HSC Science (General) 11th Standard - Maharashtra State Board Question Bank Solutions

Answer the following :

A wire of length 10 cm is bent so as to form an arc of a circle of radius 4 cm. What is the angle subtended at the centre in degree ?

Show that the minute-hand of clock gains 5°30' on the hour-hand in one minute.

Answer the following :

A train is running on a circular track of radius 1 km at the rate of 36 km per hour. Find the angle, to the nearest minute, through which it will turn in 30 seconds.

Answer the following:

Find the

1. lengths of the principal axes
2. co-ordinates of the foci
3. equations of directrices
4. length of the latus rectum
5. distance between foci
6. distance between directrices of the ellipse:

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

Find the

1. lengths of the principal axes.
2. co-ordinates of the focii
3. equations of directrics
4. length of the latus rectum
5. distance between focii
6. distance between directrices of the ellipse:

3x² + 4y² = 12

Find the

1. lengths of the principal axes.
2. co-ordinates of the focii 
3. equations of directrics 
4. length of the latus rectum
5. distance between focii 
6. distance between directrices of the ellipse:

2x² + 6y² = 6

Find the 

1. lengths of the principal axes. 
2. co-ordinates of the focii 
3. equations of directrices 
4. length of the latus rectum
5. distance between focii 
6. distance between directrices of the ellipse:

3x² + 4y² = 1

Find the equation of the ellipse in standard form if eccentricity = `3/8` and distance between its foci = 6

Find the equation of the ellipse in standard form if the distance between directrix is 18 and eccentricity is `1/3`.

Find the equation of the ellipse in standard form if the minor axis is 16 and eccentricity is `1/3`.

Find the equation of the ellipse in standard form if the distance between foci is 6 and the distance between directrix is `50/3`.

Find the equation of the ellipse in standard form if the latus rectum has length of 6 and foci are (±2, 0).

Find the equation of the ellipse in standard form if passing through the points (−3, 1) and (2, −2)

Find the equation of the ellipse in standard form if the dist. between its directrix is 10 and which passes through `(-sqrt(5), 2)`.

Find the equation of the ellipse in standard form if eccentricity is `2/3` and passes through `(2, −5/3)`.

Find the eccentricity of an ellipse, if the length of its latus rectum is one-third of its minor axis.

Find the eccentricity of an ellipse if the distance between its directrix is three times the distance between its foci

Show that the product of the lengths of the perpendicular segments drawn from the foci to any tangent line to the ellipse `x^2/25 + y^2/16` = 1 is equal to 16

A tangent having slope `–1/2` to the ellipse 3x² + 4y² = 12 intersects the X and Y axes in the points A and B respectively. If O is the origin, find the area of the triangle

Show that the line x – y = 5 is a tangent to the ellipse 9x² + 16y² = 144. Find the point of contact