MHT CET 2026 May 21 Shift 2 PCM Question Paper- Download PDF with Solutions

MHT CET 2026 May 21 Shift 2 PCM Question Paper is available for download here. Maharashtra State CET Cell conducted MHT CET 2026 PCM Exam on May 21 in Shift 2 from 2 PM to 5 PM in CBT mode.

The MHT CET 2026 PCM Question Paper consists of 150 multiple-choice questions (MCQs) totalling 200 marks divided into 3 sections: Physics, Chemistry, and Mathematics, with 50 questions in each subject.
Physics and Chemistry questions carry 1 mark each while Mathematics questions carry 2 marks each.
There is no negative marking for incorrect answers.

Download MHT CET 2026 May 21 Shift 2 PCM Question Paper with Solutions PDF from the links provided below.

MHT CET 2026 May 21 Shift 2 PCM Question Paper PDF Download

MHT CET 2026 May 21 Shift 2 Question Paper	Download PDF	Check Solution

Question 1:

If
y = y(x)
satisfies the differential equation \[ \left(\frac{2+\sin x}{1+y}\right)\frac{dy}{dx}=-\cos x \]
and \( y(0)=2 \), then \( y\left(\frac{\pi}{2}\right) \) is equal to:

(1) \(3\)
(2) \(4\)
(3) \(2\)
(4) \(1\)

View Solution

Question 2:

The ratio of areas bounded by the curves \[ y=\cos x \]
and \[ y=\cos 2x \]
between \[ x=0,\qquad x=\frac{\pi}{3} \]
and the \(x\)-axis is:

(A) \(2:1\)
(B) \(1:2\)
(C) \(1:1\)
(D) \(1:3\)

View Solution

Question 3:

If \[ (2+\sin x)\frac{dy}{dx}+(y+1)\cos x=0 \]
and \[ y(0)=1, \]
then find the value of \[ y\left(\frac{\pi}{2}\right). \]

(A) \(-\frac23\)
(B) \(-\frac13\)
(C) \(\frac43\)
(D) \(\frac13\)

View Solution

Question 4:

If \[ \left(\frac{2+\sin x}{1+y}\right)\frac{dy}{dx}=-\cos x \]
and \[ y(0)=2, \]
then find the value of \[ y\left(\frac{\pi}{2}\right). \]

(1) \(3\)
(2) \(4\)
(3) \(2\)
(4) \(1\)

View Solution

Question 5:

If \[ (2+\sin x)\frac{dy}{dx}+(y+1)\cos x=0 \]
and \( y(0)=1 \), then \( y\left(\frac{\pi}{2}\right) \) is equal to:

(1) \( -\dfrac{2}{3} \)
(2) \( -\dfrac{1}{3} \)
(3) \( \dfrac{4}{3} \)
(4) \( \dfrac{1}{3} \)

View Solution

Question 6:

Solve for \(x\): \[ x+\log_{15}(5+3^x)=x\log_{15}5+\log_{15}24 \]

(1) \(2\)
(2) \(1\)
(3) \(5\)
(4) \(8\)

View Solution

Question 7:

For \(n\in\mathbb{N}\), if \[ y=ax^{n+1}+bx^{-n}, \]
then \[ x^2\frac{d^2y}{dx^2} \]
is equal to:

(1) \((n-1)y\)
(2) \(n(n-1)y\)
(3) \(n(n+1)y\)
(4) \((n+1)y\)

View Solution

Question 8:

Solve for \(x\): \[ x+\log_{15}(5+3^x)=x\log_{15}5+\log_{15}24 \]

(A) \(2\)
(B) \(1\)
(C) \(5\)
(D) \(8\)

View Solution

Question 9:

For \(n\in\mathbb{N}\), if \[ y=ax^{n+1}+bx^{-n}, \]
then \[ x^2\frac{d^2y}{dx^2} \]
is equal to:

(1) \((n-1)y\)
(2) \(n(n-1)y\)
(3) \(n(n+1)y\)
(4) \((n+1)y\)

View Solution

Question 10:

Let \[ f(x)=\int_{1}^{4}\log[x]\ dx, \]
where \([x]\) denotes the greatest integer function. Then the value of \(f(x)\) is:

(A) \(\log 2\)
(B) \(\log 3\)
(C) \(\log 5\)
(D) \(\log 6\)

View Solution

MHT CET PCM Exam Pattern 2026

Parameter	Details
Conducting Body	Maharashtra Common Entrance Test Cell (Maharashtra CET Cell)
Exam Mode	Online (Computer-Based Test)
Duration	180 minutes (3 hours)
Groups / Subjects	PCM (Physics, Chemistry, Mathematics) for Engineering
Total Questions	150
Total Marks	200
Question Type	Multiple Choice Questions (MCQs)
Marks Distribution	Mathematics – 2 marks/question Physics and Chemistry – 1 mark/question
Negative Marking	No
Syllabus Weightage	Class 12 – 80% Class 11 – 20%

MHT-CET 2026 Paper Analysis

MHT CET Questions

1.
If \[ (2+\sin x)\frac{dy}{dx}+(y+1)\cos x=0 \] and \( y(0)=1 \), then \( y\left(\frac{\pi}{2}\right) \) is equal to:

\( -\dfrac{2}{3} \)
\( -\dfrac{1}{3} \)
\( \dfrac{4}{3} \)
\( \dfrac{1}{3} \)

