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Most viewed questions in Engineering Mathematics
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241
TIFR ECE 2014 | Question: 8
Consider a square pulse $g(t)$ of height $1$ and width $1$ centred at $1 / 2$. Define $f_{n}(t)=\frac{1}{n}\left(g(t) *^{n} g(t)\right),$ where $*^{n}$ stands for $n$-fold convolution. Let $f(t)=\lim _{n \rightarrow \infty} f_{n}(t)$. Then, which ... $\infty$. $f(t)$ has width $\infty$ and height $1$ . $f(t)$ has width $0$ and height $\infty$. None of the above.
Consider a square pulse $g(t)$ of height $1$ and width $1$ centred at $1 / 2$. Define $f_{n}(t)=\frac{1}{n}\left(g(t) *^{n} g(t)\right),$ where $*^{n}$ stands for $n$-fol...
admin
46.4k
points
100
views
admin
asked
Dec 14, 2022
Calculus
tifr2014
calculus
limits
+
–
1
votes
0
answers
242
TIFR ECE 2021 | Question: 7
Consider the function \[f(y)=\int_{1}^{y} \frac{1}{1+x^{2}} d x-\log _{e}(1+y)\] where $\log _{e}(x)$ denotes the natural logarithm of $x$. Which of the following is true: The function $f(y)$ ... $y \geq 1$. The derivative of function $f(y)$ does not exist at $y=1$.
Consider the function\[f(y)=\int_{1}^{y} \frac{1}{1+x^{2}} d x-\log _{e}(1+y)\]where $\log _{e}(x)$ denotes the natural logarithm of $x$.Which of the following is true:Th...
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46.4k
points
99
views
admin
asked
Nov 30, 2022
Calculus
tifrece2021
calculus
definite-integrals
+
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0
votes
0
answers
243
GATE ECE 2016 Set 3 | Question: 29
The values of the integral $\large\frac{1}{2\pi j}\oint_c\frac{e^z}{(z-2)} \small dz$ along a closed contour $c$ in anti-clockwise direction for the point $z_0=2$ inside the contour $c$, and the point $z_0=2$ outside the contour $c$, respectively,are $(i)2.72, \: (ii) 0$ $(i)7.39, \: (ii) 0$ $(i)0, \: (ii) 2.72$ $(i)0, \: (ii) 7.39$
The values of the integral $\large\frac{1}{2\pi j}\oint_c\frac{e^z}{(z-2)} \small dz$ along a closed contour $c$ in anti-clockwise direction forthe point $z_0=2$ inside t...
Milicevic3306
16.0k
points
99
views
Milicevic3306
asked
Mar 27, 2018
Complex Analysis
gate2016-ec-3
complex-analysis
+
–
0
votes
0
answers
244
GATE ECE 2016 Set 1 | Question: 2
The second moment of a Poisson-distributed random variable is $2$. The mean of the random variable is _____
The second moment of a Poisson-distributed random variable is $2$. The mean of the random variable is _____
Milicevic3306
16.0k
points
99
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ec-1
numerical-answers
probability-and-statistics
probability
poisson-distribution
random-variable
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0
votes
0
answers
245
GATE ECE 2016 Set 1 | Question: 26
The integral $\frac{1}{2\pi} \iint_D(x+y+10) \,dx\,dy$, where $D$ denotes the disc: $x^2+y^2\leq 4$,evaluates to _________
The integral $\frac{1}{2\pi} \iint_D(x+y+10) \,dx\,dy$, where $D$ denotes the disc: $x^2+y^2\leq 4$,evaluates to _________
Milicevic3306
16.0k
points
99
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Milicevic3306
asked
Mar 27, 2018
Calculus
gate2016-ec-1
numerical-answers
calculus
definite-integrals
+
–
0
votes
0
answers
246
GATE ECE 2015 Set 1 | Question: 43
Two sequences $\begin{bmatrix}a, & b, & c \end{bmatrix}$ and $\begin{bmatrix}A, & B, & C \end{bmatrix}$ ... $\begin{bmatrix}p, & q, & r \end{bmatrix} = \begin{bmatrix} c, & b, & a \end{bmatrix}$
Two sequences $\begin{bmatrix}a, & b, & c \end{bmatrix}$ and $\begin{bmatrix}A, & B, & C \end{bmatrix}$ are related as,$$\begin{bmatrix}A \\ B \\ C \end{bmatrix} = \be...
