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An arc lamp requires a direct current of 10 A and 80 V to function. If it is connected to a 220 V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to :

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A diode detector is used to detect an amplitude modulated wave of 60% modulation by using a condenser of capacity 250 pico farad in parallel with a load resistance 100 kilo ohm. Find the maximum modulated frequency which could be detected by it.

If g is the inverse of a function f and $f_{_{′}}(x)=1+x_{5}1 $then g(x) is equal to

If the number of terms in the expansion of $(1−x2 +x_{2}4 )_{n},x=0,$is 28, then the sum of the coefficients of all the terms in this expansion, is :

The sum of coefficients of integral powers of x in the binomial expansion of $(1−2x )_{50}$ is:

This question has Statement I and Statement II. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement - I : A point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as \displaystyle{f{{(}}}

If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is :

A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1 %. What is the fundamental frequency of steel if density and elasticity of steel are $7.7×10_{3}kg/m_{3}and2.2×10_{11}N/m_{2}$ respectively?

A projectile is given an initial velocity of $(i^+2j^ )m/s,$ where $i^$ is along the ground and $j^ $ is along the vertical. If $g=10m/s_{2},$ the equation of its trajectory is: