Maths-

General

Easy

Question

The shortest distance between the two straight line $fraction numerator x minus 4 divided by 3 over denominator 2 end fraction equals fraction numerator y plus 6 divided by 5 over denominator 3 end fraction equals fraction numerator z minus 3 divided by 2 over denominator 4 end fraction$ and $fraction numerator 5 y plus 6 over denominator 8 end fraction equals fraction numerator 2 z minus 3 over denominator 9 end fraction equals fraction numerator 3 x minus 4 over denominator 5 end fraction$ is

$\sqrt{29}$
3
0
$6 \sqrt{10}$

Hint:

In the question two lines are given in the cartesian form $fraction numerator x minus x subscript 1 over denominator a subscript 1 end fraction equals fraction numerator y minus y subscript 1 over denominator b subscript 1 end fraction equals fraction numerator z minus z subscript 1 over denominator c subscript 1 end fraction space a n d space fraction numerator x minus x subscript 2 over denominator a subscript 2 end fraction equals fraction numerator y minus y subscript 2 over denominator b subscript 2 end fraction equals fraction numerator z minus z subscript 2 over denominator c subscript 2 end fraction$ we have to find the shortest distance between the two lines with the formula $fraction numerator 1 over denominator square root of D end fraction open vertical bar table row cell x subscript 2 minus x subscript 1 end cell cell y subscript 2 minus y subscript 1 end cell cell z subscript 2 minus z subscript 1 end cell row cell a subscript 1 end cell cell b subscript 1 end cell cell c subscript 1 end cell row cell a subscript 2 end cell cell b subscript 2 end cell cell c subscript 2 end cell end table close vertical bar space comma w h e r e space D equals left parenthesis a subscript 1 b subscript 2 minus a subscript 2 b subscript 1 right parenthesis squared plus left parenthesis b subscript 1 c subscript 2 minus b subscript 2 c subscript 1 right parenthesis squared plus left parenthesis c subscript 1 a subscript 2 minus c subscript 2 a subscript 1 right parenthesis squared$ .

The correct answer is: 0

The given equations are
$fraction numerator x minus 4 divided by 3 over denominator 2 end fraction equals fraction numerator y plus 6 divided by 5 over denominator 3 end fraction equals fraction numerator z minus 3 divided by 2 over denominator 4 end fraction$ and
$fraction numerator 5 y plus 6 over denominator 8 end fraction equals fraction numerator 2 z minus 3 over denominator 9 end fraction equals fraction numerator 3 x minus 4 over denominator 5 end fraction$
$rightwards double arrow fraction numerator x minus begin display style 4 over 3 end style over denominator begin display style 5 over 3 end style end fraction equals fraction numerator y plus begin display style 6 over 5 end style over denominator begin display style 8 over 5 end style end fraction equals fraction numerator z minus begin display style 3 over 2 end style over denominator begin display style 9 over 2 end style end fraction$
The shortest distance between the two cartesian lines
= $fraction numerator 1 over denominator square root of D end fraction open vertical bar table row cell x subscript 2 minus x subscript 1 end cell cell y subscript 2 minus y subscript 1 end cell cell z subscript 2 minus z subscript 1 end cell row cell a subscript 1 end cell cell b subscript 1 end cell cell c subscript 1 end cell row cell a subscript 2 end cell cell b subscript 2 end cell cell c subscript 2 end cell end table close vertical bar space comma w h e r e space D equals left parenthesis a subscript 1 b subscript 2 minus a subscript 2 b subscript 1 right parenthesis squared plus left parenthesis b subscript 1 c subscript 2 minus b subscript 2 c subscript 1 right parenthesis squared plus left parenthesis c subscript 1 a subscript 2 minus c subscript 2 a subscript 1 right parenthesis squared$
$equals fraction numerator 1 over denominator square root of D end fraction open vertical bar table row cell 4 over 3 minus 4 over 3 end cell cell fraction numerator negative 6 over denominator 5 end fraction plus 6 over 5 end cell cell 3 over 2 minus 3 over 2 end cell row 2 3 4 row cell 5 over 3 end cell cell 8 over 5 end cell cell 9 over 2 end cell end table close vertical bar equals fraction numerator 1 over denominator square root of D end fraction open vertical bar table row 0 0 0 row 2 3 4 row cell 5 over 3 end cell cell 8 over 5 end cell cell 9 over 2 end cell end table close vertical bar equals fraction numerator 1 over denominator square root of D end fraction cross times 0 equals 0$

