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Important Questions on Linear Inequalities

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

The number of natural numbers less than

7000

which can be formed by using the digits

0, 1, 3, 7, 9

(repetition of digits allowed) is equal to:

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

For a particle performing linear SHM, its average speed over one oscillation is (

A =

amplitude of S.H.M.,

n =

frequency of oscillation)

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

A particle of mass

m

is moving in a circular path of constant radius

r

such that its centripetal acceleration

a_{c}

is varying with time

t

a_{c} = k^{2} r t^{2}

, where

k

is a constant. The power delivered to the particle by the force acting on it is -

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

Determine the power of an engine required to lift $100000 kg$ of coal per hour from a mine which is $360 m$ deep. ( $g = 10 m / s^{2}$ )

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

The engine of a train has to apply a force of

5000 N

to overcome friction to run at a uniform rate of

90 km / h

. What is the power developed by the engine?

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

A box is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

A family uses

8 kW

of power. Direct solar energy is incident on the horizontal surface at an average rate of

200 W

per square meter. If

20 %

of this energy can be converted to useful electrical energy, how large an area is needed to supply

8 kW

? Compare this area to that of the roof of a typical house.

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

An old man does

200 J

of work in

10 s

and a young man does

100 J

of work in

4 s

. (i) Who is delivering more power? (ii) Find the ratio of the power delivered by the old man to that delivered by the young man.

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

A force

\vec{F} = 2 \hat{i} + 2 \hat{j} N

displaces a particle through

\vec{S} = 2 \hat{i} + 2 \hat{k}

m in 16 s. The power developed by

\vec{F}

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

An engine accelerates a car of mass

800 kg

to a speed of

72 k m h^{- 1}

32

seconds. If the frictional force is

10 N

per ton, the power developed by the engine is

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

A machine gun fires six bullets per second into a target. The mass of each bullet is

3 g

and the speed

500 m s^{- 1}

. The power delivered to the bullets is

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

A boy of mass

40 kg

climbs up stairs of

50

steps, each of

10 cm

high, in

5 s

. Find the power developed by the boy. (

g = 10 m / s^{2}

)

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

An electric pump is used to fill an overhead tank of capacity 9

m^{3}

kept at a height of 10 m above the ground .If the pump takes 5 min to fill the tank by consuming 10 KW .power the efficiency of the pump should be (Take g=10

m s^{- 2}

)

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

An object does

20 J

of work in

5

seconds. What is its power?

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

A car of mass $(m)$ accelerates, starting from rest, while the engine supplies constant power $P$ . Then velocity varies with time $(t)$ as

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

A body is moving uni-directionally under the influence of a source of constant power. Its displacement in time t is proportional to

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

The work done by the heart is

1 J

per beat. Find the power of the heart if it beats

72

times per minute.

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

Two girls A and B each of weight

400 N

, climb up a tree of a height of

8 m

. Girl A takes

20 s

while B takes

50 s

to accomplish this task. What is the power expended by each girl?

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

A car of mass

1000 kg

moves at a constant speed of

20 m s^{- 1}

up an incline. Assume that the frictional force is

200 N

and that where,

θ

is the angle of the incline to the horizontal.

\sin θ = \frac{1}{20}

g = 10 m s^{- 2}

. Find the power developed by the engine

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

Cotyledons are also called-

Which document formally recognizes the importance of equality in India?

Important Questions on Linear Inequalities

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