If 1 + 2 + 2² + 2³ +.......+ 2⁵⁰ is divided by 7, what will be the remainder?

If 8a + 4b = 11 and 2a + 4g = 5. The value of b = 2. You need to find the value of a and g.

a, b, c, d be real numbers in G.P. If u, v,w satisfy the equations u + 2v + 3w = 6; 4u + 5v + 6w = 12; 6u + 9v = 4 then roots of the equations (1/u + 1/v + 1/w)x² + [(b − c)² + (c − a)² + (d − b)²]x + u + v + w = 0 and 20x² + [10(a − d)²]x − 9 = 0 are

If one root of ax² + bx + c = 0 is double the other, then a, b, c are related as

A pole has to be erected on the boundary of a circular park of diameter 13 meters in such a way that the difference of its distances from two diametrical opposite fixed gates A and B on the boundary is 7 meters. The distance of the pole from one of the gates is:

If a² = b⁴ = c⁸ = d¹⁶, then logd² (abc)^1/3

If r(x) is the remainder obtained by dividing a polynomial p(x) by another polynomial q(x), then

If the cube root of the square root of a number is 5, what is the number?

The L.C.M. of 6x₂ – 5x – 6 and 12x₂ + 11x + 2 is

What is the minimum value of x for which the expression x³ – 7x² + 11x – 5 gives positive values