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Recent questions and answers in Calculus
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GATE IN 2021 | Question: 2
Consider the sequence $x_{n}=0.5x_{n-1}+1,n=1,2, \dots \:\dots$ with $x_0=0$ . Then $\displaystyle \lim_{n\rightarrow \infty} x_n$ is $0$ $1$ $2$ $\infty$
Consider the sequence $x_{n}=0.5x_{n-1}+1,n=1,2, \dots \:\dots$ with $x_0=0$ . Then $\displaystyle \lim_{n\rightarrow \infty} x_n$ is$0$$1$$2$$\infty$
Arjun
2.9k
points
Arjun
asked
Feb 19, 2021
Calculus
gatein-2021
calculus
limits
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–
0
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0
answers
2
GATE IN 2021 | Question: 23
Consider the function $f\left ( x \right )=-x^{2}+10x+100$. The minimum value of the function in interval $[5,10]$ is ___________.
Consider the function $f\left ( x \right )=-x^{2}+10x+100$. The minimum value of the function in interval $[5,10]$ is ___________.
Arjun
2.9k
points
Arjun
asked
Feb 19, 2021
Calculus
gatein-2021
numerical-answers
calculus
maxima-minima
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–
0
votes
0
answers
3
GATE2020 IN: 28
A straight line drawn on an x-y plane intercepts the x-axis at -0.5 and the y-axis at 1. The equation that describes this line is __________. $\text{y=-0.5x+1}$ $\text{y=x-0.5}$ $\text{y=0.5x-1}$ $\text{y=2x+1}$
A straight line drawn on an x-y plane intercepts the x-axis at -0.5 and the y-axis at 1.The equation that describes this line is __________.$\text{y=-0.5x+1}$$\text{y=x-0...
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 3, 2020
Calculus
gate2020-in
calculus
cartesian-coordinates
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–
0
votes
0
answers
4
GATE2020 IN: 31
Consider the function $f(x,y)=x^2+y^2.$ The minimum value the function attains on the line $x+y=1$ (rounded off to one decimal place) is __________.
Consider the function $f(x,y)=x^2+y^2.$ The minimum value the function attains on the line $x+y=1$ (rounded off to one decimal place) is __________.
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 3, 2020
Calculus
gate2020-in
numerical-answers
calculus
maxima-minima
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–
0
votes
0
answers
5
GATE2020: 1
The unit vectors along the mutually perpendicular x,y and z axes are $\hat{i},\;\hat{j}\; and \;\hat{k}$ respectively. Consider the plane $z=0$ and two vectors $\overrightarrow{a} and\;\overrightarrow{b}$ on that plane such that $\overrightarrow{a}\neq \alpha \overrightarrow{b}$ for any scalar $\alpha$. A vector perpendicular to both $\overrightarrow{a} and\;\overrightarrow{b}$ is ___________ $\hat{k}$ $\hat{i}-\hat{j}$ $-\hat{j}$ $\hat{i}$
The unit vectors along the mutually perpendicular x,y and z axes are $\hat{i},\;\hat{j}\; and \;\hat{k}$ respectively. Consider the plane $z=0$ and two vectors $\overrigh...
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 3, 2020
Calculus
gate2020-in
calculus
vector-calculus
vector-identities
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–
0
votes
0
answers
6
GATE2017: 27
The angle between two vectors $X_1=\begin{bmatrix}2 & 6 & 14\end{bmatrix}^T$ and $X_2=\begin{bmatrix}-12 & 8 & 16\end{bmatrix}^T$ in radian is __________.
The angle between two vectors $X_1=\begin{bmatrix}2 & 6 & 14\end{bmatrix}^T$ and $X_2=\begin{bmatrix}-12 & 8 & 16\end{bmatrix}^T$ in radian is __________.
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 2, 2020
Calculus
gate2017-in
numerical-answers
calculus
vector-identities
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–
0
votes
0
answers
7
GATE2019 IN: 1
$\overrightarrow{a}$,$\overrightarrow{b}$,$\overrightarrow{c}$ are three orthogonal vectors. Given that $\overrightarrow{a}$ = ${\widehat{i}}$ + 2${\widehat{j}}$ + 5${\widehat{k}}$ and $\overrightarrow{b}$ = ${\widehat{i}}$ + 2${\widehat{j}}$ – ${\widehat{k}}$, the vector $\overrightarrow{c}$ is parallel to $\widehat{i}+2\widehat{j}+3\widehat{k}$ $2\widehat{i} + \widehat{j}$ $2\widehat{i} – \widehat{j}$ $4\widehat{k}$
$\overrightarrow{a}$,$\overrightarrow{b}$,$\overrightarrow{c}$ are three orthogonal vectors. Given that $\overrightarrow{a}$ = ${\widehat{i}}$ + 2${\widehat{j}}$ + 5${\wi...
