Q 1: The system of equations,
2x+4y=10
5x+10y=25
Q 2: Four fair coins are tossed simultaneously. The probability that at least one head turns up is
Q 3: The rank of the matrix \begin{pmatrix}3&0&1&2\\4&7&3&3\\1&7&2&1\end{pmatrix} is
Q 4: The harmonic series {\textstyle\sum_{n=1}^\infty}\frac1{n^P}
Q 5: A box contains 8 balls, 2 of which are defective. The probability that none of the balls drawn are defective when two are drawn at random without replacement is
Q 6: The gradient of xy^2+yz^3 at the point (-1, 2, 1) is
Q 7: Evaluate \int_0^1\left(4x^3+x\right)dx by the trapezoidal rule. Use a step size of 0.2. Obtain the error bounds for this solution. Compute the absolute error of the numerical solution by evaluating the integral analytically.
Q 8: Solve \frac{dy}{dx}-6xy=-6x by the following methods: a. variation of parameters b. separation of variables.
Q 9: (a) At what points are the Cauchy-Reiman equations satisfied for the function, F(z)=xy^2+ix^2y ? Where is F(z) analytic? (b) Compute the distinct cube roots of (1+i).