Find the square root of the following number by the prime factorisation method 1936. The factors of 1936 is 1936 = 2 × 2 × 2 × 2 × 11 × 11 Take square root both sides, √1936 = √2 × 2... View Article
If the compound interest on a certain sum for 2 years is Rs 21. What could be the simple interest? Compound interest at rate r for 2 years becomes: (1 + r)2 = 1.21 ⇒ r = 10% At r = 10%, the simple interest in 2 years becomes 2... View Article
Prove that cos [(3Ï€ / 4) + x] – cos [(3Ï€ / 4) – x] = – √2 sinx. By taking LHS of the given expression... View Article
How many numbers are there containing 2 digits? Greatest two digit number − smallest two digit number) + 1 = (99 − 10) + 1 = 89 + 1 = 90... View Article
Find the cube root of the decimal: 19.683. The cube root of the decimal 19.683 is given by... View Article
Find the prime factors of 128. Prime factorisation of 128 = 2 x 2 x 2 x 2 x 2 x 2 x 2 Exponential form = 27... View Article
Show that the right-circular cone of the least curved surface and given volume has an altitude equal to √2 times the radius of the base. Let ABC be right-circular cone having radius r and height h.... View Article
Show that (sec θ + cos θ) (sec θ – cos θ) = tan2 θ + sin2 θ. LHS = (sec θ + cos θ) (sec θ - cos θ) = sec2 θ - cos2 θ = (1 + tan2 θ) - (1 - sin2 θ) = 1 + tan2... View Article
If x sin3 θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ then x sin3 θ + y cos3 θ = sin θ cos θ... View Article
If (z − 1) / (z + 1) is purely imaginary then what would be the locus of z? Let z=x+iy... View Article
Father’s age is three times the sum of ages of his two children. After 5 years, his age will be twice the sum of the ages of two children. Find the age of the father. Assume the age of two children to be x and y. Father’s present age = 3 (x + y) After 5 years, age of two children = (x + 5) +... View Article
True or False: The arrangement of data in rows and columns is called classification of data. The given statement is false.... View Article
In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. How many speak at least one of these two languages? F - the set of people in the committee who speak French S - the set of people in the committee who speak Spanish. n (F) = 50 n (S) = 20 n... View Article
Find three consecutive odd numbers whose sum is 219. Let the odd number be ‘x’. The next two consecutive numbers are x + 2 and x + 4. x + (x + 2) + (x + 4) =... View Article
If n arithmetic means are inserted between 20 and 80 such that the ratio of first mean to the last means is 1:3, then find the value of n. a = 20 = first term, l = 80 = last term... View Article