Arjun
2.9k
points
Arjun
asked
Feb 10, 2019
Calculus
gate2019-in
calculus
vector-calculus
vector-identities
+
–
0
votes
0
answers
8
GATE2019 IN: 2
The vector function $\overrightarrow{A}$ is given by $\overrightarrow{A}$ = $\overrightarrow{\bigtriangledown}$u , where u(x, y) is a scalar function. Then |$\overrightarrow{\bigtriangledown}$ x $\overrightarrow{A}$| is -1 0 1 $\infty$
The vector function $\overrightarrow{A}$ is given by $\overrightarrow{A}$ = $\overrightarrow{\bigtriangledown}$u , where u(x, y) is a scalar function. Then |$\overrightar...
Arjun
2.9k
points
Arjun
asked
Feb 10, 2019
Calculus
gate2019-in
calculus
vector-calculus
vector-identities
+
–
0
votes
0
answers
9
GATE2019 IN: 26
The curve y = f(x) is such that the tangent to the curve at every point (x,y) has a y-axis intercept c, given by c = -y. Then,f(x) is proportional to x$^{-1}$ x$^{2}$ x$^{3}$ x$^{4}$
The curve y = f(x) is such that the tangent to the curve at every point (x,y) has a y-axis intercept c, given by c = -y. Then,f(x) is proportional tox$^{-1}$x$^{2}$x$^{3}...
Arjun
2.9k
points
Arjun
asked
Feb 10, 2019
Calculus
gate2019-in
calculus
functions
curves
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–
0
votes
0
answers
10
GATE 2016 - 1
A straight line of the form $y=mx+c$ passes through the origin and the point $(x,y)$ =$(2,6)$. The value of $m$ is _____.
A straight line of the form $y=mx+c$ passes through the origin and the point $(x,y)$ =$(2,6)$. The value of $m$ is _____.
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2016-in
numerical-answers
calculus
cartesian-coordinates
+
–
0
votes
0
answers
11
GATE2016-2
$\underset{n\rightarrow \infty }{\lim}\:\left(\sqrt{n^2+n}-\sqrt{n^2+1}\right)$ is __________.
$\underset{n\rightarrow \infty }{\lim}\:\left(\sqrt{n^2+n}-\sqrt{n^2+1}\right)$ is __________.
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2016-in
numerical-answers
calculus
limits
+
–
0
votes
0
answers
12
GATE2016-4
The vector that is $NOT$ perpendicular to the vectors $(i+j+k)$ and $(i+2j+3k)$ is ______. $(i-2j+k)$ $(-i+2j-k)$ $(0i+0j+0k)$ $(4i+3j+5k)$
The vector that is $NOT$ perpendicular to the vectors $(i+j+k)$ and $(i+2j+3k)$ is ______.$(i-2j+k)$ $(-i+2j-k)$$(0i+0j+0k)$$(4i+3j+5k)$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2016-in
calculus
vector-calculus
vector-identities
+
–
0
votes
0
answers
13
GATE2016-26
Let $f: [-1,1]\rightarrow \mathbb{R}$, where $f(x)=2x^3-x^4-10$. The minimum value of $f(x)$ is $\_\_\_\_\_\_\_.$
Let $f: [-1,1]\rightarrow \mathbb{R}$, where $f(x)=2x^3-x^4-10$. The minimum value of $f(x)$ is $\_\_\_\_\_\_\_.$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2016-in
numerical-answers
calculus
maxima-minima
+
–
0
votes
0
answers
14
GATE2015-13
The double integral $\int_0^a \int_0^y f(x,y) dx\;dy$ is equivalent to $\int_0^x\int_0^y f(x,y) dx\;dy$ $\int_0^a \int_x^y f(x,y) dx\;dy$ $\int_0^a \int_x^a f(x,y) dy\;dx$ $\int_0^a \int_0^a f(x,y) dx\;dy$
The double integral $\int_0^a \int_0^y f(x,y) dx\;dy$ is equivalent to$\int_0^x\int_0^y f(x,y) dx\;dy$$\int_0^a \int_x^y f(x,y) dx\;dy$$\int_0^a \int_x^a f(x,y) dy\;dx$$\...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2015-in
calculus
definite-integrals
double-integrals
+
–
0
votes
0
answers
15
GATE2015-14
The magnitude of the directional derivative of the function $f(x,y)=x^2+3y^2$ in a direction normal to the circle $x^2+y^2=2,$ at the point $(1,1),$ is $4\sqrt{2}$ $5\sqrt{2}$ $7\sqrt{2}$ $9\sqrt{2}$
The magnitude of the directional derivative of the function $f(x,y)=x^2+3y^2$ in a direction normal to the circle $x^2+y^2=2,$ at the point $(1,1),$ is$4\sqrt{2}$$5\sqrt{...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2015-in
calculus
directional-derivatives
+
–
0
votes
0
answers
16
GATE2015-57
The fundamental period of the signal $x(t)=2\cos(\frac{2\pi t}{3})+\cos(\pi t)$, in seconds, is ________________ s.
