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A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.

The volume of the cone is obtained as follows.... View Article

Solve the equations using the cross multiplication method: 3x + 2y = 10 and 4x − 2y = 4.

The given equations are... View Article

If the radius of one circle is twice the radius of another circle whose centres are (2, 0) and (1, 2) respectively are cutting orthogonally, then the radius of the second circle is

If angle between circle is 90, then the circles are cutting orthogonally. By applying Pythagoras theorem... View Article

Solve the following equations using matrix inversion method. 2x − 3y + 6 = 0 and 6x + y + 8 = 0.

The given equations are... View Article

Show that the local maximum value of x + (1 / x) is less than the local minimum value.

The local maximum value of y is at x = - 1 and the local maximum value = - 2. The local minimum value of y is at x = 1 and the local minimum... View Article

From a point in the interior of an equilateral triangle perpendiculars are drawn on the

From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides.... View Article

Which number would replace the question mark in the series? 7, 12, 19, ?, 39

7 + 5 = 12 12 + 7 = 19 19 + 9 = 28 28 + 11 = 39 '28' replaces the question mark.... View Article

6, 13, 25, 51, 101, ?

The pattern is * 2 + 1, * 2 - 1, * 2 + 1, * 2 - 1 ,..... The missing term = 101 x 2 + 1 = 203... View Article

The instrument used to measure or construct angle is

The instrument used to measure or construct angle is a protractor.... View Article

If a number is divisible by 2 and 3, then it satisfies the divisibility rule of

If the number is divisible by 2 and 3, then it satisfies the divisibility rule of 6. Example: 306 is divisible by both 2 and 3. The last digit is... View Article

Divide the sum of 65 / 12 and 12 / 7 by their difference.

The sum is = (65 / 12) + (12 / 7) The difference is = (65 / 12) – (12 / 7) When we divide = (65 / 12 + 12 / 7) / (65 / 12... View Article

Find the general term in the expansion of (1 – x)^-3.

The r+1th term is given by... View Article

Find the eccentricity of the ellipse if the length of the latus rectum = half of the major axis.

Here... View Article

Fill in the blank with >, < or = sign (- 25) - (- 42) ________ (- 42) - (- 25).

L.H.S = − 25 + 42 = 17 R.H.S = − 42 + 25 = − 17 L.H.S is greater than R.H.S... View Article

Find three positive numbers in the ratio 2 : 3 : 5, the sum of whose squares is 950.

The ratio of three positive numbers = 2 : 3 : 5 Sum of their squares = 950 Assume the first number to be 2x, the second number to be 3x and the... View Article

In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English?

H = set of people speaking Hindi E = set of people speaking English n (H ∪ E) = 400; n (H) = 250; n (E) = 200 n (H ∩ E) = n... View Article

Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.

Let ABCD be the parallelogram with ∠A = ∠B. The sum of adjacent angles of a parallelogram is 180. ⇒ ∠A + ∠B =... View Article

An exterior angle of a triangle measures 110° and its interior opposite angles are in the ratio 2: 3. Find the angles of the triangle.

Let the given interior opposite angles are (2x) and (3x). An exterior angle of a triangle is equal to the sum of its interior opposite... View Article

Express as cm using decimals: 9 cm 8 mm.

1 mm = (1 / 10) cm 9 cm 8 mm = 9 + (1 / 10) x 8 = 9 + 0.8 = 9.8... View Article

What must be subtracted from p (x) = 8x⁴ +14x³ – 2x² + 7x – 8 so that the resulting polynomial is exactly divisible by g (x) = 4x² + 3x – 2?

Let y be subtracted from p(x). (14x − 10) should be subtracted from p (x) so that it will be exactly divisible by g(x).... View Article