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GATE BT 2021 | Question: 5
The Cartesian coordinates $(x,y)$ of a point $A$ with polar coordinates $\left ( 4, \pi/4 \right)$ is $ \left( \sqrt{3}, 2 \sqrt{2} \right ) \\$ $ \left( 2, 2 \sqrt{3} \right ) \\$ $ \left( 2\sqrt{2}, \sqrt{3} \right ) \\$ $ \left( 2 \sqrt{2}, 2 \sqrt{2} \right )$
The Cartesian coordinates $(x,y)$ of a point $A$ with polar coordinates $\left ( 4, \pi/4 \right)$ is$ \left( \sqrt{3}, 2 \sqrt{2} \right ) \\$$ \left( 2, 2 \sqrt{3} \rig...
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GATE BT 2021 | Question: 8
$\dfrac{d}{dx} \left [ \ln (2x) \right ]$ is equal to $1/2x \\$ $1/x \\$ $1 /2 \\$ $x$
$\dfrac{d}{dx} \left [ \ln (2x) \right ]$ is equal to$1/2x \\$$1/x \\$$1 /2 \\$$x$
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GATE BT 2021 | Question: 20
The sum of the infinite geometric series $1 + 1/3 + 1/3^2+ 1/3^3+ \dots$ (rounded off to one decimal place) is ___________
The sum of the infinite geometric series $1 + 1/3 + 1/3^2+ 1/3^3+ \dots$ (rounded off to one decimal place) is ___________
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GATE BT 2021 | Question: 23
The value of $\underset{x \to 0} \lim \left [ \dfrac{x- \sin 2x}{x-\sin 5x} \right]$ (rounded off to two decimal places) is __________
The value of $\underset{x \to 0} \lim \left [ \dfrac{x- \sin 2x}{x-\sin 5x} \right]$ (rounded off to two decimal places) is __________
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GATE BT 2021 | Question: 41
If the area of a triangle with the vertices $(k,0), (2,0)$ and $(0, -2)$ is $2$ square units, the value of $k$ is _________
If the area of a triangle with the vertices $(k,0), (2,0)$ and $(0, -2)$ is $2$ square units, the value of $k$ is _________
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GATE BT 2021 | Question: 43
If the values of two random variables $(X,Y)$ are $(121, 360)$, $(242, 364)$ and $(363, 362)$, the value of correlation coefficient between $X$ and $Y$ (rounded off to one decimal place) is ________.
If the values of two random variables $(X,Y)$ are $(121, 360)$, $(242, 364)$ and $(363, 362)$, the value of correlation coefficient between $X$ and $Y$ (rounded off to on...
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GATE BT 2021 | Question: 44
The determinant of matrix $A = \begin{pmatrix} 1 & 1& 1 & 1 \\ -1 & 1 & 1 & 1 \\ -1 & -1 & 1 & 1 \\ 1 & 1 & 1 & 3 \end{pmatrix}$ is __________.
The determinant of matrix $A = \begin{pmatrix} 1 & 1& 1 & 1 \\ -1 & 1 & 1 & 1 \\ -1 & -1 & 1 & 1 \\ 1 & 1 & 1 & 3 \end{pmatrix}$ is __________.
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GATE BT 2021 | Question: 49
Calculate the following integral $\int \limits_0^{\pi^2/4} \sin \sqrt{x} dx =$____________.
Calculate the following integral $\int \limits_0^{\pi^2/4} \sin \sqrt{x} dx =$____________.
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GATE2020: 23
The largest eigenvalue of the matrix $\begin{bmatrix} 4 &1 \\ -2& 1 \end{bmatrix}$ is ______________.
The largest eigenvalue of the matrix $\begin{bmatrix} 4 &1 \\ -2& 1 \end{bmatrix}$ is ______________.
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GATE2020: 46
The system of linear equations $cx+y=5$ $3x+3y=6$ has no solution when $c$ is equal to _______________________.
The system of linear equations$$cx+y=5$$$$3x+3y=6$$has no solution when $c$ is equal to _______________________.
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GATE2020: 50
A function $f$ is given as : $f(X)=4X-X^{2}$ The function $f$ is maximized when $X$ is equal to _________________.
A function $f$ is given as :$$f(X)=4X-X^{2}$$The function $f$ is maximized when $X$ is equal to _________________.
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GATE2020: 51
An infinite series $S$ is given as: $S=1+2/3+3/9+4/27+5/81+\:.\dots$ (to infinity) The value of $S$ is ______________________ (round off to $2$ decimal places).
An infinite series $S$ is given as:$S=1+2/3+3/9+4/27+5/81+\:.\dots$ (to infinity)The value of $S$ is ______________________ (round off to $2$ decimal places).