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 $θ$ at which the speed of the bob is half of that at A, satisfies

Velocity of the bob at the point A

v = \sqrt{5 g L}

(i)

{(\frac{v}{2})}^{2} = v^{2} - 2 g h (i i)

h = L (1 - \cos θ) (i i i)

S o l v i n g E q s . (i), (i i) a n d (i i i), w e g e t

\cos θ = - \frac{7}{8}

o r θ = {c o s}^{- 1} (- \frac{7}{8}) = 151 °

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 $θ$ 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{5 g L}

(i)

{(\frac{v}{2})}^{2} = v^{2} - 2 g h (i i)

h = L (1 - \cos θ) (i i i)

S o l v i n g E q s . (i), (i i) a n d (i i i), w e g e t

\cos θ = - \frac{7}{8}

o r θ = {c o s}^{- 1} (- \frac{7}{8}) = 151 °

General

Physics-

A piece of wire is bent in the shape of a parabola $y equals k x to the power of 2 end exponent blank left parenthesis y$ -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

m a cos invisible function application theta equals m g cos invisible function application left parenthesis 90 minus theta right parenthesis

rightwards double arrow fraction numerator a over denominator g end fraction equals tan invisible function application theta rightwards double arrow fraction numerator a over denominator g end fraction equals fraction numerator d y over denominator d x end fraction

rightwards double arrow fraction numerator d over denominator d x end fraction open parentheses k x close parentheses to the power of 2 end exponent equals fraction numerator a over denominator g end fraction rightwards double arrow x equals fraction numerator a over denominator 2 g k end fraction

A piece of wire is bent in the shape of a parabola $y equals k x to the power of 2 end exponent blank left parenthesis y$ -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

m a cos invisible function application theta equals m g cos invisible function application left parenthesis 90 minus theta right parenthesis

rightwards double arrow fraction numerator a over denominator g end fraction equals tan invisible function application theta rightwards double arrow fraction numerator a over denominator g end fraction equals fraction numerator d y over denominator d x end fraction

rightwards double arrow fraction numerator d over denominator d x end fraction open parentheses k x close parentheses to the power of 2 end exponent equals fraction numerator a over denominator g end fraction rightwards double arrow x equals fraction numerator a over denominator 2 g k end fraction

General

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 $s equals t to the power of 3 end exponent plus 5 comma$ where $s$ 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

G i v e n comma blank s equals t to the power of 3 end exponent plus 5

S p e e d comma blank v equals fraction numerator d s over denominator d t end fraction equals 3 t to the power of 2 end exponent

a n d blank r a t e blank o f blank c h a n g e blank o f blank s p e e d comma blank a subscript t end subscript equals fraction numerator d v over denominator d t end fraction equals 6 t

therefore T a n g e n t i a l blank a c c e l e r a t i o n blank a t blank t equals 2 blank s comma

a subscript t end subscript equals 6 cross times 2 equals 12 blank m s to the power of negative 2 end exponent

a n d blank a t blank t equals 2 s comma blank v equals 3 left parenthesis 2 right parenthesis to the power of 2 end exponent equals 12 m s to the power of negative 1 end exponent

therefore C e n t r i p e t a l blank a c c e l e r a t i o n comma blank a subscript c end subscript equals fraction numerator v to the power of 2 end exponent over denominator R end fraction equals fraction numerator 144 over denominator 20 end fraction m s to the power of negative 2 end exponent

therefore N e t blank a c c e l e r a t i o n equals a subscript t end subscript superscript 2 end superscript plus a subscript i end subscript superscript 2 end superscript almost equal to 14 m s to the power of negative 2 end exponent

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 $s equals t to the power of 3 end exponent plus 5 comma$ where $s$ 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

