ISRO Scientist or Engineer Electrical 2017

$$\lim_{x \rightarrow \infty}\left(\frac{x + \sin x}{x}\right)$$ is equal to

A fair (unbiased) coin was tossed four times in succession and resulted in the following outcomes: (i) Head (ii) Head (iii) Head (iv) Head. The probability of getting a ‘Tail’
when the coin is tossed again is

What are the eigen values of the following $$2 \times 2$$ matrix $$\begin{bmatrix}2 & -1 \\-4 & 5 \end{bmatrix}$$ ?

$$\int_{0}^{\frac{\pi}{2}} \int_{0}^{\frac{\pi}{2}} \sin (x + y)dx dy $$ is

In the Taylor series expansion of $$e^x + \sin x$$ about the point $$x = \pi$$ , the coefficient

A deck of five cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then removed from the deck, one at a time. What is the probability that the two cards are selected with the number of the first card being one higher than the number on the second card?

Using trapezoidal rule for the table given below $$\int_{4}^{5.2} \ln x dx$$ will be

Find the z transform of $$(n + 1)^2$$

Consider the following system of equations in three real variables $$x_1, x_2$$ and $$x_3$$
$$2x_1 - x_2 + 3x_3 = 1$$
$$3x_1 - 2x_2 + 5x_3 = 2$$
$$-x_1 - 4x_2 + x_3 = 3$$
The system of equations has :

Which of the following functions would have only odd powers of x in its Taylor series expansion about the point x = 0?