The fundamental period of the signal $x(t)=2\cos(\frac{2\pi t}{3})+\cos(\pi t)$, in seconds, is ________________ s.
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2015-in
numerical-answers
calculus
trigonometry
+
–
0
votes
0
answers
17
GATE2014-4
A vector is defined as $f=y\hat{i}+x\hat{j}+z\hat{k}$ where $\hat{i},\hat{j},\hat{k}$ are unit vectors in Cartesian $(x,y,z)$ coordinate system. The surface integral $f.ds$ over the closed surface S of a cube with vertices having the following coordinates: $(0,0,0), (1,0,0),(1,1,0),(0,1,0),(0,0,1),(1,0,1),(1,1,1),(0,1,1)$ is __________.
A vector is defined as $$f=y\hat{i}+x\hat{j}+z\hat{k}$$where $\hat{i},\hat{j},\hat{k}$ are unit vectors in Cartesian $(x,y,z)$ coordinate system.The surface integral $f....
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2014-in
numerical-answers
calculus
vector-calculus
surface-integral
+
–
0
votes
0
answers
18
GATE2013-5
For a vector $E$, which one of the following statements is $\text{NOT TRUE}$? If $\Delta.E=0,\;E$ is called solenoidal If $\Delta \times E=0,\;E$ is called conservative If $\Delta\times E=0,\;E$ is called irrotational If $\Delta.E=0,\;E$ is called irrotational
For a vector $E$, which one of the following statements is $\text{NOT TRUE}$?If $\Delta.E=0,\;E$ is called solenoidalIf $\Delta \times E=0,\;E$ is called conservativeIf $...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2013-in
calculus
vector-calculus
+
–
0
votes
0
answers
19
GATE2012-29
The maximum value of $f(x)=x^3-9x^2+24x+5$ in the interval $[1, 6]$ is $21$ $25$ $41$ $46$
The maximum value of $f(x)=x^3-9x^2+24x+5$ in the interval $[1, 6]$ is $21$$25$$41$$46$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2012-in
calculus
maxima-minima
+
–
0
votes
0
answers
20
GATE2012-28
The direction of vector $\text{A}$ is radially outward from the origin, with $|A|=kr^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\nabla.$ $\text{A=0}$ is $-2$ $2$ $1$ $0$
The direction of vector $\text{A}$ is radially outward from the origin, with $|A|=kr^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\nabla....
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2012-in
calculus
curl
divergence
+
–
0
votes
0
answers
21
GATE2012-1
If $x=\sqrt{-1},$ then the value of $x^x$ is $e^{-\pi/2}$ $e^{\pi/2}$ $x$ $1$
If $x=\sqrt{-1},$ then the value of $x^x$ is $e^{-\pi/2}$$e^{\pi/2}$$x$$1$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2012-in
calculus
functions
complex-number
+
–
0
votes
0
answers
22
GATE2018IN: 26
Given $\overrightarrow{F}$ = (x$^2$ – 2y) $\overrightarrow{i}$ – 4xz$\overrightarrow{j}$ + 4xz$^2$\overrightarrow{k}$, the value of the linear integral $\int_c$\overrightarrow{F}$ . d$\overrightarrow{l}$ along the straight line c from (0,0,0) to (1,1,1) is 3/16 0 -5/12 -1
Given $\overrightarrow{F}$ = (x$^2$ – 2y) $\overrightarrow{i}$ – 4xz$\overrightarrow{j}$ + 4xz$^2$$\overrightarrow{k}$, the value of the linear integral $\int_c$$\ove...
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Calculus
gate2018-in
calculus
vector-calculus
line-integral
+
–
0
votes
0
answers
23
GATE2018IN: 4
Consider two functions f(x) = (x – 2)$^2$ and g(x) = 2x – 1, where x is real. The smallest value of x for which f(x) = g(x) is $\_\_\_\_\_\_$
Consider two functions f(x) = (x – 2)$^2$ and g(x) = 2x – 1, where x is real. The smallest value of x for which f(x) = g(x) is $\_\_\_\_\_\_$
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Calculus
gate2018-in
numerical-answers
calculus
maxima-minima
+
–
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