Milicevic3306
16.0k
points
99
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Milicevic3306
asked
Mar 27, 2018
Linear Algebra
gate2015-ec-1
linear-algebra
matrices
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0
votes
0
answers
247
GATE ECE 2014 Set 4 | Question: 26
With initial values $y(0) =y’(0)=1$, the solution of the differential equation $\frac{d^2y}{dx^2}+4 \frac{dy}{dx}+4y=0$ at $x=1$ is ________
With initial values $y(0) =y’(0)=1$, the solution of the differential equation $$\frac{d^2y}{dx^2}+4 \frac{dy}{dx}+4y=0$$ at $x=1$ is ________
Milicevic3306
16.0k
points
99
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Milicevic3306
asked
Mar 26, 2018
Differential Equations
gate2014-ec-4
numerical-answers
differential-equations
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1
votes
0
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248
TIFR ECE 2014 | Question: 13
Let function $f: \mathbf{R} \rightarrow \mathbf{R}$ be convex, i.e., for $x, y \in \mathbf{R}, \alpha \in[0,1], f(\alpha x+(1-\alpha) y) \leq$ $\alpha f(x)+(1-\alpha) f(y)$. Then which of the following is $\text{TRUE?}$ $f(x) \leq f(y)$ whenever ... $f$ and $g$ are both convex, then $\min \{f, g\}$ is also convex. For a random variable $X, E(f(X)) \geq f(E(X))$.
Let function $f: \mathbf{R} \rightarrow \mathbf{R}$ be convex, i.e., for $x, y \in \mathbf{R}, \alpha \in[0,1], f(\alpha x+(1-\alpha) y) \leq$ $\alpha f(x)+(1-\alpha) f(y...
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46.4k
points
98
views
admin
asked
Dec 14, 2022
Calculus
tifr2014
calculus
functions
+
–
1
votes
0
answers
249
TIFR ECE 2013 | Question: 11
Two matrices $A$ and $B$ are called similar if there exists another matrix $S$ such that $S^{-1} A S=B$. Consider the statements: If $A$ and $B$ are similar then they have identical rank. If $A$ and $B$ ... Both $\text{I}$ and $\text{II}$ but not $\text{III}$. All of $\text{I}, \text{II}$ and $\text{III}$.
Two matrices $A$ and $B$ are called similar if there exists another matrix $S$ such that $S^{-1} A S=B$. Consider the statements:If $A$ and $B$ are similar then they have...
admin
46.4k
points
98
views
admin
asked
Dec 12, 2022
Linear Algebra
tifr2013
linear-algebra
rank-of-matrix
+
–
1
votes
0
answers
250
TIFR ECE 2021 | Question: 3
Consider the following statements: $\lim _{x \rightarrow 0} \frac{\sin x}{x}=1$. $\lim _{x \rightarrow 0} \frac{1-\cos x}{x^{2}}=1$. $\lim _{x \rightarrow 0} \frac{1-\cos x}{x}=1$. Which of the following is $\text{TRUE?}$ Only Statement $1$ ... $1$ and $3$ are correct. All of Statements $1, 2,$ and $3$ are correct. None of the three Statements $1,2,$ and $3$ are correct.
