AP EAMCET 2024 previous year paper practice · PYQ-pattern set

AP EAMCET 2024 PYQ-pattern questions

Showing 10 of the 13 PYQ-pattern questions in this set — freshly worded in that year's pattern, not the original questions. Answers and solutions open under each question.

1. Q1 · Hyperbolic Functions

   If cosh x = 5/3, then the value of sinh x (x > 0) is

   • A. 3/4
   • B. 4/3
   • C. 5/4
   • D. 7/3
   Answer and solution

   Answer: B

   Using cosh²x - sinh²x = 1, we get (5/3)² - sinh²x = 1 ⇒ 25/9 - sinh²x = 1 ⇒ sinh²x = 16/9. Since x > 0, sinh x > 0, so sinh x = 4/3.

2. Q2 · Straight Lines

   The equation of the line passing through the point (2, 3) and perpendicular to the line 3x - 4y + 7 = 0 is

   • A. 4x + 3y = 17
   • B. 3x + 4y = 18
   • C. 4x - 3y = -1
   • D. 3x - 4y = -6
   Answer and solution

   Answer: A

   Slope of given line = 3/4. Perpendicular slope = -4/3. Equation: y - 3 = (-4/3)(x - 2) → 3y - 9 = -4x + 8 → 4x + 3y = 17.

3. Q3 · Parabola

   The length of the latus rectum of the parabola y² + 6y - 4x + 13 = 0 is

   • A. 2
   • B. 4
   • C. 6
   • D. 8
   Answer and solution

   Answer: B

   Converting to standard form: (y+3)² = 4(x-1), comparing with (y-k)² = 4a(x-h), we get 4a = 4, so the length of latus rectum is 4.

4. Q4 · Physical World

   Which of the following is NOT a fundamental force in nature?

   • A. Gravitational force
   • B. Electromagnetic force
   • C. Frictional force
   • D. Weak nuclear force
   Answer and solution

   Answer: C

   Friction is a macroscopic manifestation of electromagnetic forces between atoms at surfaces, not a fundamental force.

5. Q5 · Motion in a Plane

   A projectile is launched at an angle of 30° with the horizontal with a velocity of 40 m/s. What is the maximum height attained by the projectile? (Take g = 10 m/s²)

   • A. 20 m
   • B. 40 m
   • C. 60 m
   • D. 80 m
   Answer and solution

   Answer: A

   Maximum height H = u²sin²θ/(2g) = (40)²(sin30°)²/(2×10) = 1600×0.25/20 = 20 m.

6. Q6 · Gravitation

   The acceleration due to gravity on the surface of Earth is 10 m/s². What will be the acceleration due to gravity at a height equal to the radius of Earth above its surface?

   • A. 2.5 m/s²
   • B. 5.0 m/s²
   • C. 7.5 m/s²
   • D. 10 m/s²
   Answer and solution

   Answer: A

   At height h = R, g' = g/(1 + h/R)² = g/(1 + 1)² = g/4 = 10/4 = 2.5 m/s².

7. Q7 · Wave Optics

   In Young's double slit experiment, the slits are separated by 0.5 mm and the screen is placed 1 m away. If light of wavelength 600 nm is used, the distance between the 4th bright fringe on one side and the 3rd dark fringe on the other side of the central maximum is

   • A. 7.8 mm
   • B. 9.0 mm
   • C. 10.2 mm
   • D. 11.4 mm
   Answer and solution

   Answer: A

   Fringe width β = λD/d = (600e-9×1)/(0.5e-3) = 1.2 mm. 4th bright fringe = 4β = 4.8 mm. 3rd dark fringe = 2.5β = 3.0 mm. On opposite sides, total distance = 4.8 + 3.0 = 7.8 mm.

8. Q8 · Current Electricity

   A wire of resistance 12 Ω is stretched uniformly to double its original length. What is the new resistance of the wire?

   • A. 24 Ω
   • B. 36 Ω
   • C. 48 Ω
   • D. 60 Ω
   Answer and solution

   Answer: C

   When a wire is stretched to double its length, its volume remains constant, so the cross-sectional area halves. Since R = ρL/A, if L becomes 2L and A becomes A/2, the new resistance is R' = ρ(2L)/(A/2) = 4R = 48 Ω.

9. Q9 · Electromagnetic Waves

   An electromagnetic wave has a frequency of 6 × 10¹⁴ Hz. What is its wavelength in vacuum? (Speed of light c = 3 × 10⁸ m/s)

   • A. 500 nm
   • B. 600 nm
   • C. 700 nm
   • D. 800 nm
   Answer and solution

   Answer: A

   Wavelength λ = c/f = (3×10⁸)/(6×10¹⁴) = 5×10⁻⁷ m = 500 nm.

10. Q10 · Nuclei

    A radioactive substance has a half-life of 30 minutes. What fraction of the initial sample will remain undecayed after 90 minutes?

    • A. 1/4
    • B. 1/8
    • C. 1/16
    • D. 1/2
    Answer and solution

    Answer: B

    Number of half-lives = 90/30 = 3. Remaining fraction = (1/2)³ = 1/8.