Physics-

#### A bob of mass is suspended by a massless string of length . The horizontal velocity at position is just sufficient to make it reach the point . The angle at which the speed of the bob is half of that at , satisfies

Physics-General

#### Answer:The correct answer is:

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### Related Questions to study

maths-

The foot of the perpendicular on the line drown from the origin is C if the line cuts the x-axis and y-axis at A and B respectively then BC : CA is

Let direction ratios of the required line be <a, b, c>

Therefore a - 2 b - 2 c = 0

And 2 b + c = 0

Þ c = - 2 b

a - 2 b + 4b = 0 Þ a = - 2 b

Therefore direction ratios of the required line are <- 2b, b, - 2b> = <2, - 1, 2>

direction cosines of the required line

=

Therefore a - 2 b - 2 c = 0

And 2 b + c = 0

Þ c = - 2 b

a - 2 b + 4b = 0 Þ a = - 2 b

Therefore direction ratios of the required line are <- 2b, b, - 2b> = <2, - 1, 2>

direction cosines of the required line

=

The foot of the perpendicular on the line drown from the origin is C if the line cuts the x-axis and y-axis at A and B respectively then BC : CA is

maths-General

Let direction ratios of the required line be <a, b, c>

Therefore a - 2 b - 2 c = 0

And 2 b + c = 0

Þ c = - 2 b

a - 2 b + 4b = 0 Þ a = - 2 b

Therefore direction ratios of the required line are <- 2b, b, - 2b> = <2, - 1, 2>

direction cosines of the required line

=

Therefore a - 2 b - 2 c = 0

And 2 b + c = 0

Þ c = - 2 b

a - 2 b + 4b = 0 Þ a = - 2 b

Therefore direction ratios of the required line are <- 2b, b, - 2b> = <2, - 1, 2>

direction cosines of the required line

=

maths-

(where a, b are integers) =

The centre of the sphere is (1, 2, –3) so if other extremity of diameter is (x

= 1, = 2, = –3

\ Required point is (0, 5, 7).

Hence (c) is the correct answer.

_{1}, y_{1}, z_{1}), then= 1, = 2, = –3

\ Required point is (0, 5, 7).

Hence (c) is the correct answer.

(where a, b are integers) =

maths-General

The centre of the sphere is (1, 2, –3) so if other extremity of diameter is (x

= 1, = 2, = –3

\ Required point is (0, 5, 7).

Hence (c) is the correct answer.

_{1}, y_{1}, z_{1}), then= 1, = 2, = –3

\ Required point is (0, 5, 7).

Hence (c) is the correct answer.

maths-

maths-General

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 $\frac{x-2}{-1}=\frac{y+1}{1}=\frac{z+1}{3}$.
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

maths-General

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 $\frac{x-2}{-1}=\frac{y+1}{1}=\frac{z+1}{3}$.
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

maths-General

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 x-axis as 0.1 + 1.0 + 1.0 = 0
but normal to the plane will be perpendicular to x-axis.
Hence (c) is the correct answer.

#### The value of ${\int}_{0}^{1}\u200a|\mathrm{sin}2\pi x|\mid dx$ is equal to

maths-General

Given plane y + z + 1 = 0 is parallel to x-axis as 0.1 + 1.0 + 1.0 = 0
but normal to the plane will be perpendicular to x-axis.
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

maths-General

physics-

#### A given ray of light suffers minimum deviation in an equilateral prism *P*. Additional prisms *Q* and *R* of identical shape and material are now added to *P* as shown in the figure. The ray will suffer

As the prisms

*Q*and*R*are of the same material and have identical shape they combine to form a slab with parallel faces. Such a slab does not cause any deviation.#### A given ray of light suffers minimum deviation in an equilateral prism *P*. Additional prisms *Q* and *R* of identical shape and material are now added to *P* as shown in the figure. The ray will suffer

physics-General

As the prisms

*Q*and*R*are of the same material and have identical shape they combine to form a slab with parallel faces. Such a slab does not cause any deviation.maths-

#### The shortest distance between the two straight line$\frac{x-4/3}{2}=\frac{y+6/5}{3}=\frac{z-3/2}{4}$ and $\frac{5y+6}{8}=\frac{2z-3}{9}=\frac{3x-4}{5}$ is

#### The shortest distance between the two straight line$\frac{x-4/3}{2}=\frac{y+6/5}{3}=\frac{z-3/2}{4}$ and $\frac{5y+6}{8}=\frac{2z-3}{9}=\frac{3x-4}{5}$ is

maths-General

physics-

#### In the given figure, what is the angle of prism

Angle of prism is the angle between incident and emergent surfaces.

#### In the given figure, what is the angle of prism

physics-General

Angle of prism is the angle between incident and emergent surfaces.

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

physics-General

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 ray of light is incident on an equilateral glass prism placed on a horizontal table. For minimum deviation which of the following is true

In minimum deviation position refracted ray inside the prism is parallel to the base of the prism

#### A ray of light is incident on an equilateral glass prism placed on a horizontal table. For minimum deviation which of the following is true

physics-General

In minimum deviation position refracted ray inside the prism is parallel to the base of the prism

physics-

#### A piece of wire is bent in the shape of a parabola $y=k{x}^{2}(y$-axis vertical) with a bead of mass $m$ 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 $x$-axis with a constant acceleration $a$. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the $y$-axis is

$ma\mathrm{cos}\theta =mg\mathrm{cos}(90-\theta )$
$\Rightarrow \frac{a}{g}=\mathrm{tan}\theta \Rightarrow \frac{a}{g}=\frac{dy}{dx}$
$\Rightarrow \frac{d}{dx}{\left(kx\right)}^{2}=\frac{a}{g}\Rightarrow x=\frac{a}{2gk}$

#### A piece of wire is bent in the shape of a parabola $y=k{x}^{2}(y$-axis vertical) with a bead of mass $m$ 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 $x$-axis with a constant acceleration $a$. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the $y$-axis is

physics-General

$ma\mathrm{cos}\theta =mg\mathrm{cos}(90-\theta )$
$\Rightarrow \frac{a}{g}=\mathrm{tan}\theta \Rightarrow \frac{a}{g}=\frac{dy}{dx}$
$\Rightarrow \frac{d}{dx}{\left(kx\right)}^{2}=\frac{a}{g}\Rightarrow x=\frac{a}{2gk}$

physics-

#### A point *P* moves in counter-clockwise 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 counter-clockwise 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

physics-General

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

maths-General

Hence (c) is the correct answer.