BITSAT 2026 May 24 Shift 2 Question Paper: Download Answer Key with Solutions PDF

Two capillary tubes of radii \(r_1\) and \(r_2\) \((r_1 > r_2)\) are dipped vertically in the same liquid. The rise of liquid in the tubes \(h_1\) and \(h_2\) satisfies:

• (A) \(h_1 > h_2\)
• (B) \(h_1 < h_2\)
• (C) \(h_1 = h_2\)
• (D) \(h_1 r_2 = h_2 r_1\)

An ideal gas heat engine operates in a Carnot cycle between \(227^°C\) and \(127^°C\). It absorbs \(6 \times 10^4 cal\) of heat at the higher temperature. The amount of heat converted into work is:

• (A) \(1.2 \times 10^4 cal\)
• (B) \(4.8 \times 10^4 cal\)
• (C) \(2.4 \times 10^4 cal\)
• (D) \(6.0 \times 10^3 cal\)

The root mean square (rms) speed of the molecules of an ideal gas at a given temperature \(T\) is \(v\). If the temperature is increased to \(4T\) and the gas dissociates into atoms, the new rms speed becomes:

• (A) \(v\)
• (B) \(2v\)
• (C) \(4v\)
• (D) \(2\sqrt{2}\,v\)

A fundamental harmonic standing wave is generated in a string fixed at both ends. If the tension in the string is increased by \(21%\), the percentage change in the fundamental frequency will be:

• (A) \(10%\)
• (B) \(21%\)
• (C) \(11%\)
• (D) \(10.5%\)

Ionisation energy of H-atom is \(13.6 eV\). The wavelength of the spectral line emitted when an electron in \(Be^{3+}\) comes from \(5^{th}\) energy level to \(2^{nd}\) energy level is:

• (A) \(43.5 nm\)
• (B) \(4350 nm\)
• (C) \(4.35 nm\)
• (D) \(435 nm\)

\(10 g\) each of \(CH_4\) and \(O_2\) are kept in cylinders of same volume under same temperature, give the pressure ratio of two gases:

• (A) \(3 : 4\)
• (B) \(2 : 3\)
• (C) \(1 : 4\)
• (D) \(2 : 1\)

In a cyclic \(pV\) process forming a square loop from \((p = 1 atm, V = 2L)\) to \((p = 3 atm, V = 4L)\), then, the net heat absorbed by the gas is:

• (A) \(2L \cdot atm\)
• (B) \(4L \cdot atm\)
• (C) \(8L \cdot atm\)
• (D) \(6L \cdot atm\)

The temperature in K at which \(\Delta G = 0\), for a given reaction with \(\Delta H = -20.5 kJ mol^{-1}\) and \(\Delta S = -50.0 J K^{-1} mol^{-1}\) is:

• (A) \(-410\)
• (B) \(410\)
• (C) \(2.44\)
• (D) \(-2.44\)

The value of \(\lim_{n \rightarrow \infty} \prod_{r=3}^{n} \frac{r^3 - 8}{r^3 + 8}\) equals to:

• (A) \(2/7\)
• (B) \(3/7\)
• (C) \(4/7\)
• (D) \(6/7\)

The point of inflexion for the curve \(y = (x - a)^n\), where \(n\) is an odd integer and \(n \ge 3\) is:

• (A) \((a, 0)\)
• (B) \((0, a)\)
• (C) \((0, 0)\)
• (D) None of these

If \(y^x = e^{y - x}\), then \(\frac{dy}{dx}\) is equal to:

• (A) \(\frac{1 + \log y}{y \log y}\)
• (B) \(\frac{(1 + \log y)^2}{y \log y}\)
• (C) \(\frac{1 + \log y}{(\log y)^2}\)
• (D) \(\frac{(1 + \log y)^2}{\log y}\)

The domain of the function \(f(x) = \sqrt{x - \sqrt{1 - x^2}}\) is:

• (A) \[ \left[-1,\,-\frac{1}{\sqrt{2}}\right] \cup \left[\frac{1}{\sqrt{2}},\,1\right] \]
• (B) \[ \left[-1,\,1\right] \]
• (C) \[ \left(-\infty,\,-\frac{1}{\sqrt{2}}\right] \cup \left[\frac{1}{\sqrt{2}},\,+\infty\right] \]
• (D) \[ \left[\frac{1}{\sqrt{2}},\,1\right] \]