MHT CET 2024 3 May Shift 2 question paper is available here for Download. The paper comprises 150 MCQs carrying a total weightage of 200 marks.

MHT CET 2024 3 May Shift 2 Question Paper for PCM is divided into three subjects- Physics, Chemistry and Mathematics with 50 questions for each section (10 questions from Class 11 and 40 questions from Class 12th syllabus).

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MHT CET 2024 3 May Shift 2 Question Paper PDF Download

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MHT CET 2024 3 May Shift 2 Question Paper Solution

Question 1:

If y = sec(tan⁻¹ x), then dy/dx at x = 1 is:

  1. 1/2
  2. 1
  3. 1/√2
  4. 2
Correct Answer: (3) 1/√2.
View Solution

Step 1: Let y = sec(tan⁻¹ x).

Let θ = tan⁻¹(x), so tan(θ) = x.

Step 2: Differentiate y.

We know sec²(θ) = 1 + tan²(θ) = 1 + x², so sec(θ) = √(1 + x²).

Thus, y = √(1 + x²).

Step 3: Differentiate with respect to x:

dy/dx = (1/2√(1 + x²)) × 2x = x/√(1 + x²).

Step 4: Evaluate at x = 1:

dy/dx = 1/√(1 + 1²) = 1/√2.

Question 2:

If y = loge [e3x × ((x - 4)/(x + 3))3/2], then find dy/dx:

  1. 3 + 21 / [2(x - 4)(x + 3)]
  2. 3 + 21 / [(x - 4)(x + 3)]
  3. 3 + 21 / [2(x + 3)(x - 4)]
  4. 3 + 7 / [(x - 4)(x + 3)]
View Solution

Question 3:

Find the differential equation of the family of all circles, whose center lies on the x-axis and touches the y-axis at the origin.

  1. 2xy dy/dx = y^2 - x^2
  2. 2xy dy/dx = x^2 - y^2
  3. x^2 + y^2 = 2xy dy/dx
  4. x^2 + y^2 = 2y dy/dx
View Solution

Question 4:

If f(x) = 3x + 6, g(x) = 4x + k, and f ∘ g(x) = g ∘ f(x), then find k:

  1. 3
  2. 6
  3. 9
  4. 12
View Solution

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