Problem 1:

The following system of

x + y + 2z = 3

x + 2y + 3z = 6

x + 4y + kz = 12

has unique solution. The only possible value(s) of k is/are -

Problem 2:

The number of linearly independent Eigen vectors of

[a   b]

[0   a]

is/are

Problem 3:

Probability that the divisors of 6¹⁰ is a multiple of 6⁶ is

Problem 4:

What would be the expectation of the number of successes preceeding the first failure in an infinite series of independent trials with constant probability of success p = 0.4

Problem 5:

A Variate X has the following distribution

         X:    0     1    2     3 

  P(X = x):1/3   1/6  1/3   1/6

The E [2x +3)² is

Problem 6:

What will be the value of y(0.04), from the differential equation dy/dx + 4 = 0 with 4(0) = 1, h = 0.04, by Runge-Kutta Method.

Problem 7:

A real root of equation cos x = 4x - 1 correct to seven decimal places by method of successive approximation is

Problem 8 :

The number of linearly independent Eigen vectors of

[a   b]

[0   a]

is/are

Problem 9:

The solution of differential equation

dy/dx + y/x = x² with y(1) = 1

is

Problem 10:

The general solution of

(xe^xy + 2y)dy + ye^xydx = 0

is

Problem 11:

If

f(x) = -x², x ≤ 0

      = 5x -4,0 < x ≤ 1

      = 4x² -3x, 1 < x < 2

      = 3x + 4,x ≥ 2

then f(x) is discontinuous at x =

Problem 12:

Find the directional derivative of

f(x, y, z) = x²yz + 4xz²

at (1, -2, -1) along 2i^ -j^ - 2k^.

Problem 13:

∫√x² -a²dx is

Problem 14:

I = ₀∫^Π₀∫^acosθ rdrdθ is

Problem 15:

Find c of Rolle‘s Theorem for

f(x) = e^x sinx in [0, Π]