G i v e n comma blank s equals t to the power of 3 end exponent plus 5

S p e e d comma blank v equals fraction numerator d s over denominator d t end fraction equals 3 t to the power of 2 end exponent

a n d blank r a t e blank o f blank c h a n g e blank o f blank s p e e d comma blank a subscript t end subscript equals fraction numerator d v over denominator d t end fraction equals 6 t

therefore T a n g e n t i a l blank a c c e l e r a t i o n blank a t blank t equals 2 blank s comma

a subscript t end subscript equals 6 cross times 2 equals 12 blank m s to the power of negative 2 end exponent

a n d blank a t blank t equals 2 s comma blank v equals 3 left parenthesis 2 right parenthesis to the power of 2 end exponent equals 12 m s to the power of negative 1 end exponent

therefore C e n t r i p e t a l blank a c c e l e r a t i o n comma blank a subscript c end subscript equals fraction numerator v to the power of 2 end exponent over denominator R end fraction equals fraction numerator 144 over denominator 20 end fraction m s to the power of negative 2 end exponent

therefore N e t blank a c c e l e r a t i o n equals a subscript t end subscript superscript 2 end superscript plus a subscript i end subscript superscript 2 end superscript almost equal to 14 m s to the power of negative 2 end exponent

General

maths-

The equation of the plane containing the line $fraction numerator x with not stretchy bar on top minus alpha over denominator 1 end fraction equals fraction numerator y minus beta over denominator m end fraction equals fraction numerator z minus gamma over denominator n end fraction text is end text stack a with _ below with _ below left parenthesis x minus alpha right parenthesis plus b left parenthesis y minus beta right parenthesis plus c left parenthesis z minus gamma right parenthesis equals 0$ 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.

The equation of the plane containing the line $fraction numerator x with not stretchy bar on top minus alpha over denominator 1 end fraction equals fraction numerator y minus beta over denominator m end fraction equals fraction numerator z minus gamma over denominator n end fraction text is end text stack a with _ below with _ below left parenthesis x minus alpha right parenthesis plus b left parenthesis y minus beta right parenthesis plus c left parenthesis z minus gamma right parenthesis equals 0$ where al + bm + cn 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.

General

physics-

A small body of mass $m$ slides down from the top of a hemisphere of radius $r$ . The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is

physics-General

General

physics-

Average torque on a projectile of mass $m$ , initial speed $u$ and angles of projection $theta$ , between initial and final position $P$ and $Q$ as shown in figure about the point of projection is

Time of flight.

T equals fraction numerator 2 u sin invisible function application theta over denominator g end fraction

Horizontal range,

R equals fraction numerator u to the power of 2 end exponent sin invisible function application 2 theta over denominator g end fraction

Change in angular momentum,

open vertical bar d stack L with rightwards arrow on top close vertical bar equals open vertical bar stack L with rightwards arrow on top subscript f end subscript minus stack L with rightwards arrow on top subscript i end subscript close vertical bar

about point of projection

equals left parenthesis m u sin invisible function application theta right parenthesis cross times fraction numerator u to the power of 2 end exponent sin invisible function application 2 theta over denominator g end fraction

equals fraction numerator m u to the power of 3 end exponent sin invisible function application theta sin invisible function application 2 theta over denominator g end fraction

T o r q u e blank open vertical bar stack tau with rightwards arrow on top close vertical bar equals fraction numerator c h a n g e blank i n blank a n g u l a r blank m o m e n t u m over denominator t i m e blank o f blank f l i g h t end fraction

equals open vertical bar fraction numerator d stack L with rightwards arrow on top over denominator T end fraction close vertical bar

Average torque on a projectile of mass $m$ , initial speed $u$ and angles of projection $theta$ , between initial and final position $P$ and $Q$ as shown in figure about the point of projection is

physics-General

Time of flight.

T equals fraction numerator 2 u sin invisible function application theta over denominator g end fraction

Horizontal range,

R equals fraction numerator u to the power of 2 end exponent sin invisible function application 2 theta over denominator g end fraction

Change in angular momentum,

open vertical bar d stack L with rightwards arrow on top close vertical bar equals open vertical bar stack L with rightwards arrow on top subscript f end subscript minus stack L with rightwards arrow on top subscript i end subscript close vertical bar

about point of projection

equals left parenthesis m u sin invisible function application theta right parenthesis cross times fraction numerator u to the power of 2 end exponent sin invisible function application 2 theta over denominator g end fraction

equals fraction numerator m u to the power of 3 end exponent sin invisible function application theta sin invisible function application 2 theta over denominator g end fraction

