AP EAPCET 2026 May 12 Shift 1 Engineering Question Paper Available- Download Solution PDF

Let \( f(x) = \int \frac{\sqrt{x}}{(1+x)^2}\, dx \;\; (x \geq 0) \). Then \( f(3) - f(1) \) is equal to:

• (A) \( -\dfrac{\pi}{12} + \dfrac{1}{2} + \dfrac{\sqrt{3}}{4} \)
• (B) \( \dfrac{\pi}{12} + \dfrac{1}{2} - \dfrac{\sqrt{3}}{4} \)
• (C) \( -\dfrac{\pi}{6} + \dfrac{1}{2} + \dfrac{\sqrt{3}}{4} \)
• (D) \( \dfrac{\pi}{6} + \dfrac{1}{2} - \dfrac{\sqrt{3}}{4} \)

Gas is being pumped into a spherical balloon at the rate of \( 30\, \text{ft}^3/\text{min} \). Then the rate at which the radius increases when it reaches the value \( 15\, \text{ft} \) is:

• (A) \( \dfrac{1}{30\pi}\, \text{ft/min} \)
• (B) \( \dfrac{1}{15\pi}\, \text{ft/min} \)
• (C) \( \dfrac{1}{20\pi}\, \text{ft/min} \)
• (D) \( \dfrac{1}{25\pi}\, \text{ft/min} \)

Let the function \( f(x) \) be defined as \( f(x) = \dfrac{x - |x|}{x} \), then:

• (A) the function is continuous everywhere
• (B) the function is not continuous
• (C) the function is continuous when \( x < 0 \)
• (D) the function is continuous for all \( x \) except zero

If the direction ratios of two lines are given by \( l + m + n = 0 \) and \( mn - 2ln + lm = 0 \), then the angle between the lines is:

• (A) \( \dfrac{\pi}{4} \)
• (B) \( \dfrac{\pi}{3} \)
• (C) \( \dfrac{\pi}{2} \)
• (D) \( 0 \)

The equation of the normal to the curve \( y = \log_e x \) at the point \( P(1,0) \) is ____.

• (A) \( 2x + y = 2 \)
• (B) \( x - 2y = 1 \)
• (C) \( x - y = 1 \)
• (D) \( x + y = 1 \)

The radius of the hydrogen atom in the ground state is \(0.53\) Å. The radius of \(Li^{2+}\) ion (atomic number \(= 3\)) in a similar state is:

• (a) \(0.53\) Å
• (b) \(1.06\) Å
• (c) \(0.17\) Å
• (d) \(0.265\) Å

The energy of the second Bohr orbit of the hydrogen atom is \(-328\, \text{kJ mol}^{-1}\); hence the energy of the fourth Bohr orbit would be:

• (a) \(-41\, \text{kJ/mol}\)
• (b) \(-82\, \text{kJ/mol}\)
• (c) \(-164\, \text{kJ/mol}\)
• (d) \(-1312\, \text{kJ/mol}\)

The IUPAC name of an element with atomic number 119 is:

• (a) Ununennium
• (b) Unnilennium
• (c) Unununium
• (d) Ununoctium

Which of the following orders is not correct for the given property?

• (a) \( Li < Na < K \) — metallic radius
• (b) \( Br < F < Cl \) — electron gain enthalpy
• (c) \( C < N < O \) — first ionisation enthalpy
• (d) \( Mg^{2+} < Na^{+} < F^{-} \) — ionic radius

Identify the correct set of molecules with zero dipole moment:

• (a) \( CO_2,\, NH_3,\, H_2O \)
• (b) \( NH_3,\, NF_3,\, BF_3 \)
• (c) \( PF_3,\, NH_3,\, CH_4 \)
• (d) \( CH_4,\, BF_3,\, CO_2 \)

The potential energy of a simple harmonic oscillator when the particle is half way to its end point is (where \( E \) is the total energy):

• (A) \( \dfrac{2}{3}E \)
• (B) \( \dfrac{1}{8}E \)
• (C) \( \dfrac{1}{4}E \)
• (D) \( \dfrac{1}{2}E \)

A current loop of magnetic moment \( 0.5\, \text{Am}^2 \) is placed in a magnetic field of \( 0.4\, \text{T} \). If the loop is rotated from an angle of \( 0^\circ \) to \( 180^\circ \), what is the change in potential energy?

• (A) \( -0.4\, \text{J} \)
• (B) \( 0.4\, \text{J} \)
• (C) \( -0.2\, \text{J} \)
• (D) \( 0.2\, \text{J} \)

Twenty seven drops of the same size are charged at \(220\, \text{V}\) each. They combine to form a bigger drop. Calculate the potential of the bigger drop.

• (A) \(1320\, \text{V}\)
• (B) \(1520\, \text{V}\)
• (C) \(1980\, \text{V}\)
• (D) \(660\, \text{V}\)

Two polaroids are oriented with their principal planes making an angle of \(60^\circ\). Then the percentage of incident unpolarized light which passes through the system is:

• (A) \(100\%\)
• (B) \(50\%\)
• (C) \(12.5\%\)
• (D) \(37.5\%\)

The equation of path of a projectile moving in the x-y plane is given by \( y = x - \dfrac{x^2}{25} \), then the initial speed and maximum height of the particle will be (take \( g = 10\, \text{m/s}^2 \)):

• (A) \( 4\sqrt{10}\, \text{m/s} \) and \( \dfrac{29}{4}\, \text{m} \)
• (B) \( 25\sqrt{10}\, \text{m/s} \) and \( \dfrac{21}{4}\, \text{m} \)
• (C) \( 2\sqrt{10}\, \text{m/s} \) and \( \dfrac{31}{4}\, \text{m} \)
• (D) \( 5\sqrt{10}\, \text{m/s} \) and \( \dfrac{25}{4}\, \text{m} \)