AP EAPCET (AP EAMCET) 2025 Question Paper May 23 Shift 1(Available): Download Solutions with Answer Key

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Shivam Yadav

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The AP EAPCET 2025 Engineering Exam for the May 23rd shift 1 was conducted from 9:00 A.M. to 12:00 P.M. in a CBT Mode in 117+ examination centres in Andhra Pradesh and Telangana, conducted by JNTU on behalf of APSCHE.

In the AP EAPCET 2025 Engineering question paper, candidates will have to attempt 160 MCQs, including 80 questions from mathematics and 40 each from physics and chemistry, with 1 mark for each correct answer and without any negative marking.

AP EAPCET 2025 Question Paper with Answer Key PDF May 23 Shift 1

AP EAPCET 2025 May 23 Shift 1 Question Paper with Answer Key Download Check Solution
AP EAPCET 2025 Question Paper May 23 Shift 1 Download MPC Question Paper With Answer Key PDF

Question 1:

If \( f(x) = 2x^3 - 3x^2 + 4 \), then the minimum value of \( f(x) \) in the interval \( [0, 3] \) is:


Question 2:

If \( z \) is a complex number such that \( |z| = 5 \) and \( Re(z) = 3 \), then the value of \( z^2 \) is:

  • (A) \( 9 + 40i \)
  • (B) \( 9 - 40i \)
  • (C) 25
  • (D) \( -7 + 24i \)

Question 3:

Let a circle pass through the point \( (1, 2) \) and touch the \( x \)-axis at \( (3, 0) \). Then the equation of the circle is:

  • (A) \( (x - 3)^2 + (y - 4)^2 = 16 \)
  • (B) \( (x - 3)^2 + y^2 = 16 \)
  • (C) \( (x - 3)^2 + (y - 2)^2 = 4 \)
  • (D) \( (x - 3)^2 + (y - 1)^2 = 1 \)

Question 4:

If \( \tan A + \tan B + \tan C = \tan A \tan B \tan C \) and \( A + B + C = \pi \), then which of the following is true?

  • (A) One of the angles is \( \frac{\pi}{2} \)
  • (B) All angles are equal
  • (C) \( \tan A = \tan B = \tan C \)
  • (D) \( A = B = \frac{\pi}{4} \)

Question 5:

If \( \vec{a} = 2\hat{i} - \hat{j} + 3\hat{k} \), \( \vec{b} = \hat{i} + 2\hat{j} - \hat{k} \), then the angle \( \theta \) between \( \vec{a} \) and \( \vec{b} \) is:


Question 6:

Let \( A = \begin{bmatrix} 1 & 2
3 & 4 \end{bmatrix} \), then \( A^2 - 5A + 6I = ? \)

  • (A) \( \begin{bmatrix} -1 & 0
    0 & -1 \end{bmatrix} \)
  • (B) \( \begin{bmatrix} 8 & 0
    0 & 8 \end{bmatrix} \)
  • (C) \( \begin{bmatrix} 1 & 1
    1 & 1 \end{bmatrix} \)
  • (D) \( \begin{bmatrix} 2 & 0
    0 & 2 \end{bmatrix} \)

Question 7:

Two numbers are selected at random (without replacement) from the first 50 natural numbers. The probability that their sum is even is:

  • (A) \( \frac{24}{50} \)
  • (B) \( \frac{24}{29} \)
  • (C) \( \frac{26}{49} \)
  • (D) \( \frac{1}{2} \)

Question 8:

Let \( f(x) = 2x^3 - 3x \neq 4 \). Then the inverse function \( f^{-1}(x) \) is:


Question 9:

A solid sphere of mass \( M \) and radius \( R \) is rolling without slipping with speed \( v \). Its total kinetic energy is:

  • (A) \( \frac{1}{2} M v^2 \)
  • (B) \( \frac{7}{10} M v^2 \)
  • (C) \( \frac{3}{10} M v^2 \)
  • (D) \( \frac{9}{10} M v^2 \)

Question 10:

A Carnot engine operates between \( 500 \, K \) and \( 300 \, K \). If it absorbs \( 1000 \, J \) of heat from the source, the amount of work done by the engine is:

