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Find the principal value of tan^-1 (- √3).

The principal value of tan-1 (- √3) is as follows.... View Article

Read these numbers and write in words: i] 5,06,45,075 ii] 12,36,99,140 iii] 2,50,00,350

i] Five crores six lakhs forty five thousand seventy five ii] Twelve crores thirty six lakhs ninety nine thousand one hundred and forty iii] Two... View Article

Convert each part of the ratio to percentage: 3 : 1.

3 : 1 Total part = 3 + 1 = 4 Fractional part = (3 / 4) : (1 / 4) ⇒ Percentage of parts = (3 / 4) * 100 : (1 / 4) * 100 ⇒ Percentage of... View Article

A man whose bowling average is 12.4 takes 5 wickets for 26 runs and thereby decreases his average by 0.4. The number of wickets, taken by him, before his last match is ___________.

Let the wickets taken by him before the match be X. The bowling average is given to be 12.4. Total run = 12.4X The runs scored including this... View Article

Factorise the equation x² – 9x + 18 = 0.

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

The coefficient of mean deviation from median of observations 40 62 54 90 68 76 is

Arranging the given data in ascending order.... View Article

Write the following rational numbers in decimal form and find out the block of repeating digits n the quotient (1 / 3)

(1 / 3) = 0.333333 The block of the digit, repeating in the quotient is 3.... View Article

The coefficient of xⁿ in the binomial expansion of (1 – x)^-2 is

(1 - x)-2 = 1 + 2x + 3x2 + . . . + (n + 1) xn + . . . The coefficient of xn = n + 1.... View Article

The approximate value of 1e is

The approximate value of 1e is 2.718.... View Article

The difference between two whole numbers is 66 and the ratio of the two numbers is 2 : 5. What are the two numbers?

Let the first number be 2x and the second number will be 5x. According to question 5x - 2x = 66 3x = 66 x = 22 The two... View Article

Find the square root of 5929.

5929 = 7 × 7 × 11 × 11 ⇒ √5929 = √7 × 7 × 11 × 11 = √72 × 112 = 7 ×... View Article

A tetrahedron has 4 faces and 6 edges. How many vertices does it have?

V − E + F = 2 V = number of vertices = ? E = number of edges = 6 F = number of faces = 4 V − 6 + 4 = 2 V − 2 = 2 V = 4... View Article

Prove that 1 + 2 + 3 + . . . . . + n = [n (n + 1)] / 2 for n being a natural numbers.

p (n) = 1 + 2 + 3 + … … + n... View Article

Evaluate sin^-1 (sin 2).

The given expression is sin-1 (sin 2).... View Article

Natural numbers are also known as

Natural numbers are also known as counting numbers.... View Article

Prove that the square of any positive integer is of the form 5q, 5q + 1, 5q + 4 for some integer q.

By Euclid’s division algorithm a = bm + r, where 0 ≤ r ≤ b Put b = 5 a = 5m + r, where 0 ≤ r ≤ 4 If r = 0,... View Article

What is the multiplicative inverse of 6?

The multiplicative inverse of 6 is 1 / 6.... View Article

If p = √(1 – sin x) / (1 + sin x), q = (1 – sin x) / (cos x), r = cos x / (1 + sin x), then find the relation between p, q and r.

Consider... View Article

Where does today come before yesterday?

The answer for the riddle where does today come before yesterday is in a dictionary.... View Article

The line segment joining the points P (3, 3) and Q (6, – 6) is trisected at the points A and B such that A is nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.

Assume the coordinates of point A to be (x1, y1). A divides PQ in the ratio 1 : 2. (x1, y1) = [(1 * 6) + (2 * 3)] / (1 + 2), [(1 * - 6) + (2 *... View Article

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