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GATE2020: 17
A function $f$ is as follows: $f(x) = \begin{cases} 15 & \text{if }x<1 \\ cx& \text{if } x\geq 1 \end{cases}$ The function $f$ is a continuous function when $c$ is equal to ____________________ (answer in an integer).
A function $f$ is as follows:$$f(x) = \begin{cases} 15 & \text{if }x<1 \\ cx& \text{if } x\geq 1 \end{cases}$$The function $f$ is a continuous function when $c$ is equal ...
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GATE2018-43
If $1+r + r^2+ r^3 +\dots \infty = 1.5$, then, $1 + 2r + 3r^2 + 4r^3 + \dots \infty = $ (up to two dcimal places) ________
If $1+r + r^2+ r^3 +\dots \infty = 1.5$, then, $1 + 2r + 3r^2 + 4r^3 + \dots \infty = $ (up to two dcimal places) ________
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16
GATE2015-33
Consider the following infinite series: $1+ r+r^2 +r^3+ \dots \dots \infty$ If $r = 0.3$, then the sum of this infinite series is ____________
Consider the following infinite series:$$1+ r+r^2 +r^3+ \dots \dots \infty$$ If $r = 0.3$, then the sum of this infinite series is ____________
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GATE2019: 13
Which of the following are geometric series? $1,\:6,\:11,\:16,\:21,\:26,\:\dots$ $9,\:6,\:3,\:0,\:-3,\:-6,\:\dots$ $1,\:3,\:9,\:27,\:81,\:\dots$ $4,\:-8,\:16,\:-32,\:64,\:\dots$ $P$ and $Q$ only $R$ and $S$ only $Q$ and $S$ only $P, Q$ and $R$ only
Which of the following are geometric series?$1,\:6,\:11,\:16,\:21,\:26,\:\dots$$9,\:6,\:3,\:0,\:-3,\:-6,\:\dots$$1,\:3,\:9,\:27,\:81,\:\dots$$4,\:-8,\:16,\:-32,\:64,\:\do...
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GATE2019: 21
The solution of $ \underset{x\rightarrow 8 }\lim\left ( \dfrac{x^{2}-64}{x-8} \right )$ is _____________.
The solution of $ \underset{x\rightarrow 8 }\lim\left ( \dfrac{x^{2}-64}{x-8} \right )$ is _____________.
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GATE2019: 22
The median value for the dataset $\left ( 12, 10,16,8,90,50,30,24 \right )$ is ______________.
The median value for the dataset $\left ( 12, 10,16,8,90,50,30,24 \right )$ is ______________.
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GATE2019: 50
$\int _{-1}^{1}\:f\left ( x \right )dx$ calculated using trapezoidal rule for the values given in the table is ______ (rounded off to $2$ ...
$\int _{-1}^{1}\:f\left ( x \right )dx$ calculated using trapezoidal rule for the values given in the table is ______ (rounded off to $2$ decimal places).$$\begin{array}{...
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GATE2019: 20
Matrix $A=\begin{bmatrix} 0&6 \\ p&0 \end{bmatrix}$ will be skew-symmetric when $p$= ____.
Matrix $A=\begin{bmatrix} 0&6 \\ p&0 \end{bmatrix}$ will be skew-symmetric when $p$= ____.
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22
GATE2018-22
The variable $z$ has a standard normal distribution. If $P(0 \leq z \leq 1)= 0.34$ then $P(z^2 > 1)$ is equal to (up to two decimal places) ____________
The variable $z$ has a standard normal distribution. If $P(0 \leq z \leq 1)= 0.34$ then $P(z^2 1)$ is equal to (up to two decimal places) ____________
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GATE2018-21
The determinant of the matrix $\begin{pmatrix} 4 & -6 \\ -3 & 2 \end{pmatrix}$ is _________
The determinant of the matrix $\begin{pmatrix} 4 & -6 \\ -3 & 2 \end{pmatrix}$ is _________
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25
GATE2018-1
Consider an unfair coin. The probability of getting heads is $0.6$. If you toss this coin twice, what is the probability that the fast or the second toss is heads? $0.56$ $0.64$ $0.84$ $0.96$
Consider an unfair coin. The probability of getting heads is $0.6$. If you toss this coin twice, what is the probability that the fast or the second toss is heads?$0.56$$...
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27
GATE2018-41
Calculate the following integral (up to two decimal places) $\displaystyle \int_0^1 (x + 3)(x + 1)dx = \text{ ___________}$
Calculate the following integral (up to two decimal places)$$\displaystyle \int_0^1 (x + 3)(x + 1)dx = \text{ ___________}$$
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28
GATE2018-19
Which one of the following is the solution for $\cos^2 x + 2 \cos x + 1 = 0$, for values of $x$ in the range of $0^\circ < x < 360^\circ$ $45^\circ$ $90^\circ$ $180^\circ$ $270^\circ$
Which one of the following is the solution for $\cos^2 x + 2 \cos x + 1 = 0$, for values of $x$ in the range of $0^\circ < x < 360^\circ$$45^\circ$$90^\circ$$180^\circ$$2...