T o r q u e blank open vertical bar stack tau with rightwards arrow on top close vertical bar equals fraction numerator c h a n g e blank i n blank a n g u l a r blank m o m e n t u m over denominator t i m e blank o f blank f l i g h t end fraction

equals open vertical bar fraction numerator d stack L with rightwards arrow on top over denominator T end fraction close vertical bar

General

physics-

A string of length $L$ is fixed at one end and the string makes $fraction numerator 2 over denominator pi end fraction$ rev/s around the vertical axis through, the fixed and as shown in the figure, then tension in the string is

T sin invisible function application theta equals M omega to the power of 2 end exponent R

(i)

T sin invisible function application theta equals M omega to the power of 2 end exponent L blank s i n blank theta

(ii)

T equals M omega to the power of 2 end exponent L

equals M bullet 4 pi to the power of 2 end exponent n to the power of 2 end exponent L

equals M bullet 4 pi to the power of 2 end exponent open parentheses fraction numerator 2 over denominator pi end fraction close parentheses to the power of 2 end exponent L

equals 16 blank M L

A string of length $L$ is fixed at one end and the string makes $fraction numerator 2 over denominator pi end fraction$ rev/s around the vertical axis through, the fixed and as shown in the figure, then tension in the string is

physics-General

T sin invisible function application theta equals M omega to the power of 2 end exponent R

(i)

T sin invisible function application theta equals M omega to the power of 2 end exponent L blank s i n blank theta

(ii)

T equals M omega to the power of 2 end exponent L

equals M bullet 4 pi to the power of 2 end exponent n to the power of 2 end exponent L

equals M bullet 4 pi to the power of 2 end exponent open parentheses fraction numerator 2 over denominator pi end fraction close parentheses to the power of 2 end exponent L

equals 16 blank M L

General

physics-

A thin prism $P subscript 1 end subscript$ with angle $6 to the power of ring operator end exponent$ and made from glass of refractive index 1.54 is combined with another thin prism $P subscript 2 end subscript$ of refractive index 1.72 to produce dispersion without deviation. The angle of prism $P subscript 2 end subscript$ will be

fraction numerator A to the power of ´ end exponent over denominator A end fraction equals fraction numerator left parenthesis mu subscript y end subscript minus 1 right parenthesis over denominator left parenthesis mu subscript y ´ end subscript minus 1 right parenthesis end fraction rightwards double arrow fraction numerator A to the power of ´ end exponent over denominator 6 end fraction equals negative fraction numerator left parenthesis 1.54 minus 1 right parenthesis over denominator left parenthesis 1.72 minus 1 right parenthesis end fraction

Þ A'

equals negative 4.5 to the power of o end exponent equals 4 to the power of o end exponent 3 0 to the power of ´ end exponent

A thin prism $P subscript 1 end subscript$ with angle $6 to the power of ring operator end exponent$ and made from glass of refractive index 1.54 is combined with another thin prism $P subscript 2 end subscript$ of refractive index 1.72 to produce dispersion without deviation. The angle of prism $P subscript 2 end subscript$ will be

physics-General

fraction numerator A to the power of ´ end exponent over denominator A end fraction equals fraction numerator left parenthesis mu subscript y end subscript minus 1 right parenthesis over denominator left parenthesis mu subscript y ´ end subscript minus 1 right parenthesis end fraction rightwards double arrow fraction numerator A to the power of ´ end exponent over denominator 6 end fraction equals negative fraction numerator left parenthesis 1.54 minus 1 right parenthesis over denominator left parenthesis 1.72 minus 1 right parenthesis end fraction

Þ A'

equals negative 4.5 to the power of o end exponent equals 4 to the power of o end exponent 3 0 to the power of ´ end exponent

General

physics-

A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if $theta equals 4 5 to the power of o end exponent$ . The index of refraction of glass is

For total internal reflection

theta greater than C

rightwards double arrow

sin invisible function application theta greater than sin invisible function application C rightwards double arrow sin invisible function application theta greater than fraction numerator 1 over denominator mu end fraction

mu greater than fraction numerator 1 over denominator sin invisible function application theta end fraction rightwards double arrow mu greater than fraction numerator 1 over denominator sin invisible function application 4 5 to the power of o end exponent end fraction rightwards double arrow mu greater than square root of 2 rightwards double arrow mu greater than 1.41

