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A triple star system consists of two stars, each of mass m, in the same circular orbit about central star with mass M equals 2 cross times 10 to the power of 30 end exponent k g. The two outer stars always lie at opposite ends of a diameter of their common circular orbit. The radius of the circular orbit is r = 10 to the power of 11 end exponent m, and the orbital period of each star is 1.6 cross times 10 to the power of 7 end exponents. [Take pi to the power of 2 end exponent= 10 and G = 20 divided by 3 cross times 10 to the power of negative 11 end exponent N m to the power of 2 end exponent k g to the power of negative 2 end exponent] The orbital velocity of each star is

  1. fraction numerator 5 over denominator 4 end fraction square root of 10 cross times 10 to the power of 3 end exponent m divided by s    
  2. fraction numerator 5 over denominator 4 end fraction square root of 10 cross times 10 to the power of 5 end exponent m divided by s    
  3. fraction numerator 5 over denominator 4 end fraction square root of 10 cross times 10 to the power of 2 end exponent m divided by s    
  4. fraction numerator 5 over denominator 4 end fraction square root of 10 cross times 10 to the power of 4 end exponent m divided by s    

The correct answer is: fraction numerator 5 over denominator 4 end fraction square root of 10 cross times 10 to the power of 4 end exponent m divided by s

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General
physics-

A triple star system consists of two stars, each of mass m, in the same circular orbit about central star with mass M equals 2 cross times 10 to the power of 30 end exponent k g. The two outer stars always lie at opposite ends of a diameter of their common circular orbit. The radius of the circular orbit is r = 10 to the power of 11 end exponent m, and the orbital period of each star is 1.6 cross times 10 to the power of 7 end exponents. [Take pi to the power of 2 end exponent= 10 and G = 20 divided by 3 cross times 10 to the power of negative 11 end exponent N m to the power of 2 end exponent k g to the power of negative 2 end exponent] The mass m of the outer stars is

A triple star system consists of two stars, each of mass m, in the same circular orbit about central star with mass M equals 2 cross times 10 to the power of 30 end exponent k g. The two outer stars always lie at opposite ends of a diameter of their common circular orbit. The radius of the circular orbit is r = 10 to the power of 11 end exponent m, and the orbital period of each star is 1.6 cross times 10 to the power of 7 end exponents. [Take pi to the power of 2 end exponent= 10 and G = 20 divided by 3 cross times 10 to the power of negative 11 end exponent N m to the power of 2 end exponent k g to the power of negative 2 end exponent] The mass m of the outer stars is

physics-General
General
physics-

A planet is revolving around the sun is an elliptical orbit as shown in figure. Select correct alternative(s)

A planet is revolving around the sun is an elliptical orbit as shown in figure. Select correct alternative(s)

physics-General
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If the law of gravitation be such that the force of attraction between two particles vary inversely as the 5 divided by 2 to the power of text th  end text end exponent power of their separation, then the graph of orbital velocity v0 plotted against the distance r of a satellite from the earth's centre on a log-log scale is shown alongside. The slope of line will be-

If the law of gravitation be such that the force of attraction between two particles vary inversely as the 5 divided by 2 to the power of text th  end text end exponent power of their separation, then the graph of orbital velocity v0 plotted against the distance r of a satellite from the earth's centre on a log-log scale is shown alongside. The slope of line will be-

physics-General
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General
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A particle is projected from point A, that is at a distance 4R from the centre of the Earth, with speed V subscript 1 end subscript in a direction making 30 to the power of ring operator end exponent with the line joining the centre of the Earth and point A, as shown. Find the speed V subscript 1 end subscript of particle (in m/s) if particle passes grazing the surface of the earth. Consider gravitational interaction only between these two.
text (use  end text open fraction numerator G M over denominator R end fraction equals 6.4 cross times fraction numerator 10 to the power of 7 end exponent m to the power of 2 end exponent over denominator s to the power of 2 end exponent end fraction close parentheses

A particle is projected from point A, that is at a distance 4R from the centre of the Earth, with speed V subscript 1 end subscript in a direction making 30 to the power of ring operator end exponent with the line joining the centre of the Earth and point A, as shown. Find the speed V subscript 1 end subscript of particle (in m/s) if particle passes grazing the surface of the earth. Consider gravitational interaction only between these two.
text (use  end text open fraction numerator G M over denominator R end fraction equals 6.4 cross times fraction numerator 10 to the power of 7 end exponent m to the power of 2 end exponent over denominator s to the power of 2 end exponent end fraction close parentheses

physics-General
General
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The figure shows elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded area SAB. If t subscript 1 end subscript be the time for the planet to move from C to D and t subscript 2 end subscript is the time to move from A to B, then :

The figure shows elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded area SAB. If t subscript 1 end subscript be the time for the planet to move from C to D and t subscript 2 end subscript is the time to move from A to B, then :

physics-General
General
physics-

Velocity of efflux in Torricelli's theorem is given by v equals square root of 2 g h end root, here h is the height of hole from the top surface, after that, motion of liquid can be treated as projectile motion. Liquid is filled in a vessel of square base left parenthesis 2 m cross times 2 m right parenthesis up to a height of 2m as shown in figure (i). In figure (ii) the vessel is tilted from horizontal at 30 to the power of ring operator end exponent What is the velocity of efflux in this case. Liquid does not spills out?

