distance travelled in kilometres. If a man travels 80 km, he pays Rs.1330, and travelling 90 km, he pays Rs.1490.Find the fixed charges and rate per km.

The solution set x= $\frac{(b_1{c}_2-b_2{c}_1)}{(a_1{b}_2-a_2{b}_1)}$ and y= $\frac{(c_1{a}_2-c_2{a}_1)}{(a_1{b}_2-a_2{b}_1)}$ to the pair of linear equations $a_1$x + $b_1$y + $c_1$=0 and $a_2$x + $b_2$y + $c_2$=0 can be written as

Solve the following systems of equations:

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

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

A survey regarding the height (in cm) of 51 girls of class X of a school was conducted
and the following data was obtained:
$$\begin{array}{cc}& \\ \text{Height in cm}& \text{Number of Girls}\\ \text{Less than 140}& 4\\ \text{Less than 145}& 11\\ \text{Less than 150}& 29\\ \text{Less than 155}& 40\\ \text{Less than 160}& 46\\ \text{Less than 165}& 51\end{array}$$
Find the median height.

The area of following triangle is 30 cm². If BC = 5 cm then AP = ?

The length of the tangent drawn to a circle with radius 7 cm from a point 25 cm away from the centre is = ___ cm.

At the expiry of the maturity period, the depositor is paid a lumpsum amount which is called ___

ABCD is a parallelogram with diagonal AC. If a line XY is drawn such that it cuts the side AD at point Z and XY $\parallel$ AB, then $\frac{BX}{XC}=$

The dimensions of a room are $14m\times 10m\times 6.5m$.There are two doors and 4 windows in the room.Each door measures $2.5m\times 1.2m$ and window measures $1.5m\times 1m$.Find the cost of painting walls of the room ar Rs.35 per $m^2$.

The surface area of a sphere is 2464 $c{m}^2.$ If its radius be doubled, what will be the surface area of the new sphere?

The chord of circle of radius 10 cm subtends a right angle at its centre. The length of the chord (in cm) is

(a) $\frac{5}{\sqrt{2}}$ (b) $5\sqrt{2}$ (c) $10\sqrt{2}$ (d) $10\sqrt{3}$

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$x^2-(2b-1)x+(b^2-b-20)=0$

A hemispherical bowl fits exactly on the open surface of a right cone with height $5cm$ and radius $3.5cm.$ The volume of the solid formed is

$\sin$(90-$\theta$) =