  • (A) \( 400 \, J \)
  • (B) \( 600 \, J \)
  • (C) \( 200 \, J \)
  • (D) \( 500 \, J \)

Question 11:

A charged particle of mass \( m \) and charge \( q \) moves with a velocity \( \vec{v} \) perpendicular to a magnetic field \( \vec{B} \). The radius of the circular path it follows is:

  • (A) \( \frac{qB}{mv} \)
  • (B) \( \frac{qv}{mB} \)
  • (C) \( \frac{mv}{qB} \)
  • (D) \( \frac{mB}{qv} \)

Question 12:

A pipe closed at one end and open at the other resonates at a fundamental frequency of 340 Hz. If the speed of sound in air is 340 m/s, the length of the pipe is:

  • (A) 0.25 m
  • (B) 0.50 m
  • (C) 1.00 m
  • (D) 2.00 m

Question 13:

In a potentiometer experiment, a cell of emf 1.5 V gives a balance point at 75 cm. If the cell is replaced by another cell and the balance point is at 60 cm, the emf of the second cell is:

  • (A) 1.2 V
  • (B) 1.0 V
  • (C) 1.8 V
  • (D) 2.0 V

Question 14:

For a first-order reaction, the rate constant \( k \) is \( 1.386 \times 10^{-3} \, s^{-1} \). What is the half-life \( t_{1/2} \) of the reaction? (Use \( \ln 2 = 0.693 \))

  • (A) 300 s
  • (B) 500 s
  • (C) 200 s
  • (D) 1000 s

Question 15:

Calculate the molality of a solution prepared by dissolving 10 g of NaCl (\( M = 58.5 \, g/mol \)) in 500 g of water:

  • (A) 0.171 mol/kg
  • (B) 0.342 mol/kg
  • (C) 0.017 mol/kg
  • (D) 0.34 mol/kg

Question 16:

In a redox titration, 25 mL of 0.1 M KMnO\(_4\) is required to completely react with oxalic acid in acidic medium. The volume of 0.2 M oxalic acid used is:

(Balanced reaction: \( 2MnO_4^- + 5C_2O_4^{2-} + 16H^+ \rightarrow 2Mn^{2+} + 10CO_2 + 8H_2O \))

  • (A) 25 mL
  • (B) 31.25 mL
  • (C) 12.5 mL
  • (D) 62.5 mL

Question 17:

Calculate the volume occupied by 4.4 g of CO\(_2\) gas at 27°C and 1 atm pressure. (\( R = 0.0821 \, L-atm/mol-K \), Molar mass of CO\(_2\) = 44 g/mol)

  • (A) 2.46 L
  • (B) 1.68 L
  • (C) 4.48 L
  • (D) 5.6 L

Question 18:

For the reaction \( N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) \) at 298 K, the enthalpy change \( \Delta H = -92.4 \, kJ/mol \). What happens to the equilibrium when temperature is increased?

  • (A) Shifts to the right
  • (B) Shifts to the left
  • (C) Remains unchanged
  • (D) Pressure increases

AP EAPCET 2025 Topic-Wise Weightage

The AP EAPCET 2025 Engineering (MPC) Exam will be of 160 questions for all three sections (Mathematics – 80 questions, Physics – 40 questions, and Chemistry – 40 questions).

For candidates to prepare with a strategy, knowing the topic-wise weightage of the last few years provides a good idea of key and recurring areas.

Mathematics – Topic-Wise Weightage (80 Questions)

Topic Expected No. of Questions
Algebra 15–18
Calculus 10–12
Coordinate Geometry 8–10
Trigonometry 6–8
Probability & Statistics 6–8
Vector Algebra 5–6
Complex Numbers & Theory of Equations 5–6
Matrices & Determinants 4–5

Physics – Topic-Wise Weightage (40 Questions)

Topic Expected No. of Questions
Laws of Motion & Work, Power, Energy 5–6
Thermodynamics & Kinetic Theory 4–5
Current Electricity & Magnetism 4–5
Oscillations & Waves 3–4
Ray & Wave Optics 3–4
Units, Dimensions & Errors 2–3
Modern Physics & Nuclei 2–3
Motion in a Plane/Projectile Motion 2–3