A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if $theta equals 4 5 to the power of o end exponent$ . The index of refraction of glass is

physics-General

For total internal reflection

theta greater than C

rightwards double arrow

sin invisible function application theta greater than sin invisible function application C rightwards double arrow sin invisible function application theta greater than fraction numerator 1 over denominator mu end fraction

mu greater than fraction numerator 1 over denominator sin invisible function application theta end fraction rightwards double arrow mu greater than fraction numerator 1 over denominator sin invisible function application 4 5 to the power of o end exponent end fraction rightwards double arrow mu greater than square root of 2 rightwards double arrow mu greater than 1.41

General

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

physics-General

Because in dispersion of white light, the rays of different colours are not parallel to each other. Also deviation takes place in same direction.

General

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

physics-General

General

physics-

A ray of monochromatic light is incident on one refracting face of a prism of angle $75 to the power of ring operator end exponent$ . It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the material of the prism is $square root of 2$ , the angle of incidence on the first face of the prism is

From figure

A equals r subscript 1 end subscript plus c equals r subscript 1 end subscript plus sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator mu end fraction close parentheses

rightwards double arrow r subscript 1 end subscript equals 75 minus sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator mu end fraction close parentheses

rightwards double arrow 75 minus 45 equals 3 0 to the power of o end exponent

From Snell’s law At B

mu equals fraction numerator sin invisible function application i over denominator sin invisible function application r subscript 1 end subscript end fraction rightwards double arrow square root of 2 equals fraction numerator sin invisible function application i over denominator sin invisible function application 3 0 to the power of o end exponent end fraction

A ray of monochromatic light is incident on one refracting face of a prism of angle $75 to the power of ring operator end exponent$ . It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the material of the prism is $square root of 2$ , the angle of incidence on the first face of the prism is

physics-General

From figure

A equals r subscript 1 end subscript plus c equals r subscript 1 end subscript plus sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator mu end fraction close parentheses

rightwards double arrow r subscript 1 end subscript equals 75 minus sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator mu end fraction close parentheses

rightwards double arrow 75 minus 45 equals 3 0 to the power of o end exponent

From Snell’s law At B

mu equals fraction numerator sin invisible function application i over denominator sin invisible function application r subscript 1 end subscript end fraction rightwards double arrow square root of 2 equals fraction numerator sin invisible function application i over denominator sin invisible function application 3 0 to the power of o end exponent end fraction

General

physics-

A light ray is incident upon a prism in minimum deviation position and suffers a deviation of 34°. If the shaded half of the prism is knocked off, the ray will

By formula

delta equals left parenthesis n minus 1 right parenthesis A rightwards double arrow 34 equals left parenthesis n minus 1 right parenthesis A

and in the second position

delta to the power of ´ end exponent equals left parenthesis n minus 1 right parenthesis fraction numerator A over denominator 2 end fraction

therefore

fraction numerator 34 over denominator delta to the power of ´ end exponent end fraction equals fraction numerator left parenthesis n minus 1 right parenthesis A over denominator left parenthesis n minus 1 right parenthesis fraction numerator A over denominator 2 end fraction end fraction

delta to the power of ´ end exponent equals fraction numerator 34 over denominator 2 end fraction equals 1 7 to the power of o end exponent

A light ray is incident upon a prism in minimum deviation position and suffers a deviation of 34°. If the shaded half of the prism is knocked off, the ray will

physics-General

By formula

delta equals left parenthesis n minus 1 right parenthesis A rightwards double arrow 34 equals left parenthesis n minus 1 right parenthesis A

and in the second position

delta to the power of ´ end exponent equals left parenthesis n minus 1 right parenthesis fraction numerator A over denominator 2 end fraction

therefore

fraction numerator 34 over denominator delta to the power of ´ end exponent end fraction equals fraction numerator left parenthesis n minus 1 right parenthesis A over denominator left parenthesis n minus 1 right parenthesis fraction numerator A over denominator 2 end fraction end fraction

delta to the power of ´ end exponent equals fraction numerator 34 over denominator 2 end fraction equals 1 7 to the power of o end exponent