View Solution

2.
Let \[ \vec a=\hat i+\hat j+\hat k \] \[ \vec b=\hat i-\hat j+2\hat k \] If a vector \( \vec c \) is coplanar with \( \vec a \) and \( \vec b \) such that \[ \vec c\cdot \vec a=1 \] and \[ \vec c\cdot \vec b=2 \] then \( \vec c \) is:

\( \dfrac13(-\hat i+5\hat j+3\hat k) \)
\( \dfrac13(5\hat i-\hat j+3\hat k) \)
\( \hat i-\hat j+\hat k \)
\( \dfrac12(\hat j+\hat k) \)

View Solution

3.
Let \[ f(x)=\int_{1}^{4}\log[x]\ dx, \] where \([x]\) denotes the greatest integer function. Then the value of \(f(x)\) is:

\(\log 2\)
\(\log 3\)
\(\log 5\)
\(\log 6\)

View Solution

4.
The ratio of areas bounded by the curves \[ y=\cos x \] and \[ y=\cos 2x \] between \[ x=0,\qquad x=\frac{\pi}{3} \] and the \(x\)-axis is:

\(2:1\)
\(1:2\)
\(1:1\)
\(1:3\)

View Solution

5.
Which of the following is a soft metal?

Iron
Sodium
Aluminium
Copper

View Solution

6.
Solve for \(x\): \[ x+\log_{15}(5+3^x)=x\log_{15}5+\log_{15}24 \]

\(2\)
\(1\)
\(5\)
\(8\)

View Solution

MHT CET 2026 May 21 Shift 2 PCM Question Paper- Download PDF with Solutions

MHT CET 2026 May 21 Shift 2 PCM Question Paper PDF Download

MHT CET PCM Exam Pattern 2026

MHT-CET 2026 Paper Analysis

MHT CET Questions

1.
If \[ (2+\sin x)\frac{dy}{dx}+(y+1)\cos x=0 \] and \( y(0)=1 \), then \( y\left(\frac{\pi}{2}\right) \) is equal to:

2.
Let \[ \vec a=\hat i+\hat j+\hat k \] \[ \vec b=\hat i-\hat j+2\hat k \] If a vector \( \vec c \) is coplanar with \( \vec a \) and \( \vec b \) such that \[ \vec c\cdot \vec a=1 \] and \[ \vec c\cdot \vec b=2 \] then \( \vec c \) is:

3.
Let \[ f(x)=\int_{1}^{4}\log[x]\ dx, \] where \([x]\) denotes the greatest integer function. Then the value of \(f(x)\) is:

4.
The ratio of areas bounded by the curves \[ y=\cos x \] and \[ y=\cos 2x \] between \[ x=0,\qquad x=\frac{\pi}{3} \] and the \(x\)-axis is:

5.
Which of the following is a soft metal?

6.
Solve for \(x\): \[ x+\log_{15}(5+3^x)=x\log_{15}5+\log_{15}24 \]

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MHT CET 2026 May 21 Shift 2 PCM Question Paper PDF Download

MHT CET PCM Exam Pattern 2026

MHT-CET 2026 Paper Analysis

MHT CET Questions

1.If \[ (2+\sin x)\frac{dy}{dx}+(y+1)\cos x=0 \] and \( y(0)=1 \), then \( y\left(\frac{\pi}{2}\right) \) is equal to:

2.Let \[ \vec a=\hat i+\hat j+\hat k \] \[ \vec b=\hat i-\hat j+2\hat k \] If a vector \( \vec c \) is coplanar with \( \vec a \) and \( \vec b \) such that \[ \vec c\cdot \vec a=1 \] and \[ \vec c\cdot \vec b=2 \] then \( \vec c \) is:

3.Let \[ f(x)=\int_{1}^{4}\log[x]\ dx, \] where \([x]\) denotes the greatest integer function. Then the value of \(f(x)\) is:

4.The ratio of areas bounded by the curves \[ y=\cos x \] and \[ y=\cos 2x \] between \[ x=0,\qquad x=\frac{\pi}{3} \] and the \(x\)-axis is:

5.Which of the following is a soft metal?

6.Solve for \(x\): \[ x+\log_{15}(5+3^x)=x\log_{15}5+\log_{15}24 \]

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1.
If \[ (2+\sin x)\frac{dy}{dx}+(y+1)\cos x=0 \] and \( y(0)=1 \), then \( y\left(\frac{\pi}{2}\right) \) is equal to:

2.
Let \[ \vec a=\hat i+\hat j+\hat k \] \[ \vec b=\hat i-\hat j+2\hat k \] If a vector \( \vec c \) is coplanar with \( \vec a \) and \( \vec b \) such that \[ \vec c\cdot \vec a=1 \] and \[ \vec c\cdot \vec b=2 \] then \( \vec c \) is:

3.
Let \[ f(x)=\int_{1}^{4}\log[x]\ dx, \] where \([x]\) denotes the greatest integer function. Then the value of \(f(x)\) is:

4.
The ratio of areas bounded by the curves \[ y=\cos x \] and \[ y=\cos 2x \] between \[ x=0,\qquad x=\frac{\pi}{3} \] and the \(x\)-axis is:

5.
Which of the following is a soft metal?

6.
Solve for \(x\): \[ x+\log_{15}(5+3^x)=x\log_{15}5+\log_{15}24 \]