Reference no: EM133150134

Question 1: If λ be the ratio of the roots of the quadratic equation in x, 3m² x² + m(m - 4)x + 2 = 0. What is the least value of m for which λ + 1/λ = 1.

Question 2: Let and Q = [q_ij] be two 3 x 3 matrices such that Q - P⁵ = I₃. Then (q₂₁ + q₃₁)/q₃₂ is equal to:

Question 3: The value of ₀∫^Π/2 sin³x/(sin x + cos x) dx is:

Question 4: lim_n→∞ ((n+1)^1/3/n^4/3 + (n+2)^1/3/n^4/3 + .......+ (2n)^1/3/n^4/3) is equal to

Question 5: Consider three boxes, each containing 10 balls labelled 1, 2,..., 10. Suppose one ball is randomly drawn from each of the boxes. Denote by n_i, the label of the ball drawn from the i^th box, (i = 1, 2, 3). Then, the number of ways in which the balls can be chosen such that n₁ < n₂ < n₃ is: