MHT CET 2025 April 26 Shift 2 Question Paper (Available): Download Question Paper (PCM) with Answers PDF

Given the vectors: \[ \mathbf{a} = i + 3j - k, \quad \mathbf{b} = 3i - j + 2k, \quad \mathbf{c} = i + 2j - 2k \]
and the following information: \[ \frac{\mathbf{a} \cdot \mathbf{c}}{|\mathbf{c}|} = \frac{10}{3} \]
Find the value of \( \alpha + \beta \) and the projection of \( \mathbf{a} \) on \( \mathbf{c} \).

• (A) \( \alpha + \beta = 30^\circ \), Projection of \( \mathbf{a} \) on \( \mathbf{c} = 5 \)
• (B) \( \alpha + \beta = 45^\circ \), Projection of \( \mathbf{a} \) on \( \mathbf{c} = 4 \)
• (C) \( \alpha + \beta = 60^\circ \), Projection of \( \mathbf{a} \) on \( \mathbf{c} = 6 \)
• (D) \( \alpha + \beta = 90^\circ \), Projection of \( \mathbf{a} \) on \( \mathbf{c} = 7 \)

A medicine compound having an amide linkage was asked.
Which of the following compounds contains an amide linkage?

• (A) Acetanilide
• (B) Aspirin
• (C) Benzene
• (D) Acetic acid

Which is the weakest ligand?

• (A) \( F^- \)
• (B) EDTA
• (C) en
• (D) CO

What is the product obtained on the reaction of chlorobenzene with concentrated HNO3?

• (A) Para nitro chloro benzene
• (B) Ortho nitro chloro benzene
• (C) Mixture of ortho and para nitro benzene

Find the radius of a BCC molecule having an edge length of \( 2.0 \times 10^{-11} \) m.

• (A) \( 1.0 \times 10^{-11} \) m
• (B) \( 1.5 \times 10^{-11} \) m
• (C) \( 2.0 \times 10^{-11} \) m
• (D) \( 3.0 \times 10^{-11} \) m

Which of the following elements shows a +4 oxidation state with the given configuration?

• (A) Ce
• (B) Tb
• (C) Eu
• (D) Lu

Given the formula for depression of freezing point: \[ \Delta T_f = K_f \cdot m \]
where \( \Delta T_f \) is the depression of freezing point, \( K_f \) is the freezing point depression constant, and \( m \) is the molality, calculate the value of \( m \).

• (A) \( m = \frac{\Delta T_f}{K_f} \)
• (B) \( m = \frac{K_f}{\Delta T_f} \)
• (C) \( m = K_f \cdot \Delta T_f \)
• (D) \( m = \frac{\Delta T_f}{K_f^2} \)

What is the number of unpaired electrons in Lutetium (Lu) in the +3 oxidation state?

• (A) 0
• (B) 1
• (C) 2
• (D) 3

Total pressure of the solution is 500, the partial pressure of component A is 400, and the partial pressure of component B is 575. What is the mole fraction of component B?

• (A) 0.5
• (B) 0.6
• (C) 0.8
• (D) 0.9

Which of the following elements has the most electronegativity: Li, Na, K, or Rb?

• (A) Li
• (B) Na
• (C) K
• (D) Rb

Which of the following has the lowest boiling point?

• (A) Butanol
• (B) Propanol
• (C) Ethanol
• (D) Methanol