TS EAMCET 2026 May 10 Shift 2 Engineering Question Paper with Solution PDF

If \( \omega \) is a complex cube root of unity, then \[ \cos\left(\left(\omega^{1234} + \omega^{2021}\right)\pi - \frac{\pi}{4}\right) = \]

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

If the system of equations \[ x + y + z = 1,\quad x + 2y + 4z = K,\quad x + 4y + 10z = K^2 \]
is consistent, then \(K =\)

• (A) \(1, -2\)
• (B) \(-1, 2\)
• (C) \(1, 2\)
• (D) \(-1, -2\)

If 2 and 3 are the two roots of the equation \[ 2x^3 + mx^2 - 13x + n = 0, \]
then the values of \(m, n\) are respectively

• (A) \(-5, 30\)
• (B) \(5, -30\)
• (C) \(-5, -30\)
• (D) \(5, 30\)

If \( -1 + i \) is a root of the equation \( x^4 + 4x^3 + 5x^2 + 2x - 2 = 0 \), then the real roots of this equation are

• (A) \( -1 \pm \sqrt{3} \)
• (B) \( -1 \pm \sqrt{2} \)
• (C) \( \sqrt{2} \pm 3 \)
• (D) \( \sqrt{3} \pm \sqrt{2} \)

\( T_m \) denotes the number of triangles that can be formed with the vertices of a regular polygon of \( m \) sides. If \( T_{m+1} - T_m = 15 \), then \( m = \)

• (A) \( 3 \)
• (B) \( 6 \)
• (C) \( 9 \)
• (D) \( 12 \)

A car is moving with velocity V at the top of a semi-circular hill of radius 40 m such that the normal force on it is zero. Find the velocity (V) of the car. [use \( g = 10 \, ms^{-2} \)]

• (A) \( 10 \, m/s \)
• (B) \( 15 \, m/s \)
• (C) \( 20 \, m/s \)
• (D) \( 25 \, m/s \)

If the average terminal velocity of rain drop is 2 ms\(^{-1}\), then the energy transferred by rain to each square meter of the surface at a place which receives 100 cm of rain in a year is

• (A) \( 1 \times 10^4 \, J \)
• (B) \( 1 \times 10^3 \, J \)
• (C) \( 2 \times 10^3 \, J \)
• (D) \( 2 \times 10^4 \, J \)

A particle executes simple harmonic motion according to the equation \( x(t) = A \sin^2(\alpha t) \). If the time period of the S.H.M is 0.2 s, then the value of \( \alpha \) (in units of rad/s) is:

• (A) \( 2\pi \)
• (B) \( 10\pi \)
• (C) \( 5\pi \)
• (D) \( 2.5\pi \)

Consider a series of measurements of the length of a box in an experiment. The readings are 2.4m, 2.5m, 2.6m, 2.8m, 3.0m. What would be the relative error?

• (A) \( 0.110 \)
• (B) \( 0.089 \)
• (C) \( 0.079 \)
• (D) \( 0.072 \)

The volume of a material reduces by 2% when the pressure is increased from 1 atm to 2 atm. What is its bulk modulus?

• (A) \( 10^5 \, N/m^2 \)
• (B) \( 5 \times 10^5 \, N/m^2 \)
• (C) \( 10^6 \, N/m^2 \)
• (D) \( 5 \times 10^6 \, N/m^2 \)

A balloon filled with an air sample occupies 3 L volume at 35 °C. On lowering the temperature to T, the volume decreases to 2.5 L. The temperature T is [Assume P constant]

• (A) \( 25.67 \, ^\circ C \)
• (B) \( 29.17 \, ^\circ C \)
• (C) \( -16.33 \, ^\circ C \)
• (D) \( -20.55 \, ^\circ C \)

The order of the average bond length of the given bonds is

• (A) \( C = O < C = N < C = C < N - O \)
• (B) \( C = C < C = O < C = N < N - O \)
• (C) \( C = C < C = O < N - O < C = N \)
• (D) \( C = N < C = O < N - O < C = C \)

The volume of a material reduces by 2% when the pressure is increased from 1 atm to 2 atm. What is its bulk modulus?

• (A) \( 10^5 \, N/m^2 \)
• (B) \( 5 \times 10^5 \, N/m^2 \)
• (C) \( 10^6 \, N/m^2 \)
• (D) \( 5 \times 10^6 \, N/m^2 \)

Which of the following is not a periodic property?

• (A) Atomic size
• (B) Electron affinity
• (C) Radioactivity
• (D) Ionisation potential

The number of radial nodes in 3s and 2p orbitals, respectively are

• (A) \( 2 : 2 \)
• (B) \( 2 : 0 \)
• (C) \( 0 : 0 \)
• (D) \( 3 : 2 \)