Velocity of efflux in Torricelli's theorem is given by v equals square root of 2 g h end root, here h is the height of hole from the top surface, after that, motion of liquid can be treated as projectile motion. Liquid is filled in a vessel of square base left parenthesis 2 m cross times 2 m right parenthesis up to a height of 2m as shown in figure (i). In figure (ii) the vessel is tilted from horizontal at 30 to the power of ring operator end exponent What is the velocity of efflux in this case. Liquid does not spills out?

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General
maths-

The number of values of c such that the straight line y = 4x + c touches the curve fraction numerator x to the power of 2 end exponent over denominator 4 end fraction+ y2 = 1 is

The number of values of c such that the straight line y = 4x + c touches the curve fraction numerator x to the power of 2 end exponent over denominator 4 end fraction+ y2 = 1 is

maths-General
General
maths-

If P(x, y), F1=(3,0), F2 = (– 3, 0)and16x2 + 25 y2 = 400, then P F1 + P F2 =

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maths-General
General
Maths-

Let P be a variable point on the ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction+ fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction= 1 with foci F1 and F2. If A is the area of the triangle PF1 F2, then the maximum value of A is-

Area of triangle with given vertices can be calculated using the matrix determimnant method.

Let P be a variable point on the ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction+ fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction= 1 with foci F1 and F2. If A is the area of the triangle PF1 F2, then the maximum value of A is-

Maths-General

Area of triangle with given vertices can be calculated using the matrix determimnant method.

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General
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The eccentricity of an ellipse, with its centre at the origin, is fraction numerator 1 over denominator 2 end fraction. If one of the directrices is x = 4, then the equation of the ellipse is-

standard equation of ellipse is
x2/a2+y2/b2=1

The eccentricity of an ellipse, with its centre at the origin, is fraction numerator 1 over denominator 2 end fraction. If one of the directrices is x = 4, then the equation of the ellipse is-

Maths-General

standard equation of ellipse is
x2/a2+y2/b2=1

General
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The foci of the ellipse fraction numerator x to the power of 2 end exponent over denominator 16 end fraction+ fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction = 1 and the hyperbola fraction numerator x to the power of 2 end exponent over denominator 144 end fractionfraction numerator y to the power of 2 end exponent over denominator 81 end fraction= fraction numerator 1 over denominator 25 end fraction coincide. Then the value of b2 is-

focus of ellispe  = ae,0

The foci of the ellipse fraction numerator x to the power of 2 end exponent over denominator 16 end fraction+ fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction = 1 and the hyperbola fraction numerator x to the power of 2 end exponent over denominator 144 end fractionfraction numerator y to the power of 2 end exponent over denominator 81 end fraction= fraction numerator 1 over denominator 25 end fraction coincide. Then the value of b2 is-

Maths-General

focus of ellispe  = ae,0

General
Maths-

The equation of an ellipse, whose major axis = 8 and eccentricity = 1/2, is

The equation of an ellipse, whose major axis = 8 and eccentricity = 1/2, is

Maths-General
parallel
General
Maths-

Arrangement of the following ellipses in ascending order of the radii of their director circles
P) 4x2 + 9y2 = 36
Q) 3x2 + 4y2 = 12
R) 9x2 + 16y2 = 144
S) x2 + 2y2 = 4

the radius of director circle is equal to the length of semi major axis.

Arrangement of the following ellipses in ascending order of the radii of their director circles
P) 4x2 + 9y2 = 36
Q) 3x2 + 4y2 = 12
R) 9x2 + 16y2 = 144
S) x2 + 2y2 = 4

Maths-General

the radius of director circle is equal to the length of semi major axis.

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If p and p' denote the lengths of the perpendicular from a focus and the centre of an ellipse with semi-major axis of length a, respectively, on a tangent to the ellipse and r denotes the focal distance of the point, then

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the distances of the points from a line can be calculated by using the distance formula.

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An ellipse and a hyperbola have the same centre “origin”, the same foci. The minor-axis of the one is the same as the conjugate axis of the other. If e1, e2 be their eccentricities respectively, then fraction numerator 1 over denominator e subscript 1 end subscript superscript 2 end superscript end fraction+ fraction numerator 1 over denominator e subscript 2 end subscript superscript 2 end superscript end fractionis equal to

the conjugate axis of a hyperbola is the line through the center of the hyperbola and perpendicular to the line joining the focii.

An ellipse and a hyperbola have the same centre “origin”, the same foci. The minor-axis of the one is the same as the conjugate axis of the other. If e1, e2 be their eccentricities respectively, then fraction numerator 1 over denominator e subscript 1 end subscript superscript 2 end superscript end fraction+ fraction numerator 1 over denominator e subscript 2 end subscript superscript 2 end superscript end fractionis equal to

Maths-General

the conjugate axis of a hyperbola is the line through the center of the hyperbola and perpendicular to the line joining the focii.

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