Mathematics quiz 2018

MATHEMATICS QUIZ

Q. 1. A watch uses two electronic circuits (ECs). Each EC has a failure probability of 0.1 in one year of operation. Both ECs are required for functioning of the watch. The probability of the watch functioning for one year without failure is

0.99
0.90
0.81
0.80

Q. 2. The fourth order Runge-Kutta (RK4) method to solve an ordinary differential equation is given as

For a special case when the function 'f' depends solely on x, the above RK4 method reduces to

Euler's explicit method
Trapezoidal rule
Euler's implicit method
Simpson's 1/3 rule

Q. 3 Consider the following two equations:

The above set of equations is represented by

Q. 4 A person is drowning in sea at location R and the lifeguard is standing at location P. The beach boundary is straight and horizontal, as shown in the figure.

The lifeguard runs at a speed of VL and swims at a speed of VS. In order to reach to the drowning person in optimum time, the lifeguard should choose point Q such that

Q. 5 For the matirx if det stands for the determinant and A^T is the transpose of A then the value of det(A^TA) is ....................

Q. 6 The initial water level in a tank is 4m. When the valve located at the bottom is opened, the rate of change of water level (L) with respect to time (t) is, dL/dt = -k √t,where k = 0.6 ms^-3/2. The level of water (in m) in the tank at time 0.5s after opening the valve is ....................(rounded off to second decimal place).

Q. 7 If y = e^-x2 then the value of is..........