Chemistry – Topic-Wise Weightage (40 Questions)

Topic Expected No. of Questions
Organic Chemistry (General & Named Reactions) 8–10
Thermodynamics & Thermochemistry 4–5
Chemical Bonding & Molecular Structure 4–5
Coordination Compounds 3–4
Equilibrium (Ionic + Chemical) 3–4
Periodic Table & Periodicity 2–3
s, p, d, f-Block Elements 3–4
Surface Chemistry & Solutions 2–3

AP EAPCET 2025 May 23 Shift 1 – Expected Paper Analysis

The AP EAPCET 2025 Engineering Examination for May 23rd, Shift 1 will be conducted from 9:00 AM to 12:00 PM in CBT mode at over 117 test centres in Andhra Pradesh and Telangana.

Conducted by JNTU Kakinada on behalf of APSCHE, the exam will consist of a total of 160 questions, with 80 from Mathematics, 40 from Physics, and 40 from Chemistry.

Subject Expected Difficulty Important Topics Remarks
Mathematics Moderate to Difficult
  • Algebra
  • Calculus
  • Coordinate Geometry
It is expected to be Time-consuming and requires speed & accuracy
Physics Moderate
  • Laws of Motion
  • Current Electricity
  • Thermodynamics
This section will be more concept-based with a mix of theory and numericals
Chemistry Easy to Moderate
  • Organic Chemistry
  • Chemical Bonding
  • Thermodynamics
This Section will be Mostly NCERT-based and scoring

AP EAPCET Questions

  • 1.
    If \(\alpha\) is the angle made by the perpendicular drawn from origin to the line \(12x - 5y + 13 = 0\) with the positive X-axis in anti-clockwise direction, then \(\alpha =\)

      • \(\operatorname{Tan}^{-1} \frac{5}{12} \)
      • \(2\pi - \operatorname{Tan}^{-1} \frac{5}{12} \)
      • \(\pi - \operatorname{Tan}^{-1} \frac{5}{12} \)
      • \(\pi + \operatorname{Tan}^{-1} \frac{5}{12} \)

    • 2.
      The number of ways of dividing 15 persons into 3 groups containing 3, 5 and 7 persons so that two particular persons are not included into the 5 persons group is

        • $\frac{117(11!)}{3!(7!)}$
        • ${15 \choose 5} {10 \choose 3}$
        • $90 \times \frac{13!}{7!}$
        • ${15 \choose 5} {8 \choose 3}$

      • 3.
        If the line $$ 4x - 3y + 7 = 0 $$ touches the circle $$ x^2 + y^2 - 6x + 4y - 12 = 0 $$ at $ (\alpha, \beta) $, then find $ \alpha + 2\beta $.

          • 3
          • -1
          • 1
          • -3

        • 4.
          Three blocks A, B and C are arranged as shown in the figure such that the distance between two successive blocks is 10 m. Block A is displaced towards block B by 2 m and block C is displaced towards block B by 3 m. The distance through which the block B should be moved so that the centre of mass of the system does not change is
          Three blocks A, B and C are arranged as shown in the figure

            • 1.4 m, towards block C
            • 1.5 m, towards block A
            • 2 m, towards block A
            • 1 m, towards block C

          • 5.
            Which of the following enzymatic reaction is not correctly matched with enzyme shown against it in brackets?

              • Proteins → Peptides (Pepsin)
              • Starch → Maltose (Zymase)
              • Sucrose → Glucose and fructose (Invertase)
              • Maltose → Glucose (Maltase)

            • 6.
              The domain and range of a real valued function \( f(x) = \cos (x-3) \) are respectively.

                • \(\mathbb{R} \setminus \{0\}\) and \([-1, 1]\)
                • \(\mathbb{R} \setminus \{0\}\) మరియు \([-1, 1]\)
                • \(\mathbb{R} \setminus \{0\}\) and \([-4, -2]\)
                • \(\mathbb{R}\) and \([-4, -2]\)
                  \(\mathbb{R}\) మరియు \([-4, -2]\)

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              CategoriesState
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