MATHEMATICS QUIZ 2019

Q. 1. A system of n homogeneous linear equations containing n unknowns will have non-trivial solutions if and only if the determinant of the coefficient matrix is

1
-2
0
∞

Q. 2. The values of the expression is

∞
0
1
-1

Q. 3 The solution of the ordinary differential equation

subject to the initial condition y = 1 at x = 0, is

Q. 4 The value of the complex number i^-1/2 (where i = √-1) is

Q. 5 The product of the eigen values of the matrix is ........(rounded off to one decimal place).

Q. 6 If x,y and z are directions in a Cartesian coordinate system and i, j and k are the respective unit vectors, the directional derivative of the function u(x, y, z) = x₂ - 3yz at the point (2,0,-4) in the direction (i + j - 2k) / √6 is .......(rounded off to two decimal places).

Q. 7 Two unbiased dice are thrown. Each dice can show any number between 1 and 6. The probability that the sum of the outcomes of the two dice is divisible by 4 is ...........(rounded off to two decimal places).

Q. 8 The Newton-Raphson method is used to determine the root of the equation f(x) =e^-x - x. If the initial guess for the root is 0, the estimate of the root after two iterations is______ (rounded off to three decimal places).