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132
TIFR ECE 2019 | Question: 3
Consider a function $f: \mathbf{R} \rightarrow \mathbf{R}$ such that $f(x)=1$ if $x$ is rational, and $f(x)=1-\epsilon,$ where $0<\epsilon<1$, if $x$ is irrational. Which of the following is $\text{TRUE}?$ $\lim _{x \rightarrow \infty} f(x)=1$ ... $1-\epsilon$ $\max _{x \geq 1} f(x)=1$ None of the above
Consider a function $f: \mathbf{R} \rightarrow \mathbf{R}$ such that $f(x)=1$ if $x$ is rational, and $f(x)=1-\epsilon,$ where $0<\epsilon<1$, if $x$ is irrational. Which...
1 votes
0 answers
135
TIFR ECE 2019 | Question: 5
Consider the function $f(x)=e^{x^{2}}-8 x^{2}$ for all $x$ on the real line. For how many distinct values of $x$ do we have $f(x)=0?$ $1$ $4$ $2$ $3$ $5$
Consider the function $f(x)=e^{x^{2}}-8 x^{2}$ for all $x$ on the real line. For how many distinct values of $x$ do we have $f(x)=0?$ $1$$4$$2$$3$$5$
1 votes
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145
TIFR ECE 2016 | Question: 15
What is \[ \max _{x, y}\left[\begin{array}{ll} x & y \end{array}\right]\left[\begin{array}{cc} 3 & \sqrt{2} \\ \sqrt{2} & 2 \end{array}\right]\left[\begin{array}{l} x \\ y \end{array}\right] \] subject to \[ x^{2}+y^{2}=1 ? \] $1$ $\sqrt{2}$ $2$ $3$ $4$
What is\[\max _{x, y}\left[\begin{array}{ll}x & y\end{array}\right]\left[\begin{array}{cc}3 & \sqrt{2} \\\sqrt{2} & 2\end{array}\right]\left[\begin{array}{l}x \\y\end{arr...
1 votes
0 answers
148
GATE ECE 2009 | Question: 1
The order of the differential equation $\dfrac{d^{2} y}{d t^{2}}+\left(\dfrac{d y}{d t}\right)^{3}+y^{4}=e^{-t} \quad$ is $1$ $2$ $3$ $4$
The order of the differential equation $\dfrac{d^{2} y}{d t^{2}}+\left(\dfrac{d y}{d t}\right)^{3}+y^{4}=e^{-t} \quad$ is$1$$2$$3$$4$
1 votes
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149
GATE ECE 2010 | Question: 27
A fair coin is tossed independently four times. The probability of the event "the number of times heads show up is more than the number of times tails show up" is $\frac{1}{16}$ $\frac{1}{8}$ $\frac{1}{4}$ $\frac{5}{16}$
A fair coin is tossed independently four times. The probability of the event "the number of times heads show up is more than the number of times tails show up" is$\frac{1...
1 votes
0 answers
150
GATE ECE 2010 | Question: 30
Consider a differential equation $\dfrac{d y(x)}{d x}-y(x)=x$ with the initial condition $y(0)=0$. Using Euler's first order method with a step size of $0.1$, the value of $y(0.3)$ is $0.01$ $0.031$ $0.0631$ $0.1$
Consider a differential equation $\dfrac{d y(x)}{d x}-y(x)=x$ with the initial condition $y(0)=0$. Using Euler's first order method with a step size of $0.1$, the value o...
1 votes
0 answers
151
GATE ECE 2010 | Question: 1
The eigenvalues of a skew-symmetric matrix are always zero always pure imaginary either zero or pure imaginary always real
The eigenvalues of a skew-symmetric matrix arealways zeroalways pure imaginaryeither zero or pure imaginaryalways real
1 votes
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152
GATE ECE 2010 | Question: 26
If $e^{y}=x^{\frac{1}{x}}$, then $y$ has a maximum at $x=e$ minimum at $x=e$ maximum at $x=e^{-1}$ minimum at $x=e^{-1}$
If $e^{y}=x^{\frac{1}{x}}$, then $y$ has amaximum at $x=e$minimum at $x=e$maximum at $x=e^{-1}$minimum at $x=e^{-1}$
1 votes
0 answers
154
GATE ECE 2011 | Question: 25
The solution of the differential equation $\frac{d y}{d x}=k y, y(0)=c$ is $x=c e^{-k y}$ $x=k e^{c y}$ $y=c e^{k x}$ $y=c e^{-k x}$
The solution of the differential equation $\frac{d y}{d x}=k y, y(0)=c$ is$x=c e^{-k y}$$x=k e^{c y}$$y=c e^{k x}$$y=c e^{-k x}$
1 votes
0 answers
155
GATE ECE 2011 | Question: 36
A fair dice is tossed two times. The probability that the second toss results in a value that is higher than the first toss is $2 / 36$ $2 / 6$ $5 / 12$ $1 / 2$
A fair dice is tossed two times. The probability that the second toss results in a value that is higher than the first toss is$2 / 36$$2 / 6$$5 / 12$$1 / 2$
0 votes
1 answer
156
GATE ECE 2021 | Question: 1
The vector function $F\left ( r \right )=-x\hat{i}+y\hat{j}$ is defined over a circular arc $C$ shown in the figure. The line integral of $\int _{C} F\left ( r \right ).dr$ is $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{6}$ $\frac{1}{3}$
The vector function $F\left ( r \right )=-x\hat{i}+y\hat{j}$ is defined over a circular arc $C$ shown in the figure.The line integral of $\int _{C} F\left ( r \right ).dr...
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