Consider the following statements:$\lim _{x \rightarrow 0} \frac{\sin x}{x}=1$.$\lim _{x \rightarrow 0} \frac{1-\cos x}{x^{2}}=1$.$\lim _{x \rightarrow 0} \frac{1-\cos x}...
admin
46.4k
points
98
views
admin
asked
Nov 30, 2022
Calculus
tifrece2021
calculus
limits
+
–
1
votes
0
answers
251
TIFR ECE 2018 | Question: 11
Assume the following well known result: If a coin is flipped independently many times and its probability of heads $(H)$ is $p \in(0,1)$ and probability of tails $(T)$ is $(1-p)$, then the expected number of coin flips till the first time a heads is observed is $1 / p$. What is the ... $\frac{1}{1-(1-p)^{2}}(4+1 / p)$ $\frac{1}{p}+\frac{1}{1-p}$
Assume the following well known result: If a coin is flipped independently many times and its probability of heads $(H)$ is $p \in(0,1)$ and probability of tails $(T)$ is...
admin
46.4k
points
98
views
admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2018
probability-and-statistics
probability
expectation
+
–
0
votes
0
answers
252
GATE ECE 2014 Set 3 | Question: 1
The maximum value of the function $f(x) = \text{ln } (1+x) – x $ (where $x >-1$) occurs at $x=$_______.
The maximum value of the function $f(x) = \text{ln } (1+x) – x $ (where $x >-1$) occurs at $x=$_______.
Milicevic3306
16.0k
points
98
views
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2014-ec-3
calculus
maxima-minima
numerical-answers
+
–
0
votes
0
answers
253
GATE ECE 2013 | Question: 39
The $\text{DFT}$ of a vector $\begin{bmatrix} a & b & c & d \end{bmatrix}$ is the vector $\begin{bmatrix} \alpha & \beta & \gamma & \delta \end{bmatrix}.$ ... $\begin{bmatrix} \alpha & \beta & \gamma & \delta \end{bmatrix}$
The $\text{DFT}$ of a vector $\begin{bmatrix} a & b & c & d \end{bmatrix}$ is the vector $\begin{bmatrix} \alpha & \beta & \gamma & \delta \end{bmatrix}.$ consider the...
Milicevic3306
16.0k
points
98
views
Milicevic3306
asked
Mar 25, 2018
Vector Analysis
gate2013-ec
vector-analysis
+
–
1
votes
0
answers
254
TIFR ECE 2014 | Question: 5
The matrix \[ A=\left(\begin{array}{ccc} 1 & a_{1} & a_{1}^{2} \\ 1 & a_{2} & a_{2}^{2} \\ 1 & a_{3} & a_{3}^{2} \end{array}\right) \] is invertible when $a_{1}>a_{2}>a_{3}$ $a_{1}<a_{2}<a_{3}$ $a_{1}=3, a_{2}=2, a_{3}=4$ All of the above None of the above
The matrix\[A=\left(\begin{array}{ccc}1 & a_{1} & a_{1}^{2} \\1 & a_{2} & a_{2}^{2} \\1 & a_{3} & a_{3}^{2}\end{array}\right)\]is invertible when$a_{1}>a_{2}>a_{3}$$a_{1}...
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46.4k
points
97
views
admin
asked
Dec 14, 2022
Linear Algebra
tifr2014
linear-algebra
matrices
+
–
0
votes
0
answers
255
GATE ECE 2013 | Question: 7
The divergence of the vector field $\overrightarrow{A} = x\hat{a}_{x} + y\hat{a}_{y} + z\hat{a}_{z}$ is $0$ $1/3$ $1$ $3$
The divergence of the vector field $\overrightarrow{A} = x\hat{a}_{x} + y\hat{a}_{y} + z\hat{a}_{z}$ is $0$$1/3$ $1$ $3$
Milicevic3306
16.0k
points
97
views
Milicevic3306
asked
Mar 25, 2018
Vector Analysis
gate2013-ec
vector-analysis
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–
1
votes
0
answers
256
TIFR ECE 2012 | Question: 12
In modeling the number of health insurance claims filed by an individual during a three year period, an analyst makes a simplifying assumption that for all non-negative integer up to $5$. \[ p_{n+1}=\frac{1}{2} p_{n} \] where $p_{n}$ denotes the probability that a ... files more than two claims in this period? $7 / 31$ $29 / 125$ $1 / 3$ $13 / 125$ None of the above
In modeling the number of health insurance claims filed by an individual during a three year period, an analyst makes a simplifying assumption that for all non-negative i...
admin
46.4k
points
96
views
admin
asked
Dec 8, 2022
Probability and Statistics
tifr2012
probability-and-statistics
probability
conditional-probability
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–
1
votes
0
answers
257
TIFR ECE 2011 | Question: 9
Consider two independent random variables $X$ and $Y$ having probability density functions uniform in the interval $[-1,1]$. The probability that $X^{2}+Y^{2}>1$ is $\pi / 4$ $1-\pi / 4$ $\pi / 2-1$ Probability that $X^{2}+Y^{2}<0.5$ None of the above
Consider two independent random variables $X$ and $Y$ having probability density functions uniform in the interval $[-1,1]$. The probability that $X^{2}+Y^{2}>1$ is$\pi /...
admin
46.4k
points
96
views
admin
asked
Dec 5, 2022
Probability and Statistics
tifr2011
probability-and-statistics
probability
probability-density-function
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–
1
votes
0
answers
258
TIFR ECE 2010 | Question: 2
For $x \in[0, \pi / 2], \alpha$ for which $\sin (x) \geq x-\alpha x^{3}$ is $\alpha>1 /(2 \pi)$ $\alpha \geq 1 / 6$ $\alpha \leq 1 /(2 \pi)$ $\alpha=1 / 4$ None of the above
For $x \in[0, \pi / 2], \alpha$ for which $\sin (x) \geq x-\alpha x^{3}$ is$\alpha>1 /(2 \pi)$$\alpha \geq 1 / 6$$\alpha \leq 1 /(2 \pi)$$\alpha=1 / 4$None of the above
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46.4k
points
96
views
admin
asked
Nov 30, 2022
Calculus
tifr2010
calculus
maxima-minima
+
–
0
votes
0
answers
259
GATE ECE 2016 Set 1 | Question: 8
Consider the sequence $x[n] = a^nu[n] + b^nu[n]$, where $u[n]$ denotes the unit-step sequence and $0<\mid a \mid < \mid b \mid<1$. The region of convergence (ROC) of the $Z$-transform of $x[n]$ is $\mid Z \mid > \mid a \mid$ $\mid Z \mid > \mid b \mid$ $\mid Z \mid < \mid a \mid$ $\mid a \mid < \mid Z \mid < \mid b \mid$
Consider the sequence $x[n] = a^nu[n] + b^nu[n]$, where $u[n]$ denotes the unit-step sequence and $0<\mid a \mid < \mid b \mid<1$. The region of convergence (ROC) of the ...
Milicevic3306
16.0k
points
96
views
Milicevic3306
asked
Mar 27, 2018
Numerical Methods
gate2016-ec-1
numerical-methods
engineering-mathematics
convergence-criteria
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–
0
votes
0
answers
260
GATE ECE 2014 Set 3 | Question: 27
Which one of the following statements is NOT true for a square matrix $A$? If $A$ is upper triangular, the eigenvalues of $A$ are the diagonal elements of it If $A$ is real symmetric, the eigenvalues of $A$ are always real and positive If $A$ ... $A$ are positive, all the eigenvalues of $A$ are also positive
Which one of the following statements is NOT true for a square matrix $A$?If $A$ is upper triangular, the eigenvalues of $A$ are the diagonal elements of itIf $A$ is real...
Milicevic3306
16.0k
points
96
views
Milicevic3306
asked
Mar 26, 2018
Linear Algebra
gate2014-ec-3
linear-algebra
matrices
eigen-values
+
–
1
votes
0
answers
261
TIFR ECE 2015 | Question: 14
Consider a frog that lives on two rocks $A$ and $B$ and moves from one rock to the other randomly. If it is at Rock $A$ at any time, irrespective of which rocks it occupied in the past, it jumps back to Rock $A$ with probability $2 / 3$ and instead jumps to Rock ... of $n$ jumps as $n \rightarrow \infty?$ $1 / 2 $ $2 / 3$ $1$ The limit does not exist None of the above
Consider a frog that lives on two rocks $A$ and $B$ and moves from one rock to the other randomly. If it is at Rock $A$ at any time, irrespective of which rocks it occupi...
admin
46.4k
points
95
views
admin
asked
Dec 15, 2022
Probability and Statistics
tifr2015
probability-and-statistics
probability
conditional-probability
limits
+
–
0
votes
0
answers
262
GATE ECE 2016 Set 2 | Question: 55
A positive charge $q$ is placed at $x=0$ between two infinte metal plates placed at $x=-d$ and at $x=+d$ respectively. The metal plates lie in the $yz$ plane. The charge is at rest at $t=0$, when a voltage $+V$ is applied to the plate at $-d$ and ... that the charge $q$ takes to reach the right plate is proportional to $d/V$ $\sqrt{d}/V$ $d/\sqrt{V}$ $\sqrt{d/V}$
A positive charge $q$ is placed at $x=0$ between two infinte metal plates placed at $x=-d$ and at $x=+d$ respectively. The metal plates lie in the $yz$ plane. ...
Milicevic3306
16.0k
points
95
views
Milicevic3306
asked
Mar 27, 2018
Vector Analysis
gate2016-ec-2
vector-analysis
+
–
0
votes
0
answers
263
GATE ECE 2015 Set 3 | Question: 51
The complex envelope of the bandpass signal $x(t)=-\sqrt{2}\left(\dfrac{\sin (\pi t/5)}{\pi t/5}\right)\sin (\pi t - \dfrac{\pi}{4}),$ centered about $f=\dfrac{1}{2}\:Hz,$ is $\left(\dfrac{\sin (\pi t/5)}{\pi t/5}\right)e^{j\dfrac{\pi}{4}}$ ... $\sqrt{2} \left(\dfrac{\sin (\pi t/5)}{\pi t/5}\right)e^{-j\dfrac{\pi}{4}}$
The complex envelope of the bandpass signal $x(t)=-\sqrt{2}\left(\dfrac{\sin (\pi t/5)}{\pi t/5}\right)\sin (\pi t – \dfrac{\pi}{4}),$ centered about $f=\dfrac{1}{2}\:H...
Milicevic3306
16.0k
points
95
views
Milicevic3306
asked
Mar 27, 2018
Complex Analysis
gate2015-ec-3
complex-analysis
+
–
1
votes
0
answers
264
TIFR ECE 2012 | Question: 13
Consider a single amoeba that at each time slot splits into two with probability $p$ or dies otherwise with probability $1-p$. This process is repeated independently infinitely at each time slot, i.e. if there are any amoebas left at time slot $t$, then they all split independently into ... $\min \left\{\frac{1 \pm \sqrt{1-4 p(1-p)}}{2(1-p)}\right\}$ None of the above
Consider a single amoeba that at each time slot splits into two with probability $p$ or dies otherwise with probability $1-p$. This process is repeated independently infi...
admin
46.4k
points
94
views
admin
asked
Dec 8, 2022
Probability and Statistics
tifr2012
probability-and-statistics
probability
independent-events
+
–
1
votes
0
answers
265
TIFR ECE 2012 | Question: 17
Let $A=U \Lambda U^{\dagger}$ be a $n \times n$ matrix, where $U U^{\dagger}=I$. Which of the following statements is TRUE. The matrix $I+A$ has non-negative eigen values The matrix $I+A$ is symmetic $\operatorname{det}(I+A)=\operatorname{det}(I+\Lambda)$ $(a)$ and $(c)$ $(b)$ and $(c)$ $(a), (b)$ and $(c)$
Let $A=U \Lambda U^{\dagger}$ be a $n \times n$ matrix, where $U U^{\dagger}=I$. Which of the following statements is TRUE.The matrix $I+A$ has non-negative eigen valuesT...
admin
46.4k
points
94
views
admin
asked
Dec 8, 2022
Linear Algebra
tifr2012
linear-algebra
eigen-values
+
–
1
votes
0
answers
266
TIFR ECE 2018 | Question: 5
Suppose $\vec{u}, \vec{v}_{1}, \vec{v}_{2} \in \mathbb{R}^{n}$ are linearly independent vectors. Let the pair of real numbers $\left(a_{1}^{*}, a_{2}^{*}\right)$ be such that they solve the following optimization problem \[d=\min _{a_{1}, a_{2} \in \mathbb{R}}\left\ ... $\left\|\vec{v}_{*}\right\|^{2}-\|\vec{u}\|^{2}$ None of the above
Suppose $\vec{u}, \vec{v}_{1}, \vec{v}_{2} \in \mathbb{R}^{n}$ are linearly independent vectors. Let the pair of real numbers $\left(a_{1}^{*}, a_{2}^{*}\right)$ be such ...
admin
46.4k
points
94
views
admin
asked
Nov 29, 2022
Vector Analysis
tifrece2018
vector-analysis
vector-in-planes
+
–
1
votes
0
answers
267
TIFR ECE 2018 | Question: 7
Let $X_{1}, X_{2}$ and $X_{3}$ be independent random variables with uniform distribution over $[0, \theta]$. Consider the following statements. $E\left[\max \left\{X_{1}, X_{2}, X_{3}\right\}\right]=\frac{3}{4} \theta$ ... $\text{(i)}$ Only $\text{(ii)}$ Only $\text{(iii)}$ Only $\text{(iv)}$ All of $\text{(i) - (iv)}$
Let $X_{1}, X_{2}$ and $X_{3}$ be independent random variables with uniform distribution over $[0, \theta]$. Consider the following statements.$E\left[\max \left\{X_{1}, ...
admin
46.4k
points
94
views
admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2018
probability-and-statistics
probability
uniform-distribution
+
–
1
votes
0
answers
268
TIFR ECE 2018 | Question: 8
Let $A$ be an $n \times n$ real matrix for which two distinct non-zero $n$-dimensional real column vectors $v_{1}, v_{2}$ satisfy the relation $A v_{1}=A v_{2}$. Consider the following statements. At least one eigenvalue of $A$ is zero. $A$ ... $\text{(i)}$ Only $\text{(ii)}$ Only $\text{(iii)}$ Only $\text{(iv)}$ All of $\text{(i) - (iv)}$
Let $A$ be an $n \times n$ real matrix for which two distinct non-zero $n$-dimensional real column vectors $v_{1}, v_{2}$ satisfy the relation $A v_{1}=A v_{2}$. Consider...
