If $y$ is a function of $x$ and $\log(x+y)=2xy$,then the value of $y'(0)$ is

$A$ conducting ring is placed around the core of an electromagnet as shown in the figure. When key $K$ is pressed,the ring

The main objective of the production/use of herbicide-resistant $GM$ crops is to

Consider the following statements $A$ and $B$ and identify the correct answer:
$A$. When a person walks on a rough surface, the direction of the frictional force exerted by the surface on the person is in the direction of his motion.
$B$. When a cycle is in motion, the force of friction exerted by the ground on the front wheel is in the backward direction.

If $A_i$ $(i=1, 2, 3, \ldots, n)$ are $n$ independent events with $P(A_i) = \frac{1}{1+i}$ for each $i$, then the probability that none of $A_i$ occurs is

$P, Q, R$ and $S$ are four points with the position vectors $3i - 4j + 5k, 2i - j + 4k, -4i + 5j + k$ and $-3i + 4j + 3k$, respectively. Then, the line $PQ$ meets the line $RS$ at the point