Engineering Mathematics GATE-2010

Watermark

Q 1: The inverse of the matrix \begin{bmatrix}1&2\\3&4\end{bmatrix} is





Ans is )

Explanation:

Q 2: The Laplace transform of the function shown in the figure below is





Ans is )

Explanation:

Q 3: The Maxwell-Boltzmann velocity distribution for the x-component of the velocity at temperature T, is

f\left(v_x\right)=\sqrt{\frac m{2\mathrm{πkT}}}exp\left(-\frac{mv_x^2}{2kT}\right)

The standard deviation of the distribution is





Ans is )

Explanation:

Q 4:  Given that i=\sqrt{-1},\;i^i is equal to





Ans is )

Explanation:

Q 5: A root of the equation x4 – 3x + 1 = 0 needs to be found using the Newton-Raphson method. If the initial guess, x0, is taken as 0, then the new estimate x1, after the first interaction is





Ans is )

Explanation:

Q 6:  The solution of the differential equation

\frac{d^2y}{dt^2}+2\frac{dy}{dt}+2y=0

with the initial conditions y(0)=0,\;{\left.\frac{dy}{dt}\right|}_{t=0}=-1 , is





Ans is )

Explanation:

Q 7: If \overrightarrow u=y\widehat i+xy\widehat j and \overrightarrow v=x^2\widehat i+xy^2\widehat j , then curl\left(\overrightarrow u\times\overrightarrow v\right) is





Ans is )

Explanation:

Q 8: X and Y are independent random variables. X follows a binomial distribution, with N = 5 and p = ½. Y takes integer values 1 and 2, with equal probability. Then the probability that X = Y is





Ans is )

Explanation:

Q 9: A box contains three red and two black balls. Four balls are removed from the box one by one without replacement. The probability of the ball remaining in the box being red is





Ans is )

Explanation:

Q 10: For a function g(x), if g(0) = 0 and g’(0) = 2, then \lim\limits_{x \to 0}\int_0^{g\left(x\right)}\frac{2t}x\operatorname dt is equal to





Ans is )

Explanation: