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Hot questions in Engineering Mathematics

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81
GATE2016-2-29
The area between the parabola $x^2=8y$ and the straight line $y=8$ is _______.
The area between the parabola $x^2=8y$ and the straight line $y=8$ is _______.
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82
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$$9$
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85
GATE2016-2-30
The quadratic approximation of $f(x)=x^3 – 3x^2 -5$ at the point $x=0$ is $3x^2 -6x-5$ $-3x^2-5$ $-3x^2+6x-5$ $3x^2-5$
The quadratic approximation of $f(x)=x^3 – 3x^2 -5$ at the point $x=0$ is$3x^2 -6x-5$$-3x^2-5$$-3x^2+6x-5$$3x^2-5$
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86
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$$1.0...
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89
GATE2016-1-28
The area of the region bounded by the parabola $y=x^2+1$ and the straight line $x+y=3$ is $\dfrac{59}{6} \\$ $\dfrac{9}{2} \\$ $\dfrac{10}{3} \\$ $\dfrac{7}{6}$
The area of the region bounded by the parabola $y=x^2+1$ and the straight line $x+y=3$ is$\dfrac{59}{6} \\$$\dfrac{9}{2} \\$$\dfrac{10}{3} \\$$\dfrac{7}{6}$
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91
GATE2016-1-1
Newton-Raphson method is to be used to find root of equation $3x-e^x+ \sin x=0$.If the initial trial value for the root is taken as $0.333$, the next approximation for the root would be _______ (note: answer up to three decimal)
Newton-Raphson method is to be used to find root of equation $3x-e^x+ \sin x=0$.If the initial trial value for the root is taken as $0.333$, the next approximation for th...
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93
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}}$$...
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94
GATE2017 CE-1: 21
$\underset{x \to 0}{\lim} \bigg( \dfrac{\tan x}{x^2-x} \bigg)$ is equal to _________
$\underset{x \to 0}{\lim} \bigg( \dfrac{\tan x}{x^2-x} \bigg)$ is equal to _________
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96
GATE Civil 2012 | Question: 27
In an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one negative value in five trials is $\dfrac{1}{32} \\$ $\dfrac{2}{32} \\$ $\dfrac{3}{32} \\$ $\dfrac{6}{32}$
In an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one negative value in five trials is$\dfrac{1}{32} \\$$\d...
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98
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$$1$
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99
GATE Civil 2012 | Question: 28
The eigenvalues of matrix $\begin{bmatrix} 9 & 5 \\ 5 & 8 \end{bmatrix}$ are $-2.42$ and $6.86$ $3.48$ and $13.53$ $4.70$ and $6.86$ $6.86$ and $9.50$
The eigenvalues of matrix $\begin{bmatrix} 9 & 5 \\ 5 & 8 \end{bmatrix}$ are$-2.42$ and $6.86$$3.48$ and $13.53$$4.70$ and $6.86$$6.86$ and $9.50$
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100
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$$n$
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101
GATE2015-1-30
The directional derivative of the field $u(x,y,z) = x^2-3yz$ in the direction of the vector $(\hat{i}+\hat{j}-2 \hat{k})$ at point $(2, -1, 4)$ is _________.
The directional derivative of the field $u(x,y,z) = x^2-3yz$ in the direction of the vector $(\hat{i}+\hat{j}-2 \hat{k})$ at point $(2, -1, 4)$ is _________.
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104
GATE2016-1-27
The value of $\int_0^{\infty} \dfrac{1}{1+x^2} dx + \int _0^{\infty} \dfrac{\sin x}{x} dx$ is $\dfrac{\pi}{2} \\$ $\pi \\$ $\dfrac{3 \pi}{2} \\$ $1$
The value of $\int_0^{\infty} \dfrac{1}{1+x^2} dx + \int _0^{\infty} \dfrac{\sin x}{x} dx$ is$\dfrac{\pi}{2} \\$$\pi \\$$\dfrac{3 \pi}{2} \\$$1$
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108
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$$1$ and $1$
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109
GATE2015-2-3
Given, $i=\sqrt{-1}$, the value of the definite integral, $I= \int_0^{\pi/2} \dfrac{\cos x+ i \sin x}{\cos x – i \sin x} dx$ is: $1$ $-1$ $i$ $-i$
Given, $i=\sqrt{-1}$, the value of the definite integral, $I= \int_0^{\pi/2} \dfrac{\cos x+ i \sin x}{\cos x – i \sin x} dx$ is:$1$$-1$$i$$-i$
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110
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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111
GATE Civil 2012 | Question: 29
For the parallelogram OPQR shown in the sketch, $\overrightarrow{OP}=a \hat{i}+b \hat{j}$ and $\overrightarrow{OR}=c \hat{i} +d \hat{j}$. The area of the parallelogram is $ad-bc$ $ac+bd$ $ad+bc$ $ab-cd$
For the parallelogram OPQR shown in the sketch, $\overrightarrow{OP}=a \hat{i}+b \hat{j}$ and $\overrightarrow{OR}=c \hat{i} +d \hat{j}$. The area of the parallelogram is...
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112
GATE2014-1-4
The sum of Eigen values of the matrix, $[M]$ is where $[M] = \begin{bmatrix} 215 & 650 & 795 \\ 655 & 150 & 835 \\ 485 & 355 & 550 \end{bmatrix}$ $915$ $1355$ $1640$ $2180$
The sum of Eigen values of the matrix, $[M]$ iswhere $[M] = \begin{bmatrix} 215 & 650 & 795 \\ 655 & 150 & 835 \\ 485 & 355 & 550 \end{bmatrix}$$915$$1355$$1640$$2180$
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115
GATE Civil 2013 | Question: 3
A $1$-h rainfall of $10$ cm magnitude at a station has a return period of $50$ years. The probability that a $1$-h rainfall of magnitude $10$ cm or more will occur in each of two successive years is $0.04$ $0.2$ $0.02$ $0.0004$
A $1$-h rainfall of $10$ cm magnitude at a station has a return period of $50$ years. The probability that a $1$-h rainfall of magnitude $10$ cm or more will occur in eac...
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118
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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120
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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