AP EAPCET 2026 May 13 Shift 2 Engineering Question Paper with Solution PDF

If \( A \) and \( B \) are both \( 3 \times 3 \) matrices, then which of the following statements are true?

(i) \( AB = 0 \Rightarrow A = 0 \) or \( B = 0 \)

(ii) \( AB = I_3 \Rightarrow A^{-1} = B \)

(iii) \( (A - B)^2 = A^2 - 2AB + B^2 \)

• (A) (i) is false and (ii), (iii) are true
• (B) (ii) is true (i), (iii) are false
• (C) (i) and (ii) are true, (iii) is false
• (D) All are true

Let \( A = \begin{bmatrix} 1 & 2
2 & 1 \end{bmatrix} \) and \( B = \begin{bmatrix} x & y
1 & 2 \end{bmatrix} \) be two matrices such that \( (A + B)(A - B) = A^2 - B^2 \).
If \( C = \begin{bmatrix} x & 2
1 & y \end{bmatrix} \), then trace \((C) = \)

• (A) \( 3 \)
• (B) \( 5 \)
• (C) \( 7 \)
• (D) \( 9 \)

If \[ A=\begin{bmatrix}3 & 4
5 & 6\end{bmatrix} \quad and \quad B=\begin{bmatrix}x & 0
0 & y\end{bmatrix}, \]
where \(x,y \in \mathbb{N}\), then:

If the system of equations \[ 2x+3y-3z=3, \qquad x+2y+\alpha z=1, \qquad 2x-y+z=\beta \]
has infinitely many solutions, then \[ \frac{\alpha}{\beta}-\frac{\beta}{\alpha} = \]

• (A) \(\dfrac{53}{14}\)
• (B) \(\dfrac{45}{14}\)
• (C) \(-\dfrac{53}{14}\)
• (D) \(-\dfrac{45}{14}\)

The positive value of \(a\) for which the system of linear homogeneous equations \[ x+ay+z=0, \qquad ax+2y-z=0, \qquad 2x+3y+z=0 \]
has non-trivial solution is

• (A) \(0\)
• (B) \(1\)
• (C) \(\dfrac{1+\sqrt{5}}{2}\)
• (D) \(\dfrac{\sqrt{5}-1}{2}\)

Escape velocity on a planet is \(10\ km/s\). If the radius remains same but the mass becomes \(4\) times, the new escape velocity is:

• (A) \(10\ km/s\)
• (B) \(20\ km/s\)
• (C) \(5\ km/s\)
• (D) \(40\ km/s\)

At what depth inside Earth does \(g\) become half of its surface value? (Earth radius \(=R\))

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

A mass \( m \) is taken from Earth's surface to infinity. Work done is:

• (A) \( +\frac{GMm}{R} \)
• (B) \( -\frac{GMm}{R} \)
• (C) \( 0 \)
• (D) \( \frac{GMm}{2R} \)

A wire of length \( 2 \) m and area \( 1 \times 10^{-6} \, m^2 \) stretches by \( 1 \) mm under force \( 200 \) N. Young's modulus is:

• (A) \( 2 \times 10^{11} \, Pa \)
• (B) \( 4 \times 10^{11} \, Pa \)
• (C) \( 1 \times 10^{11} \, Pa \)
• (D) \( 5 \times 10^{10} \, Pa \)

A wire is stretched by \( 2 \) mm under force \( 100 \) N. Elastic energy stored is:

• (A) \( 0.05 \) J
• (B) \( 0.1 \) J
• (C) \( 0.2 \) J
• (D) \( 0.01 \) J

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

• (A) Ununennium
• (B) Unnilennium
• (C) Unununium
• (D) ununoctium

Consider the following:

a) 0.0025

b) 500.0

c) 2.0034

Number of significant figures in A, B and C respectively are

• (A) 5, 4, 4
• (B) 2, 4, 2
• (C) 4, 3, 2
• (D) 2, 4, 5

Identify the correct set of molecules with zero dipole moment.

• (A) \(\mathrm{CO_2,\ NH_3,\ H_2O}\)
• (B) \(\mathrm{NH_3,\ NF_3,\ BF_3}\)
• (C) \(\mathrm{PF_3,\ NH_3,\ CH_4}\)
• (D) \(\mathrm{CH_4,\ BF_3,\ CO_2}\)

Calculate the amount of \( CO_2 \) gas produced, when \( 32 \)g of \( CH_4 \) is burned with sufficient amount of oxygen (Given atomic weight of \( C=12, O=16 \) and \( H=1 \))

• (A) \( 132 \)g
• (B) \( 44 \)g
• (C) \( 88 \)g
• (D) \( 176 \)g

Which of the following pairs of gases contains the same number of molecules?

• (A) \(11\,g of CO_2 and 7\,g of N_2\)
• (B) \(44\,g of CO_2 and 14\,g of N_2\)
• (C) \(22\,g of CO_2 and 28\,g of N_2\)
• (D) All the above pairs of gases