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If the chord joining two points whose eccentric angles are alpha and beta cuts the major axis of an 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 at a distance c from the centre, then tan alpha divided by 2. tan beta divided by 2 is equal to

Maths-General

  1. 1    
  2. c    
  3. fraction numerator c plus a over denominator c minus a end fraction    
  4. fraction numerator c – a over denominator c plus a end fraction    

    Answer:The correct answer is: fraction numerator c plus a over denominator c minus a end fraction

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    General
    maths-

    P(a costheta, b sintheta) is any 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 left parenthesis a greater than b right parenthesis Now if this ellipse is rotated anticlockwise by 90º and P reaches straight P to the power of straight prime then co-ordinate of straight P to the power of straight prime are -

    P(a costheta, b sintheta) is any 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 left parenthesis a greater than b right parenthesis Now if this ellipse is rotated anticlockwise by 90º and P reaches straight P to the power of straight prime then co-ordinate of straight P to the power of straight prime are -

    maths-General
    General
    maths-

    Normal to the ellipse fraction numerator x to the power of 2 end exponent over denominator 84 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 49 end fraction equals 1 intersects the major and minor axis at P and Q respectively then locus of the point dividing segment PQ in 2 : 1 is -

    Equation of normal 8x sectheta – 7y cosectheta = 15
    P open parentheses fraction numerator 15 over denominator 8 end fraction cos invisible function application theta comma 0 close parentheses, Q open parentheses 0 comma fraction numerator negative 15 over denominator 7 end fraction sin invisible function application theta close parentheses

    3h = fraction numerator 15 over denominator 8 end fraction cos invisible function application theta, 3k = negative fraction numerator 30 over denominator 7 end fraction sin invisible function application theta
    costheta = fraction numerator 8 h over denominator 5 end fraction, sintheta = fraction numerator negative 7 k over denominator 10 end fraction
    hence locus fraction numerator 64 x to the power of 2 end exponent over denominator 25 end fraction plus fraction numerator 49 y to the power of 2 end exponent over denominator 100 end fraction = 1

    Normal to the ellipse fraction numerator x to the power of 2 end exponent over denominator 84 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 49 end fraction equals 1 intersects the major and minor axis at P and Q respectively then locus of the point dividing segment PQ in 2 : 1 is -

    maths-General
    Equation of normal 8x sectheta – 7y cosectheta = 15
    P open parentheses fraction numerator 15 over denominator 8 end fraction cos invisible function application theta comma 0 close parentheses, Q open parentheses 0 comma fraction numerator negative 15 over denominator 7 end fraction sin invisible function application theta close parentheses

    3h = fraction numerator 15 over denominator 8 end fraction cos invisible function application theta, 3k = negative fraction numerator 30 over denominator 7 end fraction sin invisible function application theta
    costheta = fraction numerator 8 h over denominator 5 end fraction, sintheta = fraction numerator negative 7 k over denominator 10 end fraction
    hence locus fraction numerator 64 x to the power of 2 end exponent over denominator 25 end fraction plus fraction numerator 49 y to the power of 2 end exponent over denominator 100 end fraction = 1
    General
    physics-

    Given graph gives variation of fraction numerator P V over denominator T end fraction with P for 1gm of oxygen at two different temperatures T1 and T2. If density of oxygen 1.427 k g divided by m to the power of 3 end exponent. The value of fraction numerator P V over denominator T end fraction at point A and relation b divided by w T subscript 1 end subscript & T subscript 2 end subscript text  is end text

    Given graph gives variation of fraction numerator P V over denominator T end fraction with P for 1gm of oxygen at two different temperatures T1 and T2. If density of oxygen 1.427 k g divided by m to the power of 3 end exponent. The value of fraction numerator P V over denominator T end fraction at point A and relation b divided by w T subscript 1 end subscript & T subscript 2 end subscript text  is end text

    physics-General
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    biology

    Legume plants are important for crop production because they :

    Legume plants are important for crop production because they :

    biologyGeneral
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    maths-

    K equals sin invisible function application open parentheses pi over 18 close parentheses sin invisible function application open parentheses fraction numerator 5 pi over denominator 18 end fraction close parentheses sin invisible function application open parentheses fraction numerator 7 pi over denominator 18 end fraction close parentheses not stretchy rightwards double arrow K equals

    K equals sin invisible function application open parentheses pi over 18 close parentheses sin invisible function application open parentheses fraction numerator 5 pi over denominator 18 end fraction close parentheses sin invisible function application open parentheses fraction numerator 7 pi over denominator 18 end fraction close parentheses not stretchy rightwards double arrow K equals

    maths-General
    General
    physics-

    For a certain mass of a gas Isothermal relation between ‘P’ and ‘V’ are shown by the graphs at two different temperatures T1 and T2 then

