The $pK_a$ values of four carboxylic acids are $4.76, 4.19, 0.23$,and $3.41$ respectively. The $pK_a$ value of the strongest carboxylic acid among them is

The solution of $\tan y \frac{dy}{dx} = \sin(x+y) + \sin(x-y)$ is

The first diffraction minimum due to a single slit diffraction is seen at $\theta = 30^o$ for light of wavelength $5000 \, \mathring{A}$ falling perpendicularly on the slit. The width of the slit is

If $\sqrt{\frac{y}{x}}+\sqrt{\frac{x}{y}}=2$,then $\frac{d y}{d x}$ is equal to

Which genotype represents a true dihybrid condition?

Choose the incorrect statement from the following:
$S1:$ The efficiency of a heat engine can be $1$,but the coefficient of performance of a refrigerator can never be infinity.
$S2:$ The first law of thermodynamics is basically the principle of conservation of energy.
$S3:$ The second law of thermodynamics does not allow several phenomena consistent with the first law.
$S4:$ $A$ process,whose only result is to transfer heat from a colder to a hotter object,is impossible.