admin
46.4k
points
94
views
admin
asked
Nov 29, 2022
Linear Algebra
tifrece2018
linear-algebra
matrices
+
–
0
votes
0
answers
269
GATE ECE 2014 Set 3 | Question: 4
An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is $0.067$ $0.073$ $0.082$ $0.091$
An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is$0.067$$0.073$$0.082$$0.091$
Milicevic3306
16.0k
points
94
views
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2014-ec-3
probability-and-statistics
probability
+
–
0
votes
0
answers
270
GATE ECE 2014 Set 2 | Question: 3
For $0 \leq t < \infty ,$ the maximum value of the function $f(t)= e^{-t}-2e^{-2t}$ occurs at $t= log_{e}4$ $t= log_{e}2$ $t= 0$ $t= log_{e}8$
For $0 \leq t < \infty ,$ the maximum value of the function $f(t)= e^{-t}-2e^{-2t}$ occurs at$t= log_{e}4$$t= log_{e}2$$t= 0$$t= log_{e}8$
Milicevic3306
16.0k
points
94
views
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2014-ec-2
calculus
maxima-minima
+
–
0
votes
0
answers
271
GATE ECE 2014 Set 1 | Question: 26
The Taylor series expansion of $3\sin x + 2 \cos x$ is $2 + 3x-x^{2} – \frac{x^{3}}{2} + \dots$ $2 – 3x + x^{2} – \frac{x^{3}}{2} + \dots$ $2 + 3x + x^{2} + \frac{x^{3}}{2} + \dots$ $2 – 3x – x^{2} + \frac{x^{3}}{2} + \dots$
The Taylor series expansion of $3\sin x + 2 \cos x$ is$2 + 3x-x^{2} – \frac{x^{3}}{2} + \dots$$2 – 3x + x^{2} – \frac{x^{3}}{2} + \dots$$2 + 3x + x^{2} + \frac...
Milicevic3306
16.0k
points
94
views
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2014-ec-1
calculus
taylor-series
+
–
1
votes
0
answers
272
TIFR ECE 2014 | Question: 17
Let $X$ be a Gaussian random variable with mean $\mu_{1}$ and variance $\sigma_{1}^{2}$. Now, suppose that $\mu_{1}$ itself is a random variable, which is also Gaussian distributed with mean $\mu_{2}$ and variance $\sigma_{2}^{2}$. Then the distribution ... variable with mean $\mu_{2}$ and variance $\sigma_{1}^{2}+\sigma_{2}^{2}$. Has no known form. None of the above.
Let $X$ be a Gaussian random variable with mean $\mu_{1}$ and variance $\sigma_{1}^{2}$. Now, suppose that $\mu_{1}$ itself is a random variable, which is also Gaussian d...
admin
46.4k
points
93
views
admin
asked
Dec 14, 2022
Probability and Statistics
tifr2014
probability-and-statistics
probability
normal-distribution
+
–
1
votes
0
answers
273
TIFR ECE 2013 | Question: 20
A function $f: \mathbb{R} \rightarrow \mathbb{R}$ is convex if for $x, y \in \mathbb{R}, \alpha \in[0,1], f(\alpha x+(1-\alpha) y) \leq \alpha f(x)+(1-\alpha) f(y)$. Which of the following is not convex: $x^{2}$ $x^{3}$ $x$ $x^{4}$ $\mathrm{e}^{x}$
A function $f: \mathbb{R} \rightarrow \mathbb{R}$ is convex if for $x, y \in \mathbb{R}, \alpha \in[0,1], f(\alpha x+(1-\alpha) y) \leq \alpha f(x)+(1-\alpha) f(y)$.Which...
admin
46.4k
points
93
views
admin
asked
Dec 12, 2022
Calculus
tifr2013
calculus
functions
+
–
1
votes
0
answers
274
TIFR ECE 2011 | Question: 8
Let $f(x, y)$ be a function in two variables $x, y$. Then which of the following is true $\max _{x} \min _{y} f(x, y) \leq \min _{y} \max _{x} f(x, y)$. $\max _{x} \min _{y} f(x, y) \geq \min _{y} \max _{x} f(x, y)$ ... $\max _{x} \min _{y} f(x, y)=\min _{y} \max _{x} f(x, y)+\min _{y} \min _{x} f(x, y)$. None of the above.
