MHT CET 2024 4 May Shift 2 Question Paper : Download PCM Question Paper with Answers PDF

Question 1:

The variance of the first 50 even natural numbers is:

1. 833
2. (437/4)
3. (833/4)
4. 437

Question 2:

Integrate the function ∫ e^x (1 + sin(x))/(1 + cos(x)) dx:

Question 3:

The solution of the differential equation \( x \cos y \, dy = (x e^x \log x + e^x) \, dx \) is:

Question 4:

Find the expected value and variance of \( X \) for the following p.m.f:

Question 5:

If the statement \( p \leftrightarrow (q \rightarrow p) \) is false, then the true statement is:

1. p
2. p → (p ∨ ~q)
3. p ∧ (~p q)
4. (p ∨ ~q) → p

Question 6:

The statement \( [(p → q) ∧ ~q] → r \) is a tautology when \( r \) is equivalent to:

1. p ∧ ~q
2. q ∨ p
3. p ∧ q
4. ~q

Question 7:

A lot of 100 bulbs contains 10 defective bulbs. Five bulbs are selected at random from the lot and are sent to the retail store. The probability that the store will receive at most one defective bulb is:

1. (7/5)(9/10)⁴
2. (7/5)(9/10)⁵
3. (6/5)(9/10)⁴
4. (6/5)(9/10)⁵