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Most answered questions in Engineering Mathematics

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82
GATE2016-1-3
If the entries in each column of a square matrix $M$ add up to $1$, then an eigenvalue of $M$ is $4$ $3$ $2$ $1$
If the entries in each column of a square matrix $M$ add up to $1$, then an eigenvalue of $M$ is$4$$3$$2$$1$
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86
GATE2016-1-27
The value of $\int_0^{\infty} \dfrac{1}{1+x^2} dx + \int _0^{\infty} \dfrac{\sin x}{x} dx$ is $\dfrac{\pi}{2} \\$ $\pi \\$ $\dfrac{3 \pi}{2} \\$ $1$
The value of $\int_0^{\infty} \dfrac{1}{1+x^2} dx + \int _0^{\infty} \dfrac{\sin x}{x} dx$ is$\dfrac{\pi}{2} \\$$\pi \\$$\dfrac{3 \pi}{2} \\$$1$
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87
GATE2016-1-28
The area of the region bounded by the parabola $y=x^2+1$ and the straight line $x+y=3$ is $\dfrac{59}{6} \\$ $\dfrac{9}{2} \\$ $\dfrac{10}{3} \\$ $\dfrac{7}{6}$
The area of the region bounded by the parabola $y=x^2+1$ and the straight line $x+y=3$ is$\dfrac{59}{6} \\$$\dfrac{9}{2} \\$$\dfrac{10}{3} \\$$\dfrac{7}{6}$
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90
GATE2017 CE-1: 1
The matrix $P$ is the inverse of a matrix $Q$. If $I$ denotes the identity matrix, which one of the following options is correct? $PQ=I$ but $QP \neq I$ $QP=I$ but $PQ \neq I$ $PQ=I$ and $QP= I$ $PQ-QP= I$
The matrix $P$ is the inverse of a matrix $Q$. If $I$ denotes the identity matrix, which one of the following options is correct?$PQ=I$ but $QP \neq I$$QP=I$ but $PQ \neq...
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91
GATE2017 CE-1: 2
The number of parameters in the univariate exponential and Gaussian distributions, repsectively, are $2$ and $2$ $1$ and $2$ $2$ and $1$ $1$ and $1$
The number of parameters in the univariate exponential and Gaussian distributions, repsectively, are$2$ and $2$$1$ and $2$$2$ and $1$$1$ and $1$
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92
GATE2017 CE-1: 3
Let $x$ be a continuous variable defined over the interval $(- \infty, \infty)$, and $f(x) = e^{-x-e^{-x}}$. The integral $g(x)= \int f(x) \: dx$ is equal to $e^{e^{-x}}$ $e^{-e^{-x}}$ $e^{-e^{x}}$ $e^{-x}$
Let $x$ be a continuous variable defined over the interval $(- \infty, \infty)$, and $f(x) = e^{-x-e^{-x}}$. The integral $g(x)= \int f(x) \: dx$ is equal to$e^{e^{-x}}$$...
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94
GATE2017 CE-1: 21
$\underset{x \to 0}{\lim} \bigg( \dfrac{\tan x}{x^2-x} \bigg)$ is equal to _________
$\underset{x \to 0}{\lim} \bigg( \dfrac{\tan x}{x^2-x} \bigg)$ is equal to _________
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95
GATE2017 CE-1: 26
For the function $f(x)=a+bx,0\leq x\leq1,$ to be a valid probability density function,which one of the following statements is correct? $a=1,b=4$ $b=0.5,b=1$ $a=0,b=1$ $a=1,b=-1$
For the function $f(x)=a+bx,0\leq x\leq1,$ to be a valid probability density function,which one of the following statements is correct?$a=1,b=4$$b=0.5,b=1$$a=0,b=1$$a=1,b...
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96
GATE2017 CE-1: 27
The solution of the equation $\dfrac{dQ}{dt} +Q =1$ with $Q=0$ at $t=0$ is $Q(t)=e^{-t}-1$ $Q(t)=1+ e^{-t}$ $Q(t)=1 -e^t$ $Q(t)=1- e^{-t}$
The solution of the equation $\dfrac{dQ}{dt} +Q =1$ with $Q=0$ at $t=0$ is$Q(t)=e^{-t}-1$$Q(t)=1+ e^{-t}$$Q(t)=1 -e^t$$Q(t)=1- e^{-t}$
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99
GATE2015-2-1
While minimizing the function $f(x)$, necessary and sufficient conditions for a point, $x_0$ to be a minima are: $f’(x_0) > 0$ and $f’’(x_0)=0$ $f’(x_0) < 0$ and $f’’(x_0)=0$ $f’(x_0) = 0$ and $f’’(x_0)<0$ $f’(x_0) = 0$ and $f’’(x_0)>0$
While minimizing the function $f(x)$, necessary and sufficient conditions for a point, $x_0$ to be a minima are:$f’(x_0) 0$ and $f’’(x_0)=0$$f’(x_0) < 0$ and $f�...
