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The median of the following data is 525. Find the values of `x` and `y`, if the total frequency is 100. Class interval 0…

A toy in the form of cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm…

Find the area of the shaded regionin the figure below, where a circular arc of radius 6 cm has been drawn with vertex O o…

Construct a triangle similar to a given traingle ABC with its sides equal to `5/3` of the corresponding sides of the tri…

If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus. SOLUTION Let ABCD…

The shadow of a tower standing on a level ground is found to be 40 m longer when Suns altitude is 30 than when it was 60…

If the areas of two similar traingals are equal, Prove that they are congruent. SOLUTION Given, ar (`\triangle…

Solve the pair of equations by reducing them to a pair of liner equations. `\frac{1}{3x+y}+\frac{1}{3x-y}=\frac{3}{4}` `…

Find the area of the sector of a circle with radius 4 cm and angle `30^0`. Also, find the area of the corresponding majo…

Find the area of the traingle formed by joining the middle points of the sides of the traingle whose vertices are (0, -1…

D and E are points on the sides CA and CB respectively of a triangle of a traingal ABC right angled at C. Prove that `AE…

Find the sum of first 51 terms of an AP whose secound and third terms are 14 and 18 respectively. SOLUTION …

Find the coordinates of a point A, where AB is a diameter of a circle whose centre is (2,-3) and B is (1,4). SO…

Sum of the areas of two squares is `468m^2`. If the differences of their perimeters is 24 m, find the sides of two squ…

Solve `3x^2-2 \sqrt{6}x+2 = 0` SOLUTION  `3x^2-2 \sqrt{6}x+2 = 0` `3x^2-\sqrt{6}x-\sqrt{6}x+2=0` `3x^2-\sq…

A fraction becomes `9/11`, if 2 is added to both the numerator and denominator. If 3 is added to both the numerator and t…

state the Division Algorithm for polynomials. Divide the polynomial p(`x`) by the polynomial g(`x`), and the find the quo…

Prove that `\sqrt{7}` is irrational. SOLUTION Let us assume, to the contrary, that ,√7 is a rational number.…

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting . a   a king of red…

Prove that `(cosec\theta-cos\theta)^2 = \frac{1 - cos\theta}{1 + cos\theta}` SOLUTION  LHS = `(cose…