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maths
${\int}_{\pi /4}^{\pi /4}\u200a\frac{{e}^{x}(x\mathrm{sin}x)}{{e}^{2x}1}dx$ is equal to
Let direction cosines of straight line be l, m, n
\ 4l + m + n = 0
l – 2m + n = 0
Þ $\frac{l}{3}=\frac{m}{3}=\frac{n}{9}$ Þ $\frac{l}{1}=\frac{m}{+1}=\frac{n}{3}$
\ Equation of straight line is $\frac{x2}{1}=\frac{y+1}{1}=\frac{z+1}{3}$.
Hence (c) is the correct choice.
${\int}_{\pi /4}^{\pi /4}\u200a\frac{{e}^{x}(x\mathrm{sin}x)}{{e}^{2x}1}dx$ is equal to
mathsGeneral
Let direction cosines of straight line be l, m, n
\ 4l + m + n = 0
l – 2m + n = 0
Þ $\frac{l}{3}=\frac{m}{3}=\frac{n}{9}$ Þ $\frac{l}{1}=\frac{m}{+1}=\frac{n}{3}$
\ Equation of straight line is $\frac{x2}{1}=\frac{y+1}{1}=\frac{z+1}{3}$.
Hence (c) is the correct choice.
maths
Let $f:R\to R,f\left(x\right)=\left\{\begin{array}{c}x[x\left]\right,\left[x\right]\\ x[x+1\left]\right,\left[x\right]\end{array}\right.$$\begin{array}{r}\text{is odd}\\ 1\text{is even where [.]}\end{array}$ denotes greatest integer function, then ${\int}_{2}^{4}\u200af\left(x\right)dx$ is equal to
Since these two lines are intersecting so shortest distance between the lines will be 0.
Hence (c) is the correct answer.
Let $f:R\to R,f\left(x\right)=\left\{\begin{array}{c}x[x\left]\right,\left[x\right]\\ x[x+1\left]\right,\left[x\right]\end{array}\right.$$\begin{array}{r}\text{is odd}\\ 1\text{is even where [.]}\end{array}$ denotes greatest integer function, then ${\int}_{2}^{4}\u200af\left(x\right)dx$ is equal to
mathsGeneral
Since these two lines are intersecting so shortest distance between the lines will be 0.
Hence (c) is the correct answer.
maths
The value of ${\int}_{0}^{1}\u200a\mathrm{sin}2\pi x\mid dx$ is equal to
Given plane y + z + 1 = 0 is parallel to xaxis as 0.1 + 1.0 + 1.0 = 0
but normal to the plane will be perpendicular to xaxis.
Hence (c) is the correct answer.
The value of ${\int}_{0}^{1}\u200a\mathrm{sin}2\pi x\mid dx$ is equal to
mathsGeneral
Given plane y + z + 1 = 0 is parallel to xaxis as 0.1 + 1.0 + 1.0 = 0
but normal to the plane will be perpendicular to xaxis.
Hence (c) is the correct answer.
