HSC Arts (English Medium) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions

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A pendulum of 14 cm long oscillates through an angle of 12°, then the angle of the path described by its extremities is

Angle between hand’s of a clock when it shows the time 9.45 is ______.

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20 metres of wire is available for fencing off a flower-bed in the form of a circular sector of radius 5 metres, then the maximum area (in sq. m.) of the flower-bed is

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If the angles of a triangle are in the ratio 1 : 2 : 3, then the smallest angle in radian is ______.

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Find the measure of the angle between hour-hand and the minute hand of a clock at twenty minutes past two. 

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Find the number of sides of a regular polygon, if each of its interior angle is `(3pi^"c")/4`.

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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.

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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.

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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)`.