Archives

Is 0 a term of the AP 31, 28, 25, …? Justify your answer.

Let 0 be the nth term of given AP in a way that an = 0. a = 31 d = 28 – 31 = - 3 The nth term of an AP, is The value of n... View Article

Find the L.C.M. of 2.5, 0.5 and 0.175.

Multiples of 175: 175, 350, 525, 700, 875, 1050, 1225, 1400, 1575, 1750, 1925, 2100, 2275, 2450, 2625, 2800, 2975, 3150, 3325, 3500, 3675, 3850,... View Article

If cosec A + cot A = p then prove that cos A = [p² – 1] / [p² + 1].

Consider the given function.... View Article

Write a statement of Pythagoras theorem and show that the 6, 8 and 10 are Pythagorean triplets.

Statement: “In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the opposite side and adjacent... View Article

An isosceles right triangle has an area of 8 square cm. The length of its hypotenuse is

Let the height of the triangle be h. The given triangle is isosceles in nature. Let base = height = h Area of triangle = 8cm2 ⇒... View Article

tan 7 (1 / 2) =

The given expression is... View Article

Simplify a⁶ – b⁶.

The given expression is... View Article

Assume that in a family, each child is equally likely to be a boy or a girl. A family with three children is chosen at random. The probability that the eldest child is a girl given that the family has at least one girl is

Assume that in a family, each child is equally likely to be a boy or a girl.... View Article

Find the compound interest on Rs. 20000 at 10 per annum for 3 years.

P = Rs. 20,000 R = 10 % T = 3 years A = 20000 (1 + (10 / 100))3 = 20000 (110 / 100)3 A = 20000 × (110 / 100) × (110 / 100)... View Article

Verify Euler’s formula for pentagonal pyramid and square prism.

1] Pentagonal Pyramid Number of faces (F) = 7 Number of edges (E) = 15 Number of vertices (V) = 10 F + V = 7 + 10 = 17 E + 2 = 15 + 2 = 17 F + V... View Article

If a= 30, then [cos³ a – cos 3a] / [cos a] + [sin³ a + sin 3a] / [sin a] =

Consider the LHS of the given expression... View Article

64 : 9 : : 81 : ?

64 : 9 : : 81 : ? √64 = 8 : The next number to 8 is 9 : : √81 = 9 : the next number to 9 is 10. 64 : 9 : : 81 : 10 The missing... View Article

Find the correct answer for the unsolved equation. If 228 = 12 and 337 = 16 then 569 = ?

The two conditions given are 228 = 12 and 337 = 16. In first condition, 2 * 2 + 8 = 12 In second condition, 3 * 3 + 7 = 16 569 is 5 * 6 + 9 = 39... View Article

If the arithmetic mean of the numbers 27, 23, x – 4, x + 4,15, 3 and 7 is 13, then find the value of x.

It is given that the arithmetic mean is 13.... View Article

Given set: (63, 49, 35) a) (72, 40, 24) b) (72, 48, 24) c) (64, 40, 28) d) (81, 63, 45)

The given set of numbers are obtained by Xying a particular number by 9, 7 and 5 respectively. 63 = 7 × 9, 49 = 7 × 7, 35 = 7 ×... View Article

If (x³¹ + 31) is divided by (x + 1), then find the remainder.

Let p (x) = x31 + 31 Divisor = x + 1 Remainder = p (- 1) = (- 1)31 + 31 = - 1 + 31 = 30... View Article

The ratio of 4^3.5 : 2⁵ is the same as

The given expression can be written as... View Article

Find the roots of the given quadratic equation by applying the quadratic formula 4x² + 4 √3x + 3 = 0.

4x2 + 4 √3x + 3 = 0 a = 4, b = 4 √3 and c = 3 D = b2 - 4ac = (4 √3)2 - 4 * 4 * 3 = 48 - 48 = 0 D = 0 means the roots... View Article

Simplify 4x – (3y – x + 2z).

4x - (3y - x + 2z) = 4x - 3y + x - 2z = 5x - 3y - 2z... View Article

The lines which aren’t on the same plane and they neither intersect each other are called:

Skew lines are the lines that are neither on the same plane and they do not intersect each other.... View Article