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1. Consider the following set of linear algebraic equations x1 + 2x2 + 3x3 = 2 x2 + x3 = - 1 2x2 + 2x3 = 0 The system has
2. If a and b are arbitrary constants, then the solution to the ordinary differential equation d2y/dx2 - 4y = 0 is
3. For the function f(t) = e-t/T, the Taylor series approximation for t << T is
4. A box containing 10 identical compartments has 6 red balls and 2 blue balls. If each compartment can hold only one ball, then the number of different possible arrangements are
6. In a throttling process, the pressure of an ideal gas reduces by 50 %. If CP and CV are the heat capacities at constant pressure and constant volume, respectively (r = CP/CV) the specific volume will change by a factor of
1. The number of emails received on six consecutive days is 11, 9, 18, 18, 4 and 15, respectively. What are the median and the mode for these data?
2. For two rolls of a fair die, the probability of getting a 4 in the first roll and a number less than 4 in the second roll, up to 3 digits after the decimal point, is _________
3. Which of the following statements are TRUE? P. The eigenvalues of a symmetric matrix are real Q. The value of the determinant of an orthogonal matrix can only be +1 R. The transpose of a square matrix A has the same eigenvalues as those of A S. The inverse of an ‘n × n’ matrix exists if and only if the rank is less than ‘n’
5. A gaseous system contains H2, I2, and HI, which participate in the gas-phase reaction 2 HI <-----> H2 + I2 At a state of reaction equilibrium, the number of thermodynamic degrees of freedom is _________
6. The thermodynamic state of a closed system containing a pure fluid changes from (T1, p1) to (T2, p2), where T and p denote the temperature and pressure, respectively. Let Q denote the heat absorbed (> 0 if absorbed by the system) and W the work done (> 0 if done by the system). Neglect changes in kinetic and potential energies. Which one of the following is CORRECT?