Choose the incorrect statement from the follo | vedclass

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(A) The efficiency of a heat engine is given by $\eta = 1 - \frac{T_2}{T_1}$.For $\eta = 1$ (i.e.,$100\%$ efficiency),we would require either $T_1 = \

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$S1$

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(A) The efficiency of a heat engine is given by $\eta = 1 - \frac{T_2}{T_1}$.For $\eta = 1$ (i.e.,$100\%$ efficiency),we would require either $T_1 = \infty$ or $T_2 = 0\, K$.Since a source at infinite temperature or a sink at $0\, K$ is physically unattainable,a heat engine cannot have an efficiency of $1$.Thus,the statement in $S1$ claiming that the efficiency of a heat engine can be $1$ is incorrect.$S2$ is correct as the first law is a statement of the conservation of energy.$S3$ is correct because the second law imposes restrictions on processes that the first law does not.$S4$ is a statement of the Clausius form of the second law of thermodynamics,which is correct.

Column-$I$	Column-$II$
$(A)$ Blue-green algae	$(I)$ Spirogyra
$(B)$ Unicellular algae	$(II)$ Nostoc
$(C)$ Filamentous algae	$(III)$ Volvox
$(D)$ Colonial algae	$(IV)$ Chlamydomonas

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Match the following columns:
Column-$I$ Column-$II$
$(A)$ Blue-green algae $(I)$ Spirogyra
$(B)$ Unicellular algae $(II)$ Nostoc
$(C)$ Filamentous algae $(III)$ Volvox
$(D)$ Colonial algae $(IV)$ Chlamydomonas

Let $PQR$ be a right-angled isosceles triangle,with the right angle at $P(2, 1)$. If the equation of the line $QR$ is $2x + y = 3$,then the equation representing the pair of lines $PQ$ and $PR$ is:

The centre of mass of a system of particles does not depend on:

Eight spherical rain drops of the same mass and radius are falling down with a terminal speed of $6 \ cm \ s^{-1}$. If they coalesce to form one big drop,what will be the terminal speed of the bigger drop? (Neglect the buoyancy of the air) ....... $cm \ s^{-1}$

If $\frac{1}{2} \leq x \leq 1$,then $\cos ^{-1} x+\cos ^{-1}\left(\frac{x}{2}+\frac{1}{2} \sqrt{3-3 x^2}\right)$ is equal to

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