M.1)Solution of Differential Equation
$$\frac{d^2y}{dx^2} - 5\frac{dy}{dx} + 6y= 0$$is given by
(a)$ y = e^{2x}+e^{-3x}$
(b)$y = e^{-2x}+e^{-3x}$
(c)$y = e^{-2x}+e^{3x}$
(d)$y = e^{2x}+e^{3x}$
M.2)If A & B are independent , then A and $\overline{B}$ are also
(a)independent
(b)dependent
(c)cannot say
(d)none of above
M.3)Bilateral Laplace Transform of $f(t) =\begin{cases} 1 , if \leq t \leq b & &\\ 0 ,Otherwise \end{cases}$
(a)$\frac{(a-b)}{s}$
(b)$\frac{[(a-b)\times(e^{s})]}{s}$
(c)$\frac{[(e^{-as})-(e^{-bs})]}{s}$
(d)$\frac{[e^{as-bs}]}{s}$
M.4)Let $ f(x) = \left|x\right|$,then
(a)f'(0) = 0
(b)f(x) is maximum at x = 0
(c)f(x) is minimum at x = 0
(d)none of these
M.5)Decimal 43 in Hexadecimal and BCD number system is respectively
(a)B2,0100 0011
(b)2B,0100 0011
(c)2B,0011 0100
(d)B2,0011 0100
M.6)If A & B are mutually exclusive and P(A U B) = P(A) + P(B),
then P(A/A U B) =
(a)$\frac{P(A)}{P(A)+P(B)}$
(b)$\frac{P(A)}{P(A)-P(B)}$
(c)$\frac{P(B)}{P(A)+P(B)}$
(d)none of these
M.7)Given the Matrix $\begin{bmatrix} -4&2\\ 4&3 \end{bmatrix}$ eigen vector is
(a)$ \begin{bmatrix} 3\\2 \end{bmatrix}$
(b)$\begin{bmatrix}4\\3\end{bmatrix}$
(c)$\begin{bmatrix}2\\-1\end{bmatrix}$
(d)$\begin{bmatrix}-1\\2\end{bmatrix}$
M.8)Consider a matrix A = $\begin{bmatrix}-3&&2\\-1&&0\end{bmatrix}$then $A^{9}$ equals:
(a)511A+510I
(b)309A+104I
(c)154A+155I
(d)exp(9A)
M.9)If $A = \begin{bmatrix}2&&-0.1\\0&&3\end{bmatrix}$ and $A^{-1} = \begin{bmatrix}0.5 &&a\\0&&b\end{bmatrix}$ then (a+b) = ?
(a)$\frac{7}{20}$
(b)$\frac{3}{20}$
(c)$\frac{19}{60}$
(d)$\frac{11}{20}$
M.10)If A B are two matrices and if AB exists,then BA exists ;
(a)Only if A has as many rows as B has columns
(b)Only if both A & B are square matrices
(c)Only if A & B are skew matrices
(d)Only if both A & B are symmetric
M.11)The equation $x^{3}-x^{2}+4x-4=0$ is to be solved using Newton-Raphson method. If x=2 is taken as initial approximation of the solution , then the next approximation using this method is
(a)$\frac{2}{3}$
(b)$\frac{4}{3}$
(c)1
(d)$\frac{3}{2}$
M.12)A box contains 10 screws, 3 of them are defective.Two screws are drawn at random with replacement.The probability that none of the two screws are defective will be
(a)100%
(b)50%
(c)49%
(d)none of above
M.13)A fair coin is tossed three times in succession.If the first toss produces a head , then the probability of getting exactly two heads in three toses is
(a)$\frac{1}{8}$
(b)$\frac{1}{2}$
(c)$\frac{3}{8}$
(d)$\frac{3}{4}$
M.14)X is a uniformly distributed random variable that takes values between 0 & 1. The value of $E[X^{3}]$ will be
(a)0
(b)$\frac{1}{8}$
(c)$\frac{1}{4}$
(d)$\frac{1}{2}$
(a)$ y = e^{2x}+e^{-3x}$
(b)$y = e^{-2x}+e^{-3x}$
