A coil having n turns and resistance R ohm is connected with a galvanometer of resistance 4R ohm. This combination is moved in a region where magnetic flux changes from $W_{1} w e b e r t o W_{2}$ weber in t second. The induced current in the circuit is

Q. If

1, w, w^{2}, . . . w^{n - 1}

are the

n^{t h}

roots of unity, then

(1 - w) (1 - w^{2}) . . . (1 - w^{n - 1}) i s

Q. A body of mass

1 kg

begins to move under the action of a time dependent force

\to F = (2 t^i + 3 t^{2}^j) N

. Calculate the instantaneous power developed at time

t

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The weight W of a certain stock of fish is given by W=nw, where n is the size of stock and w is the average weight of a fish. If n and w change with time t as n=2t2+3 and w=t2−t+2, then the rate of change of W with respect to t at t=1 is.

The correct option is D 31(2t2+3)(t2+t+2)=2t4+2t3+4t2+3t2+3t+6W=2t4+2t3+7t2+3t+6HencedWdt=8t3+6t2+14t+3At t=1 we get dWdt at t=1=8+6+14+3=31.

The weight $W$ of a certain stock of fish is given by $W = n w$ , where n is the size of stock and $w$ is the average weight of a fish. If $n$ and $w$ change with time $t$ as $n = 2 t^{2} + 3$ and $w = t^{2} - t + 2$ , then the rate of change of $W$ with respect to $t$ at $t = 1$ is.

The correct option is D $31$
$(2 t^{2} + 3) (t^{2} + t + 2)$
$= 2 t^{4} + 2 t^{3} + 4 t^{2} + 3 t^{2} + 3 t + 6$
$W = 2 t^{4} + 2 t^{3} + 7 t^{2} + 3 t + 6$
Hence
$\frac{d W}{d t}$
$= 8 t^{3} + 6 t^{2} + 14 t + 3$
At $t = 1$ we get
$\frac{d W}{d t}$ at $t = 1$
$= 8 + 6 + 14 + 3$
$= 31$ .