MHT CET 2025 21 April Shift 1 Question Paper (Available): Download Question Paper (PCM) with Answers PDF

If \( a(4 + x^2) = x + y - x^3 = a^3 \frac{dy}{dx} \) at \( x = 1 \), then the value of \( \frac{dy}{dx} \) is:

• (A) 5
• (B) 4
• (C) 3
• (D) 2

Evaluate the definite integral: \[ \int_{0}^{\frac{\pi}{2}} \frac{dx}{1 + (\cot x)^{101}} = ? \]

• (A) \( \frac{\pi}{4} \)
• (B) \( \frac{\pi}{2} \)
• (C) \( \frac{1}{2} \)
• (D) 1

For all real \( x \), the minimum value of the function \( f(x) = \frac{1 - x + x^2}{1 + x + x^2} \) is:

• (A) \( \frac{1}{3} \)
• (B) \( 0 \)
• (C) \( 3 \)
• (D) \( 1 \)

If \( a(u + x^2) = x \) and \( y - x^3 = a^2 \), then \( \frac{dy}{dx} \) at \( x = 1 \) is:

Approximate value of \( \cos 59^\circ \) is:

• (A) \( 0.50 \)
• (B) \( 0.61 \)
• (C) \( 0.75 \)
• (D) \( 0.85 \)

Evaluate the integral: \( \int \log((2 + x)^{2 + x}) \, dx \)

• (A) \( (2 + x)^{2 + x} + C \)
• (B) \( (2 + x) \log((2 + x)^{2 + x}) + C \)
• (C) \( (2 + x) \cdot (2 + x)^{x} + C \)
• (D) \( (2 + x)(2 + x)^{x} (\log(2 + x) + 1) + C \)

If \( x^y + y^x = a^b \), then \( \frac{dy}{dx} \) at \( x = 1, y = 2 \) is:

• (A) \( -1 \)
• (B) \( 1 \)
• (C) \( 2 \)
• (D) \( \frac{1}{2} \)

What is the correct order of thermal stability of the following carbonates?

BaCO\(_3\), MgCO\(_3\), SrCO\(_3\), CaCO\(_3\)

• (A) MgCO\(_3\) \(<\) CaCO\(_3\) \(<\) SrCO\(_3\) \(<\) BaCO\(_3\)
• (B) BaCO\(_3\) \(<\) SrCO\(_3\) \(<\) CaCO\(_3\) \(<\) MgCO\(_3\)
• (C) BaCO\(_3\) \(>\) MgCO\(_3\) \(>\) SrCO\(_3\) \(>\) CaCO\(_3\)
• (D) MgCO\(_3\) \(>\) CaCO\(_3\) \(>\) SrCO\(_3\) \(>\) BaCO\(_3\)

Which of the following plots gives a straight line for a zero-order reaction?

• (A) \([A] \, vs \, t\)
• (B) \(\log[A] \, vs \, t\)
• (C) \(1/[A] \, vs \, t\)
• (D) \(\ln[A] \, vs \, t\)

For a first-order reaction, the slope of the graph between \(\log[A]\) vs time is equal to:

• (A) \(-\frac{k}{2.303}\)
• (B) \(k\)
• (C) \(2.303k\)
• (D) \(-2.303k\)

The magnetic moment of \( Mn^{3+} \) is:

• (A) \(1.73 \, BM \)
• (B) \(2.83 \, BM \)
• (C) \(4.90 \, BM \)
• (D) \(5.92 \, BM \)

Which trend is correct regarding ionic radius in the 4f-series (lanthanides)?

• (A) Radius increases from La\(^{3+}\) to Lu\(^{3+}\)
• (B) Radius remains same
• (C) Radius decreases across the series
• (D) No regular trend observed

Which of the following d-block elements has the highest melting point?

• (A) Zn
• (B) Fe
• (C) Cr
• (D) W

At a given temperature, which of the following statements is correct regarding the solubility of a solid in a liquid?

• (A) It always increases with increase in temperature.
• (B) It always decreases with increase in temperature.
• (C) It may increase or decrease depending on the enthalpy change.
• (D) It does not depend on temperature.

Which of the following is a primary alcohol?

• (A) CH\(_3\)CH\(_2\)CH\(_2\)OH
• (B) (CH\(_3\))\(_2\)CHOH
• (C) (CH\(_3\))\(_3\)COH
• (D) None of these

Which of the following monomers undergo addition polymerization?

• (A) Ethene
• (B) Acetic acid
• (C) Glucose
• (D) Glycerol

Which of the following is the polymer formed from acrylonitrile?

• (A) Polyvinyl chloride (PVC)
• (B) Polyacrylonitrile (PAN)
• (C) Teflon
• (D) Nylon-6

Thermal stability order of Group 1 hydroxides is:

• (A) LiOH \(<\) NaOH \(<\) KOH \(<\) RbOH \(<\) CsOH
• (B) CsOH \(<\) RbOH \(<\) KOH \(<\) NaOH \(<\) LiOH
• (C) LiOH \(>\) NaOH \(>\) KOH \(>\) RbOH \(>\) CsOH
• (D) LiOH = NaOH = KOH = CsOH

Which of the following is not a transition metal?

• (A) Zn
• (B) Fe
• (C) Cr
• (D) Cu