(c)$y = e^{-2x}+e^{3x}$
(d)$y = e^{2x}+e^{3x}$
Answer is (d)
M.2)If A & B are independent , then A and $\overline{B}$ are also
(a)independent
(b)dependent
(c)cannot say
(d)none of above
Answer is (a)
M.3)Bilateral Laplace Transform of $f(t) =\begin{cases} 1 , if \leq t \leq b & &\\ 0 ,Otherwise \end{cases}$
(a)$\frac{(a-b)}{s}$
(b)$\frac{[(a-b)\times(e^{s})]}{s}$
(c)$\frac{[(e^{-as})-(e^{-bs})]}{s}$
(d)$\frac{[e^{as-bs}]}{s}$
Answer is (c)
M.4)Let $ f(x) = \left|x\right|$,then
(a)f'(0) = 0
(b)f(x) is maximum at x = 0
(c)f(x) is minimum at x = 0
(d)none of these
Answer is (c)
M.5)Decimal 43 in Hexadecimal and BCD number system is respectively
(a)B2,0100 0011
(b)2B,0100 0011
(c)2B,0011 0100
(d)B2,0011 0100
Answer is (b)
M.6)If A & B are mutually exclusive and P(A U B) = P(A) + P(B),
then P(A/A U B) =
(a)$\frac{P(A)}{P(A)+P(B)}$
(b)$\frac{P(A)}{P(A)-P(B)}$
(c)$\frac{P(B)}{P(A)+P(B)}$
(d)none of these
Answer is (a)
M.7)Given the Matrix $\begin{bmatrix} -4&2\\ 4&3 \end{bmatrix}$ eigen vector is
(a)$ \begin{bmatrix} 3\\2 \end{bmatrix}$
(b)$\begin{bmatrix}4\\3\end{bmatrix}$
(c)$\begin{bmatrix}2\\-1\end{bmatrix}$
(d)$\begin{bmatrix}-1\\2\end{bmatrix}$
Answer is (c)
M.8)Consider a matrix A = $\begin{bmatrix}-3&&2\\-1&&0\end{bmatrix}$then $A^{9}$ equals:
(a)511A+510I
(b)309A+104I
(c)154A+155I
(d)exp(9A)
Answer is (a)
M.9)If $A = \begin{bmatrix}2&&-0.1\\0&&3\end{bmatrix}$ and $A^{-1} = \begin{bmatrix}0.5 &&a\\0&&b\end{bmatrix}$ then (a+b) = ?
(a)$\frac{7}{20}$
(b)$\frac{3}{20}$
(c)$\frac{19}{60}$
(d)$\frac{11}{20}$
Answer is (a)
M.10)If A B are two matrices and if AB exists,then BA exists ;
(a)Only if A has as many rows as B has columns
(b)Only if both A & B are square matrices
(c)Only if A & B are skew matrices
(d)Only if both A & B are symmetric
Answer is (a)
M.11)The equation $x^{3}-x^{2}+4x-4=0$ is to be solved using Newton-Raphson method. If x=2 is taken as initial approximation of the solution , then the next approximation using this method is
(a)$\frac{2}{3}$
(b)$\frac{4}{3}$
(c)1
(d)$\frac{3}{2}$
Answer is (b)
M.12)A box contains 10 screws, 3 of them are defective.Two screws are drawn at random with replacement.The probability that none of the two screws are defective will be
(a)100%
(b)50%
(c)49%
(d)none of above
Answer is (c)
M.13)A fair coin is tossed three times in succession.If the first toss produces a head , then the probability of getting exactly two heads in three toses is
(a)$\frac{1}{8}$
(b)$\frac{1}{2}$
(c)$\frac{3}{8}$
(d)$\frac{3}{4}$
Answer is (b)
M.14)X is a uniformly distributed random variable that takes values between 0 & 1. The value of $E[X^{3}]$ will be
(a)0
(b)$\frac{1}{8}$
(c)$\frac{1}{4}$
(d)$\frac{1}{2}$
