$A$ block can slide on a smooth inclined plane of inclination $\theta$ kept on the floor of a lift. When the lift is descending with an acceleration $a$,the acceleration of the block relative to the incline is:

$2\,g$ of steam condenses when passed through $40\,g$ of water initially at $25\,^{\circ}C$. The condensation of steam raises the temperature of water to $54.3\,^{\circ}C$. What is the latent heat of steam in $cal/g$?

If $\int f(x) \sin x \cos x \, dx = \frac{1}{2(b^2 - a^2)} \log f(x) + c$, where $c$ is the constant of integration, then $f(x)$ is equal to

$A$ railway line is taken round a circular arc of radius $1000 \ m$,and is banked by raising the outer rail $h \ m$ above the inner rail. If the lateral force on the inner rail when a train travels round the curve at $10 \ ms^{-1}$ is equal to the lateral force on the outer rail when the train's speed is $20 \ ms^{-1}$,the value of $4g \tan \theta$ is equal to: (The distance between the rails is $1.5 \ m$).

$A$ transition metal $M$ forms a volatile chloride with a vapor density of $94.8$. If it contains $74.75\%$ chlorine,what is the formula of the metal chloride?

Monocyclic compounds $\text{P , Q , R}$ and $S$ are the major products formed in the reaction sequences given below.
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The product having the highest number of unsaturated carbon atom$(s)$ is-