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29
GATE2017-4
The surface area (in $m^2$) of the largest sphere that can fit into a hollow cube with edges of length $1$ meter is ______ Given data: $\pi=3.14$
The surface area (in $m^2$) of the largest sphere that can fit into a hollow cube with edges of length $1$ meter is ______Given data: $\pi=3.14$
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30
GATE2017-47
For the probability density $P(x) = 0.5e^{-0.5x}$, the integral $\displaystyle \int_0^{\infty}P(x)dx =$ __________
For the probability density $P(x) = 0.5e^{-0.5x}$, the integral $\displaystyle \int_0^{\infty}P(x)dx =$ __________
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31
GATE2017-28
The angle (in degrees) between the vectors $\overrightarrow{x}= \hat{i}-\hat{j}+2 \hat{k}$ and $\overrightarrow{y} = 2 \hat{i} – \hat{j}-1.5 \hat{k}$ is _________
The angle (in degrees) between the vectors $\overrightarrow{x}= \hat{i}-\hat{j}+2 \hat{k}$ and $\overrightarrow{y} = 2 \hat{i} – \hat{j}-1.5 \hat{k}$ is _________
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32
GATE2017-37
The value of $c$ for which the following system of linear equations has an infinite number of solutions is ________ $\begin{bmatrix}1 & 2 \\ 1 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} c \\ 4 \end{bmatrix}$
The value of $c$ for which the following system of linear equations has an infinite number of solutions is ________ $$\begin{bmatrix}1 & 2 \\ 1 & 2 \end{bmatrix} \begin{b...
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33
GATE2017-16
For $y=f(x)$, if $\dfrac{d^2y}{dx^2}=0$, $\dfrac{dy}{dx}=0$ at $x=0$, and $y=1$ at $x=1$, the value of $y$ at $x=2$ is __________
For $y=f(x)$, if $\dfrac{d^2y}{dx^2}=0$, $\dfrac{dy}{dx}=0$ at $x=0$, and $y=1$ at $x=1$, the value of $y$ at $x=2$ is __________
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34
GATE2016-54
The value of determinant $A$ given below is ________. $A = \begin{pmatrix} 5 & 16 & 81 \\ 0 & 2 & 2 \\ 0 & 0 & 16 \end{pmatrix}$
The value of determinant $A$ given below is ________.$A = \begin{pmatrix} 5 & 16 & 81 \\ 0 & 2 & 2 \\ 0 & 0 & 16 \end{pmatrix}$
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35
GATE2016-53
$\dfrac{d^2y}{dx^2}-y=0$. The conditions for this second order homogeneous differential equation are $y(0)=1$ and $\dfrac{dy}{dx}=3$ at $x=0$. The value of $y$ when $x = 2$ is __________
$\dfrac{d^2y}{dx^2}-y=0$. The conditions for this second order homogeneous differential equation are $y(0)=1$ and $\dfrac{dy}{dx}=3$ at $x=0$. The value of $y$ when $x = ...
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GATE2016-25
The value of the integral $\displaystyle \int_0^{0.9} \dfrac{dx}{(1-x)(2-x)}$ is ____________
The value of the integral $\displaystyle \int_0^{0.9} \dfrac{dx}{(1-x)(2-x)}$ is ____________
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37
GATE2016-24
The Laplace transform $F(s)$ of the function $f(t) = \cos (at)$, where $a$ is constant, _________ $\dfrac{s^2}{s^2+a^2} \\$ $\dfrac{a}{s^2+a^2} \\$ $\dfrac{s}{s^2+a^2} \\$ $\dfrac{s}{s^2-a^2} $
The Laplace transform $F(s)$ of the function $f(t) = \cos (at)$, where $a$ is constant, _________$\dfrac{s^2}{s^2+a^2} \\$$\dfrac{a}{s^2+a^2} \\$$\dfrac{s}{s^2+a^2} \\$$\...
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GATE2016-23
The positive Eigen value of the following matrix is __________. $\begin{bmatrix} 2 & 1 \\ 5 & -2 \end{bmatrix}$
The positive Eigen value of the following matrix is __________. $$\begin{bmatrix} 2 & 1 \\ 5 & -2 \end{bmatrix}$$
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GATE2016-22
Runs scored by a batsman in five one-day matches are $55$, $75$, $67$, $88$ and $15$. The standard deviation is _________
Runs scored by a batsman in five one-day matches are $55$, $75$, $67$, $88$ and $15$. The standard deviation is _________
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