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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 0-100 100-200 200-300 300-…

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 total surface …

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

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

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. Find the height of the …

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

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}` `\frac{1}{2(3x+y)}+\frac{1…

Find the area of the sector of a circle with radius 4 cm and angle `30^0`. Also, find the area of the corresponding major sector. (`\pi`= 3.14) …

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^2+BD^2`=`AB^2+DE^2` …

Find the sum of first 51 terms of an AP whose secound and third terms are 14 and 18 respectively. SOLUTION We Know that `"a&qu…

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

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-\sqrt{2\times3}x-\sqrt{2\tim…

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

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

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

If sec 4A=cosec (A - `20^0`), find the Value of A. (4A is an acute angle) SOLUTION Given that, sec 4A = cosec (A - `20^0`) ….(i)…

Evaluate: `\frac{5cos^2 60^0+4sec^2 30^0-tan^2 45^0}{sin^2 30^0+sin^2 60^0}` SOLUTION `\frac{5cos^2 60^0+4sec^2 30^0-tan^2 45^0}…

How many two-Digit numbers are divisible by 5 ? SOLUTION Two-digit numbers divisible by 5 are 10,15,20,25 …………………95 We note …