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Find the lenght of the hypotenuse of an isosceles right-angled triangle whose area is 200 $c{m}^2$. Also, find its perimeter. [Given, $\sqrt{2}$ = 1.41.]

Which point on x-axis is equidistant from the points A(7, 6) and B(-3, 4) ?

(a) (0, 4) (b) (-4, 0) (c) (3, 0) (d) (0, 3)

If $2+\sqrt{3}$is a root of the equation $x^2+px+q=0$, then write the values of p and q.

How to find missing frequency in median
For example:
If the median of the distribution given below is 46, find the value of the missing frequencies.

If $Sin\theta =\frac{4}{5}$ and $Cos\theta =\frac{3}{5}$, then $tan\theta =$

The mean deviation from the mean for the set of observations; – 1, 0, 4 is:

In the given figure, the incircle of $△ABC$ touches the sides AB, BC and CA at the points P, Q, R respectively. Show that

$AP+BQ+CR=BP+CQ+AR$

$=\frac{1}{2}(Perimeterof△ABC)$

[3 MARKS]

Construct a triangle BCP given BC= 5 cm, BP= 4 cm and $\angle PBC={45}^o$.

(i) Complete the rectangle ABCD such that:

(a) P is equidistant from AB and BC.

(b) P is equidistant from C and D.

(ii) Measure and record the length of AB.

From a point $P$, two tangents $PA$ and $PB$ are drawn to a circle with a center $O$. If $OP=$ diameter of the circle, show that $\Delta APB$ is equilateral.

Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures $2T$ and $3T$ respectively. The temperature of the middle (i.e., second) plate under steady state condition is:

The sum of twice the sum of 5 consecutive odd numbers and thrice the sum of 4 consecutive even numbers is 178. The sum of thrice the sum of 5 consecutive odd numbers and twice the sum of 4 consecutive even numbers is 177. The middle number when all the numbers are arranged in descending order is

In a $\Delta ABC$, M and N are points on the sides AB and AC respectively such that BM = CN. If $\angle B=\angle C$ then show that MN || BC.

If the HCF of 210 and 55 is expressed in the form 210×5+55y, find y

If a building $15\sqrt{3}$ m high casts a shadow of 15 m, then the angleof elevation of the top of the building is ___.

Find a quadratic polynomial with the sum and product of its zeroes $\frac{1}{4}$ & -1 respectively

Simplify the rational expression into lowest terms $\frac{x^2-7x+10}{x^2-12x+35}$.

In $\Delta ABC$, $\angle A={60}^{\circ },\angle B={45}^{\circ }andAB=10cm$ as shown in the figure. Find the area of the triangle.

The equation $x^2+4x+c=0$ has real roots, then

Equation of the line passing through the mid-point of intercepts made by the circle $x^2+y^2-17x-16y+60=0$ is

If cosec²θ (1 + cosθ) (1 - cosθ) = λ, then the value of λ is:

Direction(5-8): Study the following table carefully and answer the given questions.

The table given below shows the number of female visitors to an amusement park on 5 days – Sunday, Monday, Tuesday, Wednesday, and Thursday and the percentage of male visitors out of the total number of visitors.On how many days, the difference between the number of male and female visitors visiting the amusement park is more than 100?

In how many ways can 5 boys and 4 girls be arranged on a bench if
(a) If boys and girls are in separate groups

Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of ${60}^0$. Find the value of $\angle$ AOB.

Solve the following systems of equations:

$21x+47y=110$

$47x+21y=162$