Vishva plays football every 4th day. He played on a Tuesday . He plays football on a Tuesday again in _________ days.

The difference between the biggest and the smallest three digit number each of which has different digits is

(A) 864 

(B) 875 

(C) 885 

(D) 895

In an elementary school 26% of the students are girls. If there are 240 less girls than boys, then the strength of the school is _________

Let a, b, c be real numbers, not all of them are equal. Prove that if a + b + c = 0, then a² + ab + b² = b² + bc + c² = c² + ca + a².

Prove the converse, if a² + ab + b² = b² + bc + c² = c² = ca + a², then a + b + c = 0.

There are 4 coins in a row and all are showing heads to start with. The coins can be flipped with the following rules :

(a) The fourth coin (from the left) can be flipped any time

(b) An intermediate coin can be changed to tail only if its immediate neighbor on the right is heads and all other coins (if any) to its right are tails.

(c) Only one coin can be flipped in one step.

The minimum number of steps required to bring all coins to show tails is _______.

Prove that x⁴ + 3x³ + 6x² + 9x + 12 cannot be expressed as a product of two polynomials of degree 2 with integer coefficients.

A cube has edge length x (an integer). three faces meeting at a corner are painted blue. The cube is then cut into smaller cubes of unit length. If exactly 343 of these cubes have no faces painted blue, then the value of x is ________ .

If x²(y + z) = a², y²(z + x) = b², z²(x + y) = c², xyz = a b c prove that a² + b² + c² + 2abc = 1

The four digit number 8ab9 is a perfect square. The value of a² + b² is

(A) 52 

(B) 62 

(C) 54 

(D) 68

The sum of the ages of a man and his wife is six times the sum of the ages of their children. Two years ago the sum of their ages was ten times the sum of the ages of their children. Six years hence the sum of their ages will be three times the sum of the ages of their children. How many children do they have?