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${\int}_{\pi /4}^{\pi /4}\u200a\frac{{e}^{x}(x\mathrm{sin}x)}{{e}^{2x}1}dx$ is equal to
${\int}_{\pi /4}^{\pi /4}\u200a\frac{{e}^{x}(x\mathrm{sin}x)}{{e}^{2x}1}dx$ is equal to
mathsGeneral
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.$$\begin{array}{r}\text{is odd}\\ 1\text{is even where [.]}\end{array}$ denotes greatest integer function, then ${\int}_{2}^{4}\u200af\left(x\right)dx$ is equal to
Let $f:R\to R,f\left(x\right)=\left\{\begin{array}{c}x[x\left]\right,\left[x\right]\\ x[x+1\left]\right,\left[x\right]\end{array}\right.$$\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
maths
The value of ${\int}_{0}^{1}\u200a\mathrm{sin}2\pi x\mid dx$ is equal to
The value of ${\int}_{0}^{1}\u200a\mathrm{sin}2\pi x\mid dx$ is equal to
mathsGeneral
Maths
The value of (where {x} is the fractional part of x) is
The value of (where {x} is the fractional part of x) is
MathsGeneral
Maths
The shortest distance between the two straight line and is
The shortest distance between the two straight line and is
MathsGeneral
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
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
Physics
A piece of wire is bent in the shape of a parabola axis vertical) with a bead of mass on it. The bead can side on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the axis with a constant acceleration . The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the axis is
A piece of wire is bent in the shape of a parabola axis vertical) with a bead of mass on it. The bead can side on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the axis with a constant acceleration . The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the axis is
PhysicsGeneral
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
The equation of the plane containing the line where al + bm + cn is equal to
mathsGeneral
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
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
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
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
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
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
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
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
physics
Which of the following diagrams, shows correctly the dispersion of white light by a prism
Which of the following diagrams, shows correctly the dispersion of white light by a prism
physicsGeneral