HSC Science (General) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

A pendulum of length 14 cm oscillates through an angle of 18°. Find the length of its path.

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`((22pi)/15)^"c"` is equal to

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156° is equal to

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A horse is tied to a post by a rope. If the horse moves along a circular path, always keeping the rope tight and describes 88 metres when it traces the angle of 72° at the centre, then the length of the rope is

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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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Find the radius of the circle in which central angle of 60° intercepts an arc of length 37.4 cm.

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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.

Prove the following:

`(tan5"A" - tan3"A")/(tan5"A" + tan3"A") = (sin2"A")/(sin8"A")`

Prove the following:

`sin  pi^"c"/8 = 1/2sqrt(2 - sqrt(2))`

Find the value of:

`cos  pi/8`

Prove the following:

`(1 - cos2theta)/(1 + cos2theta)` = tan²θ

Prove the following:

`(cosx + sinx)/(cosx - sinx) - (cosx - sinx)/(cosx + sinx)` = 2tan2x

Prove the following:

`sqrt(2 + sqrt(2 + sqrt(2 + 2cos8x)` = 2 cos x