maths
The value of ${\int}_{0}^{100}\u200a\left\{\sqrt{x}\right\}dx$ (where {x} is the fractional part of x) is
The value of ${\int}_{0}^{100}\u200a\left\{\sqrt{x}\right\}dx$ (where {x} is the fractional part of x) is
mathsGeneral
Maths
The shortest distance between the two straight line and is
The given equations are
and
The shortest distance between the two cartesian lines
=
and
The shortest distance between the two cartesian lines
=
The shortest distance between the two straight line and is
MathsGeneral
The given equations are
and
The shortest distance between the two cartesian lines
=
and
The shortest distance between the two cartesian lines
=
physics
A bob of mass M is suspended by a massless string of length L. The horizontal velocity $v$ at position A is just sufficient to make it reach the point B. The angle $\theta $ at which the speed of the bob is half of that at A, satisfies
Velocity of the bob at the point A
$v=\sqrt{5gL}$(i)
${\left(\frac{v}{2}\right)}^{2}={v}^{2}2gh\left(ii\right)$
$h=L(1\mathrm{cos}\theta )(iii)$
$SolvingEqs.\left(i\right),\left(ii\right)and\left(iii\right),weget$
$\mathrm{cos}\theta =\frac{7}{8}$
$or\theta ={cos}^{1}\left(\frac{7}{8}\right)=151\xb0$
A bob of mass M is suspended by a massless string of length L. The horizontal velocity $v$ at position A is just sufficient to make it reach the point B. The angle $\theta $ at which the speed of the bob is half of that at A, satisfies
physicsGeneral
Velocity of the bob at the point A
$v=\sqrt{5gL}$(i)
${\left(\frac{v}{2}\right)}^{2}={v}^{2}2gh\left(ii\right)$
$h=L(1\mathrm{cos}\theta )(iii)$
$SolvingEqs.\left(i\right),\left(ii\right)and\left(iii\right),weget$
$\mathrm{cos}\theta =\frac{7}{8}$
$or\theta ={cos}^{1}\left(\frac{7}{8}\right)=151\xb0$
physics
A point P moves in counterclockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out length where is in metre and t is in second. The radius of the path is 20 m. The acceleration of P when t =2s is nearly
A point P moves in counterclockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out length where is in metre and t is in second. The radius of the path is 20 m. The acceleration of P when t =2s is nearly
physicsGeneral
maths
The equation of the plane containing the line where al + bm + cn is equal to
Since these two lines are intersecting so shortest distance between the lines will be 0.
Hence (c) is the correct answer.
Hence (c) is the correct answer.
The equation of the plane containing the line where al + bm + cn is equal to
mathsGeneral
Since these two lines are intersecting so shortest distance between the lines will be 0.
Hence (c) is the correct answer.
Hence (c) is the correct answer.
physics
A small body of mass slides down from the top of a hemisphere of radius . The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is
A small body of mass slides down from the top of a hemisphere of radius . The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is
physicsGeneral
physics
Average torque on a projectile of mass , initial speed and angles of projection , between initial and final position and as shown in figure about the point of projection is
Time of flight.
Horizontal range,
Change in angular momentum,
about point of projection
Horizontal range,
Change in angular momentum,
about point of projection
Average torque on a projectile of mass , initial speed and angles of projection , between initial and final position and as shown in figure about the point of projection is
physicsGeneral
Time of flight.
Horizontal range,
Change in angular momentum,
about point of projection
Horizontal range,
Change in angular momentum,
about point of projection
physics
A string of length is fixed at one end and the string makes rev/s around the vertical axis through, the fixed and as shown in the figure, then tension in the string is
(i)
(ii)
(ii)
A string of length is fixed at one end and the string makes rev/s around the vertical axis through, the fixed and as shown in the figure, then tension in the string is
physicsGeneral
(i)
(ii)
(ii)
physics
A thin prism with angle and made from glass of refractive index 1.54 is combined with another thin prism of refractive index 1.72 to produce dispersion without deviation. The angle of prism will be
Þ A'
A thin prism with angle and made from glass of refractive index 1.54 is combined with another thin prism of refractive index 1.72 to produce dispersion without deviation. The angle of prism will be
physicsGeneral
Þ A'
physics
A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if . The index of refraction of glass is
For total internal reflection
or
or
A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if . The index of refraction of glass is
physicsGeneral
For total internal reflection
or
or
physics
Which of the following diagrams, shows correctly the dispersion of white light by a prism
Because in dispersion of white light, the rays of different colours are not parallel to each other. Also deviation takes place in same direction.
Which of the following diagrams, shows correctly the dispersion of white light by a prism
physicsGeneral
Because in dispersion of white light, the rays of different colours are not parallel to each other. Also deviation takes place in same direction.
physics
A ray of light incident normally on an isosceles right angled prism travels as shown in the figure. The least value of the refractive index of the prism must be
A ray of light incident normally on an isosceles right angled prism travels as shown in the figure. The least value of the refractive index of the prism must be
physicsGeneral