AP EAPCET 2026 May 12 Shift 2 Engineering Question Paper with Solution PDF

If \(x\) and \(y\) be the distances of the object and images formed by a concave mirror from its focus and \(f\) be the focal length then:

• (A) \(xf = y^2\)
• (B) \(xy = f^2\)
• (C) \(\frac{x}{y} = f\)
• (D) \(\frac{x}{y} = f^2\)

A particle is executing SHM of amplitude \(4 cm\) and time period \(4 s\). The time taken by it to move from positive extreme position to half the amplitude is

• (A) \(1 s\)
• (B) \(\frac{1}{3} s\)
• (C) \(\frac{2}{3} s\)
• (D) \(\sqrt{\frac{2}{3}} s\)

The masses of two particles having same kinetic energies are in the ratio \(2 : 1\). Then their de Broglie wavelengths are in the ratio.

• (A) \(2:1\)
• (B) \(1:2\)
• (C) \(\sqrt{2}:1\)
• (D) \(1:\sqrt{2}\)

The coordinates of a particle moving in x-y plane at any instant of time \(t\) is \(x = 4t^2\); \(y = 3t^2\). The speed of the particle at that instant is:

• (A) \(10 t\)
• (B) \(5 t\)
• (C) \(3 t\)
• (D) \(2 t\)

A thin metal disc of radius \(r\) floats on water surface and bends the surface downwards along the perimeter making an angle \(\theta\) with vertical edge of the disc. If the disc displaces a weight of water \(W\) and surface tension of water is \(T\), then the weight of metal disc is

• (A) \(2\pi r T + W\)
• (B) \(2\pi r \cos\theta - W\)
• (C) \(2\pi r T \cos\theta + W\)
• (D) \(W - 2\pi r T \cos\theta\)

If \(I = \int \frac{\sin x + \sin^3 x}{\cos 2x} dx = P \cos x + Q \log \left| \frac{\sqrt{2} \cos x - 1}{\sqrt{2} \cos x + 1} \right|\) (where \(c\) is a constant of integration), then values of \(P\) and \(Q\) are respectively

• (A) \(\frac{1}{2}\), \(\frac{3}{4\sqrt{2}}\)
• (B) \(\frac{1}{2}\), \(\frac{-3}{4\sqrt{2}}\)
• (C) \(\frac{1}{2}\), \(\frac{3}{2\sqrt{2}}\)
• (D) \(\frac{1}{2}\), \(\frac{-3}{2\sqrt{2}}\)

In a triangle \(\triangle ABC\), if \(a, b,\) and \(c\) are in arithmetic progression, then \(\cos A + 2 \cos B + \cos C =\)

• (A) \(1\)
• (B) \(2\)
• (C) \(3/2\)
• (D) \(\sqrt{3} + 1\)

If the area of triangle \(ABC\) is \(b^2 - (c - a)^2\), then \(\tan B =\)

• (A) \(1\)
• (B) \(13/15\)
• (C) \(1/4\)
• (D) \(8/15\)

In a \(\triangle ABC\), \(a = 1, b = \sqrt{3}\) and \(\angle C = \frac{\pi}{6}\). Then the measure of the third side \(c =\)

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

The value of
\[ \lim_{n \to \infty} \left\{ \frac{1}{n+m} + \frac{1}{n+2m} + \frac{1}{n+3m} + \dots + \frac{1}{n+nm} \right\} \]

is:

• (A) \(\dfrac{\log_e(m)}{m}\)
• (B) \(\dfrac{\log_e(1+m)}{1+m}\)
• (C) \(\dfrac{\log_e(1+m)}{m}\)
• (D) \(\dfrac{\log_e(1+m)}{1-m}\)

Consider the equilibrium reactions:

\[ H_3PO_4 \rightleftharpoons[K_1]{} H^+ + H_2PO_4^- \]

\[ H_2PO_4^- \rightleftharpoons[K_2]{} H^+ + HPO_4^{2-} \]

\[ HPO_4^{2-} \rightleftharpoons[K_3]{} H^+ + PO_4^{3-} \]

The equilibrium constant, \(K_c\), for the overall dissociation

\[ H_3PO_4 3H^+ + PO_4^{3-} \]

is:

• (A) \( \dfrac{K_1}{K_2K_3} \)
• (B) \( K_1K_2K_3 \)
• (C) \( \dfrac{K_2}{K_1K_3} \)
• (D) \( K_1 + K_2 + K_3 \)

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) \( CH_4, BF_3, CO_2 \)

Which of the following sets are correctly matched?

• (a) I and II
• (b) II and III
• (c) III and IV
• (d) I and IV

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

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

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) \( CH_4, BF_3, CO_2 \)