General

physics-

A prism ABC of angle 30° has its face AC silvered. A ray of light incident at an angle of 45° at the face AB retraces its path after refraction at face AB and reflection at face AC. The refractive index of the material of the prism is

physics-General

General

physics-

A ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the angle of emergence and each of these angles is equal to 3/4 of the angle of the prism. The angle of deviation is

Is a band spectrum
In the position of minimum deviation

2 i equals A plus delta subscript m end subscript

delta subscript m end subscript equals 2 i minus A equals 90 minus 60 equals 3 0 to the power of o end exponent

A ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the angle of emergence and each of these angles is equal to 3/4 of the angle of the prism. The angle of deviation is

physics-General

Is a band spectrum
In the position of minimum deviation

2 i equals A plus delta subscript m end subscript

delta subscript m end subscript equals 2 i minus A equals 90 minus 60 equals 3 0 to the power of o end exponent

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$\sqrt{29}$
3
0
$6 \sqrt{10}$

The correct answer is: 0

Related Questions to study

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A string of length $L$ is fixed at one end and the string makes $fraction numerator 2 over denominator pi end fraction$ rev/s around the vertical axis through, the fixed and as shown in the figure, then tension in the string is

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Which of the following diagrams, shows correctly the dispersion of white light by a prism

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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

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A light ray is incident upon a prism in minimum deviation position and suffers a deviation of 34°. If the shaded half of the prism is knocked off, the ray will

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A prism ABC of angle 30° has its face AC silvered. A ray of light incident at an angle of 45° at the face AB retraces its path after refraction at face AB and reflection at face AC. The refractive index of the material of the prism is

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The shortest distance between the two straight line and is

30

In the question two lines are given in the cartesian form we have to find the shortest distance between the two lines with the formula .

The correct answer is: 0

The given equations are andThe shortest distance between the two cartesian lines=

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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

The equation of the plane containing the line where al + bm + cn is equal to

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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

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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 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

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

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

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

A ray of monochromatic light is incident on one refracting face of a prism of angle . It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the material of the prism is , the angle of incidence on the first face of the prism is

A ray of monochromatic light is incident on one refracting face of a prism of angle . It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the material of the prism is , the angle of incidence on the first face of the prism is

A light ray is incident upon a prism in minimum deviation position and suffers a deviation of 34°. If the shaded half of the prism is knocked off, the ray will

A light ray is incident upon a prism in minimum deviation position and suffers a deviation of 34°. If the shaded half of the prism is knocked off, the ray will

A prism ABC of angle 30° has its face AC silvered. A ray of light incident at an angle of 45° at the face AB retraces its path after refraction at face AB and reflection at face AC. The refractive index of the material of the prism is

A prism ABC of angle 30° has its face AC silvered. A ray of light incident at an angle of 45° at the face AB retraces its path after refraction at face AB and reflection at face AC. The refractive index of the material of the prism is

A ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the angle of emergence and each of these angles is equal to 3/4 of the angle of the prism. The angle of deviation is

A ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the angle of emergence and each of these angles is equal to 3/4 of the angle of the prism. The angle of deviation is

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$\sqrt{29}$
3
0
$6 \sqrt{10}$

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 $θ$ 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 $θ$ at which the speed of the bob is half of that at A, satisfies

A small body of mass $m$ slides down from the top of a hemisphere of radius $r$ . 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 $m$ slides down from the top of a hemisphere of radius $r$ . The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is

Average torque on a projectile of mass $m$ , initial speed $u$ and angles of projection $theta$ , between initial and final position $P$ and $Q$ as shown in figure about the point of projection is

Average torque on a projectile of mass $m$ , initial speed $u$ and angles of projection $theta$ , between initial and final position $P$ and $Q$ as shown in figure about the point of projection is

A string of length $L$ is fixed at one end and the string makes $fraction numerator 2 over denominator pi end fraction$ 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 $L$ is fixed at one end and the string makes $fraction numerator 2 over denominator pi end fraction$ rev/s around the vertical axis through, the fixed and as shown in the figure, then tension in the string is

A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if $theta equals 4 5 to the power of o end exponent$ . 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 $theta equals 4 5 to the power of o end exponent$ . The index of refraction of glass is