# Engineering Mathematics GATE-2010

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

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

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

The standard deviation of the distribution is

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

**Q 5:** A root of the equation x^{4} – 3x + 1 = 0 needs to be found using the Newton-Raphson method. If the initial guess, x_{0}, is taken as 0, then the new estimate x_{1}, after the first interaction is

**Q 6:** The solution of the differential equation

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

**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

**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

**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

**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