    For a certain mass of a gas Isothermal relation between ‘P’ and ‘V’ are shown by the graphs at two different temperatures T1 and T2 then

    physics-General
    General
    maths-

    If the chord through the points whose eccentric angles are alpha and beta 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 plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction =1 passes through the focus (ae, 0), then the value of tan fraction numerator alpha over denominator 2 end fraction tan fraction numerator beta over denominator 2 end fraction = 0 is –

    If the chord through the points whose eccentric angles are alpha and beta 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 plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction =1 passes through the focus (ae, 0), then the value of tan fraction numerator alpha over denominator 2 end fraction tan fraction numerator beta over denominator 2 end fraction = 0 is –

    maths-General
    General
    maths-

    The limiting value of (cos x)1/sin x as x → 0 is :

    The limiting value of (cos x)1/sin x as x → 0 is :

    maths-General
    General
    maths-

    stack l i m with x rightwards arrow negative 2 below fraction numerator sin to the power of negative 1 end exponent invisible function application left parenthesis x plus 2 right parenthesis over denominator x to the power of 2 end exponent plus 2 x end fraction is equal to:

    stack l i m with x rightwards arrow negative 2 below fraction numerator sin to the power of negative 1 end exponent invisible function application left parenthesis x plus 2 right parenthesis over denominator x to the power of 2 end exponent plus 2 x end fraction is equal to:

    maths-General
    General
    maths-

    sin invisible function application A plus sin invisible function application B equals square root of 3 left parenthesis cos invisible function application B minus cos invisible function application A right parenthesis not stretchy rightwards double arrow sin invisible function application 3 A plus sin invisible function application 3 B equals

    sin invisible function application A plus sin invisible function application B equals square root of 3 left parenthesis cos invisible function application B minus cos invisible function application A right parenthesis not stretchy rightwards double arrow sin invisible function application 3 A plus sin invisible function application 3 B equals

    maths-General
    General
    physics-

    Given m subscript A end subscript equals 30 text end text k g comma text end text m subscript B end subscript equals 10 text end text k g comma text end text m subscript C end subscript equals 20 text end text k g. The coefficient of friction between A and B mu subscript 1 end subscript = 0.3, between B and C mu subscript 2 end subscript = 0.2 and between C, and ground, mu subscript 3 end subscript = 0.1. The least horizontal force F to start motion of any part of the system of three blocks resting upon one another as shown in figure is ( g = 10 m divided by s to the power of 2 end exponent )

    Given m subscript A end subscript equals 30 text end text k g comma text end text m subscript B end subscript equals 10 text end text k g comma text end text m subscript C end subscript equals 20 text end text k g. The coefficient of friction between A and B mu subscript 1 end subscript = 0.3, between B and C mu subscript 2 end subscript = 0.2 and between C, and ground, mu subscript 3 end subscript = 0.1. The least horizontal force F to start motion of any part of the system of three blocks resting upon one another as shown in figure is ( g = 10 m divided by s to the power of 2 end exponent )

    physics-General
    General
    physics-

    For the system shown in the figure, the acceleration of the mass m4 immediately after the lower thread x is cut will be, (assume that the threads are weightless and inextensible, the spring are weightless, the mass of pulley is negligible and there is no friction)

    For the system shown in the figure, the acceleration of the mass m4 immediately after the lower thread x is cut will be, (assume that the threads are weightless and inextensible, the spring are weightless, the mass of pulley is negligible and there is no friction)

    physics-General
    General
    physics-

    Three blocks A , B and C of equal mass m are placed one over the other on a smooth horizontal ground as shown in figure. Coefficient of friction between any two blocks of A,B and C is fraction numerator 1 over denominator 2 end fraction The maximum value of mass of block D so that the blocks A, B and C move without slipping over each other is

    Three blocks A , B and C of equal mass m are placed one over the other on a smooth horizontal ground as shown in figure. Coefficient of friction between any two blocks of A,B and C is fraction numerator 1 over denominator 2 end fraction The maximum value of mass of block D so that the blocks A, B and C move without slipping over each other is

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    physics-

    A block A is placed over a long rough plank B of same mass as shown in figure. The plank is placed over a smooth horizontal surface. At time t=0, block A is given a velocity v0 in horizontal direction. Let v subscript 1 end subscript and v subscript 2 end subscriptbe the velocities of A and B at time t. Then choose the correct graph between v subscript 1 end subscript or v subscript 2 end subscript and t

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    physics-General
    General
    physics-

    In figure shown, both blocks are released from rest. The time to cross each other 

    In figure shown, both blocks are released from rest. The time to cross each other 

    physics-General