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101
GATE2015-2-3
Given, $i=\sqrt{-1}$, the value of the definite integral, $I= \int_0^{\pi/2} \dfrac{\cos x+ i \sin x}{\cos x – i \sin x} dx$ is: $1$ $-1$ $i$ $-i$
Given, $i=\sqrt{-1}$, the value of the definite integral, $I= \int_0^{\pi/2} \dfrac{\cos x+ i \sin x}{\cos x – i \sin x} dx$ is:$1$$-1$$i$$-i$
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102
GATE2015-2-4
$\underset{x \to \infty}{\lim} \bigg( 1+ \dfrac{1}{x} \bigg)^{2x} $ is equal to $e^{-2}$ $e$ $1$ $e^2$
$\underset{x \to \infty}{\lim} \bigg( 1+ \dfrac{1}{x} \bigg)^{2x} $ is equal to$e^{-2}$$e$$1$$e^2$
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103
GATE2015-2-5
Let $A=[a_{ij}], \: 1 \leq i, j \leq n$ with $n \geq 3$ and $a_{ij}=i \cdot j$. The rank of $A$ is: $0$ $1$ $n-1$ $n$
Let $A=[a_{ij}], \: 1 \leq i, j \leq n$ with $n \geq 3$ and $a_{ij}=i \cdot j$. The rank of $A$ is:$0$$1$$n-1$$n$
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105
GATE2015-2-27
Consider the following second order linear differential equation $\dfrac{d^2y}{dx^2} = -12x^2 +24 x – 20$ The boundary conditions are: at $x=0, \: y=5$ and at $x=2, \: y=21$. The value of $y$ at $x=1$ is _________.
Consider the following second order linear differential equation$$\dfrac{d^2y}{dx^2} = -12x^2 +24 x – 20$$The boundary conditions are: at $x=0, \: y=5$ and at $x=2, \: ...
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106
GATE2015-2-28
The two Eigen values of the matrix $\begin{bmatrix} 2 & 1 \\ 1 & p \end{bmatrix}$ have a ratio of $3:1$ for $p=2$. What is another value of $p$ for which the Eigen values have the same ratio of $3:1$? $-2$ $1$ $7/3$ $14/3$
The two Eigen values of the matrix $\begin{bmatrix} 2 & 1 \\ 1 & p \end{bmatrix}$ have a ratio of $3:1$ for $p=2$. What is another value of $p$ for which the Eigen values...
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107
GATE2015-2-29
For step-size, $\Delta x =0.4$, the value of following integral using Simpson’s $1/3$ rule is _______. $\int_0^{0.8} (0.2 + 25 x – 200 x^2 + 675 x^3 – 900 x^4 +400 x^5) dx$
For step-size, $\Delta x =0.4$, the value of following integral using Simpson’s $1/3$ rule is _______.$$\int_0^{0.8} (0.2 + 25 x – 200 x^2 + 675 x^3 – 900 x^4 +400 ...
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108
GATE2015-1-1
For what value of $p$ the following set of equations will have no solution? $2x+3y=5$ $3x+py=10$
For what value of $p$ the following set of equations will have no solution?$2x+3y=5$$3x+py=10$
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111
GATE2015-1-26
The smallest and largest Eigen values of the following matrix are: $\begin{bmatrix} 3 & -2 & 2 \\ 4 & -4 & 6 \\ 2 & -3 & 5 \end{bmatrix}$ $1.5$ and $2.5$ $0.5$ and $2.5$ $1.0$ and $3.0$ $1.0$ and $2.0$
The smallest and largest Eigen values of the following matrix are:$\begin{bmatrix} 3 & -2 & 2 \\ 4 & -4 & 6 \\ 2 & -3 & 5 \end{bmatrix}$$1.5$ and $2.5$$0.5$ and $2.5$$1.0...
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114
GATE2015-1-29
Consider the following complex function: $f(z) = \frac{9}{(z-1)(z+2)^2}$ Which of the following is one of the residues of the above function? $-1$ $9/16$ $2$ $9$
Consider the following complex function:$$f(z) = \frac{9}{(z-1)(z+2)^2}$$Which of the following is one of the residues of the above function?$-1$$9/16$$2$$9$
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115
GATE2015-1-30
The directional derivative of the field $u(x,y,z) = x^2-3yz$ in the direction of the vector $(\hat{i}+\hat{j}-2 \hat{k})$ at point $(2, -1, 4)$ is _________.
The directional derivative of the field $u(x,y,z) = x^2-3yz$ in the direction of the vector $(\hat{i}+\hat{j}-2 \hat{k})$ at point $(2, -1, 4)$ is _________.
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116
GATE2014-2-26
The expression $\displaystyle{} \lim_{a \to 0} \dfrac{x^a-1}{a}$ is equal to $\log x$ $0$ $x \log x$ $\infty$
The expression $\displaystyle{} \lim_{a \to 0} \dfrac{x^a-1}{a}$ is equal to$\log x$$0$$x \log x$$\infty$
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117
GATE2014-2-28
The rank of the matrix $\begin{bmatrix} 6 & 0 & 4 & 4 \\ -2 & 14 & 8 & 18 \\ 14 & -14 & 0 & -10 \end{bmatrix}$ is _________
The rank of the matrix $\begin{bmatrix} 6 & 0 & 4 & 4 \\ -2 & 14 & 8 & 18 \\ 14 & -14 & 0 & -10 \end{bmatrix}$ is _________
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118
GATE2014-2-4
The integrating factor for the differential equation $\dfrac{dP}{dt}+k_2P=k_1L_0e^{-k_1t}$ is $e^{-k_1t} \\$ $e^{-k_2t} \\$ $e^{k_1t} \\$ $e^{k_2t}$
The integrating factor for the differential equation $\dfrac{dP}{dt}+k_2P=k_1L_0e^{-k_1t}$ is$e^{-k_1t} \\$$e^{-k_2t} \\$$e^{k_1t} \\$$e^{k_2t}$
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