  # ISRO Scientist or Engineer Civil 2014

Instructions

For the following questions answer them individually

Question 1

# The minimum and maximum eigen value of the matrix $$\begin{bmatrix}1 & 1& 3\\ 1& 5 &1\\3&1&1\end{bmatrix}$$ ]are —2 and 6 respectively. Whatis the other eigen value? Question 2

# Evaluate $$\lim_{X \rightarrow 1} \frac{X^{X-}X}{X-1- \log X}$$ Question 3

# If the rank of the matrix A is 2, the rank of 2A is Question 4

# The degree ofthe differential equation $$\frac{d^{2} X}{dt^{2}}+2x^{3}$$ is Question 5

# $$\int_{0}^{\frac{\pi}{2}} \sin^{2}xdx$$ equal to Question 6

# Two coins are simultaneously tossed. The probability of two heads simultaneously appearing is Question 7

# The $$\lim_{x \rightarrow 0} \sin(\frac{\frac{2}{3x}}{x})$$ is Question 8

# Evaluate $$\int_{0}^{\frac{\pi}{2}} \frac{\surd (\sin x)}{\surd (\sin x)+\surd (\cos x)}$$ dx Question 9

# Evaluate $$\lim_{x \rightarrow 0} \frac{e^{x} \sin x -x-x^{2}}{x^{2}+xlog(1-x)}$$ Question 10

# The rank of A=$$\begin{bmatrix}0 & 0& 0&0\\ 4& 2 &3&0\\1&0&0&0\\4&0&3&0\end{bmatrix}$$ is OR