Let $f(x, y)$ be a function in two variables $x, y$. Then which of the following is true$\max _{x} \min _{y} f(x, y) \leq \min _{y} \max _{x} f(x, y)$.$\max _{x} \min _{y...
admin
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admin
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Dec 5, 2022
Calculus
tifr2011
calculus
maxima-minima
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–
1
votes
0
answers
275
TIFR ECE 2010 | Question: 3
Consider two independent random variables $\text{X}$ and $\text{Y}$ having probability density functions uniform in the interval $[0,1]$. When $\alpha \geq 1$, the probability that $\max (\text{X, Y})>\alpha \min (\text{X, Y})$ is $1 /(2 \alpha)$ $\exp (1-\alpha)$ $1 / \alpha$ $1 / \alpha^{2}$ $1 / \alpha^{3}$
Consider two independent random variables $\text{X}$ and $\text{Y}$ having probability density functions uniform in the interval $[0,1]$. When $\alpha \geq 1$, the probab...
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46.4k
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93
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admin
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Nov 30, 2022
Probability and Statistics
tifr2010
probability-and-statistics
probability
probability-density-function
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–
1
votes
0
answers
276
TIFR ECE 2018 | Question: 2
A hotel has $n$ rooms numbered $1,2, \ldots, n$. For each room there is one spare key labeled with the room number. The hotel manager keeps all the spare keys in a box. Her mischievous son got hold of the box and permuted the labels uniformly at random. What is the ... Use linearity of expectation] $1$ $\frac{n-1}{n}$ $\frac{n}{n-1}$ $\frac{n}{2}$ None of the above
A hotel has $n$ rooms numbered $1,2, \ldots, n$. For each room there is one spare key labeled with the room number. The hotel manager keeps all the spare keys in a box. H...
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46.4k
points
93
views
admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2018
probability-and-statistics
probability
expectation
+
–
1
votes
0
answers
277
TIFR ECE 2017 | Question: 10
Consider a single coin where the probability of heads is $p \in(0,1)$ and probability of tails is $1-p$. Suppose that this coin is flipped an infinite number of times. Let $N_{1}$ denote the number of flips till we see heads for the first time. Let $N_{2}$ denote the number of flips after ... $\frac{2}{p}$ $\frac{1}{p^{2}+(1-p)^{2}}$ $\frac{2}{p(1-p)}$
Consider a single coin where the probability of heads is $p \in(0,1)$ and probability of tails is $1-p$. Suppose that this coin is flipped an infinite number of times. Le...
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46.4k
points
93
views
admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2017
probability-and-statistics
probability
expectation
+
–
0
votes
0
answers
278
GATE ECE 2014 Set 3 | Question: 28
A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is _______ .
A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is _______ .
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93
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asked
Mar 26, 2018
Probability and Statistics
gate2014-ec-3
probability-and-statistics
probability
expectation
numerical-answers
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1
votes
0
answers
279
TIFR ECE 2022 | Question: 10
Find the vector which is closest (in Euclidean distance) to $\left(\begin{array}{lll}-1 & 1 & 1\end{array}\right)$ which can be written in the form \[a\left(\begin{array}{lll} 1 & 1 & 1 \end{array}\right)+b\left(\begin{array}{lll} 0 ... None of the above
Find the vector which is closest (in Euclidean distance) to $\left(\begin{array}{lll}-1 & 1 & 1\end{array}\right)$ which can be written in the form\[a\left(\begin{array}{...
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46.4k
points
92
views
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asked
Nov 30, 2022
Vector Analysis
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vector-analysis
vector-in-planes
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–
1
votes
0
answers
280
TIFR ECE 2022 | Question: 12
An $n \times n$ matrix $\mathbf{P}$ is called a Permutation Matrix if each of its $n$ columns and $n$ rows contain exactly one $1$ and $n-1 \; 0$ 's. Consider the following statements: $\operatorname{det}(\mathbf{P})$ is either $+1$ or ... $1,3$ are correct Only statements $2, 3$ are correct All statements $1, 2,$ and $3$ are correct
An $n \times n$ matrix $\mathbf{P}$ is called a Permutation Matrix if each of its $n$ columns and $n$ rows contain exactly one $1$ and $n-1 \; 0$ 's. Consider the followi...
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46.4k
points
92
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asked
Nov 30, 2022
Linear Algebra
tifrece2022
linear-algebra
matrices
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