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Find the values of the letters and give reasons for the steps involved. \({3}{A}+{25}={B}{2}\)

\({3}{A}+{25}={B}{2}\)

If we add only unit digits, then,

\({A}+{5}={2}\)

Only possible value for \({A}\) is \({7}\).

So, addition is \({37}+{25}={62}\).

So, \({B}={2}\).

If we add only unit digits, then,

\({A}+{5}={2}\)

Only possible value for \({A}\) is \({7}\).

So, addition is \({37}+{25}={62}\).

So, \({B}={2}\).

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A vertical cylinder of height 100cm contians air at a constant temperatur. The top is closed by a frictionless light postpn. The atmospheric pressure pver the piston.

The velocity of a particle is zero at t=0

(A) The accelerationat t=0 must be zero

(B) the acceleration at t=0 maybet zero

(C) If the acceleratin is zero from t=0 to t=10 s, the speed is also zero in this interval.

(D) If the speed is zer4o from t=0 to t=10 s the acceleration is zero in this interval.

(A) The accelerationat t=0 must be zero

(B) the acceleration at t=0 maybet zero

(C) If the acceleratin is zero from t=0 to t=10 s, the speed is also zero in this interval.

(D) If the speed is zer4o from t=0 to t=10 s the acceleration is zero in this interval.

A car of maas M is moving on a horizontal circular path of radius r. At an instant its speed is v and is increasing at a rate a.

(A) The acceleration of the car is towards the centre of the path

(B) The magnitude the frictional force on the car is greater than \(\frac{{{m}{v}^{{2}}}}{{r}}\).

(C) The friction coefficient between the ground and the car is not less than \(\frac{{a}}{{g}}\).

(D) The friction coefficient between the ground and the car is \(\mu=\frac{{{\tan}^{{-{{1}}}}{v}^{{2}}}}{{r}}{g}\)

(A) The acceleration of the car is towards the centre of the path

(B) The magnitude the frictional force on the car is greater than \(\frac{{{m}{v}^{{2}}}}{{r}}\).

(C) The friction coefficient between the ground and the car is not less than \(\frac{{a}}{{g}}\).

(D) The friction coefficient between the ground and the car is \(\mu=\frac{{{\tan}^{{-{{1}}}}{v}^{{2}}}}{{r}}{g}\)

A projectivle is fired form the top of a 40 m hnigh cliff with an initial speed of 50 m/s at an unknown angle. Find its speed when it hits the ground.

One end of a wire 2m long and 0.2 cm^2 in cross section is fixed in a ceilign and a load of 4.8 kg is attached to the free end. Find the extension of the wire. Young modulus of steel \(={2.0}\times{10}^{{11}}{N}{m}^{{-{{2}}}}\). Take \({g}={10}{m}{s}^{{-{{2}}}}\).

The fundamental frequency of a string is proportional to

(A) inverse of its length

(B) the diameter

(C) the tension

(D) the density

(A) inverse of its length

(B) the diameter

(C) the tension

(D) the density

Three resonant frequencies of a string are 90, 150 and 210 Hz. (a) Find the highest possible fundamental frequency of vibration of this string. (b) Which harmonics of the fundamental are the given frequencies ? (c) Which overtones are these frequencies ? (d) If the length of the string is 80 cm, what would be the speed of a transverse wave on this string ?

Assume that each atom in a copper wire contributes one free electron. Estimate the numberof free electrons in a cpper wire having a mass of 6.4g (take the atomic weight of copper ot be 64g \({m}{o}{l}^{{-{1}}}.\)

An inductor coil of resistance \({10}\Omega\) and inductance 120 mH is connected across a battery of emf 6 V and internal resistance \({2}\Omega\). Find the charge which flows through the inductor in (a) 10 ms, (b) 20ms and (c ) 100ms after the connections are made.

A circuit has a resistance of 12 ohm and an impendance of 15 ohm. The power factor of the circuit will be

(A) 0.4

(B) 0.8

(C) 0.125

(D) 1.25

(A) 0.4

(B) 0.8

(C) 0.125

(D) 1.25

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