HSC Science (General) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Prove the following:

cos²2x − cos²6x = sin4x sin8x

Prove the following:

cot4x (sin5x + sin3x) = cotx (sin5x − sin3x)

Prove the following:

`sqrt(3)  "cosec"20^circ - sec20^circ` = 4

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

`x^2/25 - y^2/16` = 1

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

`x^2/25 - y^2/16` = – 1

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

16x² – 9y² = 144

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

21x² – 4y² = 84

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

3x² – y² = 4

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

x² – y² = 16

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

`y^2/25 - x^2/9` = 1

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

`y^2/25 - x^2/144` = 1

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

`x^2/100 - y^2/25` = + 1

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

x = 2 sec θ, y = `2sqrt(3) tan theta`

Find the equation of the hyperbola with centre at the origin, length of conjugate axis 10 and one of the foci (–7, 0).

Find the eccentricity of the hyperbola, which is conjugate to the hyperbola x² – 3y² = 3

If e and e' are the eccentricities of a hyperbola and its conjugate hyperbola respectively, prove that `1/"e"^2 + 1/("e""'")^2` = 1

Find the equation of the hyperbola referred to its principal axes:

whose distance between foci is 10 and eccentricity `5/2`

Find the equation of the hyperbola referred to its principal axes:

whose distance between foci is 10 and length of conjugate axis 6

Find the equation of the hyperbola referred to its principal axes:

whose distance between directrices is `8/3` and eccentricity is `3/2`

Find the equation of the hyperbola referred to its principal axes:

whose length of conjugate axis = 12 and passing through (1, – 2)