**1.** Given the system of equations 3x + ky = 1 and 6x + 3y = 2. For which values of k does this system have infinite solutions?

@raman1729

k=3/2

In the expansion of (a + b + c)^{20}, find

A.Number of terms?

B. Sum of the coefficients

If a + b + c = 6, find the maximum value of a^{3}b^{2}c, where all a, b and c are positive real

numbers.

@raman1729

108

Both x^{2} + 16x – q = 0 and x^{2} – 11qx + 25 = 0 have real roots. The number of positive integral values of q is _____ .

A. 39 B.70 C. 60 D. 64

@raman1729

64

The equation 5x + 7y = k has 7 solutions in which both x, y are non-negative integers. What is the minimum value of k?

A. 210 B. 280 C. 223 D. 290

@raman1729

210

The sum of the first eight terms of a geometric progression is 510 and the sum of the first four terms of the geometric progression is 30. Find the first term of the geometric progression, given that it is positive.

@raman1729

1st term=2

Let A = {1, 2, 3, 4, 5, 6, 7} and B = {8, 9}. The number of onto functions defined from A to B is _________

In how many ways can 144 be divided into two parts, such that one part when divided by 5 leaves a remainder of 4, whereas the other part when divided by 8 leaves a remainder of 2?