AP ECET 2025 May 6 Shift 1 Question Paper (Available): Download Solutions with Answer Key

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The AP ECET 2025 was conducted on 6th May 2025, by JNTU from 9:00 AM to 12:00 PM in a CBT Mode at multiple centers in Andhra Pradesh.

The AP ECET 2025 Question Paper with Solution PDF is available available for download here.

The AP ECET 2025 Question Paper contains 200 MCQs distributed into sections: Mathematics (50 marks), Physics (25 marks), Chemistry (25 marks), and the core engineering subject (100 marks), as per the candidate's diploma branch.

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AP ECET Previous Year Question Paper

AP ECET 2025 Question Paper with Solution PDF

AP ECET 2025 Shift-1 Question Paper with Answer Key	Download	Check Solution

AP ECET 2025 May 6 Shift 1 Question Paper with Solutions

Question 1:

The coefficient of $ (y-2) $ in the Taylor's series expansion of $ f(x, y) = x^2 + xy + y^2 $ in powers of $ (x-1) $ and $ (y-2) $ is:

(1) 5
(2) 3
(3) 2
(4) 1

Correct Answer: (1) 5
View Solution

Question 2:

The curvature of the straight line $ y = 2x + 3 $ at $ (1, 5) $ is:

(1) 2
(2) 0
(3) $ \frac{1}{2} $
(4) 3

Correct Answer: (2) 0
View Solution

Question 3:

The centre of the circle of curvature for the curve $ y = e^x $ at $ (0, 1) $ is:

(1) $ (2, 3) $
(2) $ (-2, 3) $
(3) $ (2, -3) $
(4) $ (-2, -3) $

Correct Answer: (2) $ (-2, 3) $
View Solution

Question 4:

If $ A = \begin{pmatrix} 2 & x+9
1 & 2x \end{pmatrix} $ is invertible, then $ x \neq $:

(1) 4
(2) 1
(3) 3
(4) 5

Correct Answer: (3) 3
View Solution

Question 5:

The equation of the circle with extremities $ (1, 3) $ and $ (5, 7) $ of the diameter is:

(1) $ x^2 + y^2 + 6x + 10y + 26 = 0 $
(2) $ x^2 + y^2 - 6x - 10y + 26 = 0 $
(3) $ x^2 + y^2 - 6x + 10y + 26 = 0 $
(4) $ x^2 + y^2 - 6x - 10y - 26 = 0 $

Correct Answer: (2) $ x^2 + y^2 - 6x - 10y + 26 = 0 $
View Solution

Question 6:

The integral value of $ \int \frac{\cos 2x}{\sin^2 x \cos^2 x} \, dx = $:

(1) $ \csc^2 x - \sec^2 x + c $
(2) $ \cot x + \tan x + c $
(3) $ -\cot x - \tan x + c $
(4) $ \csc x - \sec x + c $

Correct Answer: (3) $ -\cot x - \tan x + c $
View Solution

AP ECET 2025 Difficulty Level

The AP ECET 2025 examination is conducted to test the conceptual knowledge and problem-solving skills of students of the Diploma and B.Sc (Mathematics) for lateral entry into engineering and pharmacy courses.

As per the previous year's analysis, the difficulty level of the AP ECET 2025 Question Paper is expected to be easy to moderate, with some changes based on the subject and stream.

Section	No. of Questions	Expected Difficulty Level	Remarks
Mathematics	50	Moderate	It can include major time-consuming questions requiring accuracy.
Physics	25	Easy to Moderate	It is expected to be concept-based with direct formulas.
Chemistry	25	Easy	It is expected to have straightforward theory-based questions similar to previous year.
Core Engineering Subject	100	Moderate	Expected to include application-based and domain-specific questions.

AP ECET 2025 Expected Category-Wise Cut-off

The AP ECET 2025 cut-off marks differ for various categories like General, OBC, SC, and ST.

The minimum qualifying mark is 50 out of 200 (25%) for General category candidates, but SC/ST candidates have no minimum qualifying mark.

AP ECET 2025 Expected Cut-off Category-Wise

Category	Expected Cut-off Range (Out of 200)
General (UR)	100 – 130
OBC	90 – 120
SC	70 – 100
ST	65 – 95

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AP ECET Questions

1.
The curvature of the straight line $ y = 2x + 3 $ at $ (1, 5) $ is:

2
0
$ \frac{1}{2} $
3

View Solution

2.
Let $A, G, H$ and $S$ respectively denote the arithmetic mean, geometric mean, harmonic mean and the sum of the numbers $a_1 , a_2 , a_3 ....., a_n$ . Then the value of at which the function $f(x) =\displaystyle \sum^n_{k =1} (x -a_k)^2$ has minimum is

View Solution

3.
A parallel plate capacitor consists of two circular plates each of radius $2 \,cm$, separated by a distance of $0.1 \,mm$. If the potential difference across the plates is varying at the rate of $5 \times 10^{6} Vs ^{-1}$, then the value of displacement current is

5.56 A
5.56 mA
0.556 mA
2.28 mA

View Solution

4.
The equation of the circle with extremities $ (1, 3) $ and $ (5, 7) $ of the diameter is:

$ x^2 + y^2 + 6x + 10y + 26 = 0 $
$ x^2 + y^2 - 6x - 10y + 26 = 0 $
$ x^2 + y^2 - 6x + 10y + 26 = 0 $
$ x^2 + y^2 - 6x - 10y - 26 = 0 $

View Solution

5.
A solid copper sphere of density $\rho$, specific heat capacity $C$ and radius $r$ is initially at $200\, K$. It is suspended inside a chamber whose walls are at $0\, K$. The time required (in (is) for the temperature of the sphere to drop to $100 \,K$ is ($\sigma$ is Stefan's constant and all the quantities are in SI units)

$48 \frac{r\rho C}{\sigma}$
$\frac{1}{48} \frac{r\rho C}{\sigma}$
$\frac{27}{7} \frac{r\rho C}{\sigma}$
$\frac{7}{27} \frac{r\rho C}{\sigma}$

View Solution

6.
Let $M$ and $m$ respectively denote the maximum and the minimum values of $[f(\theta)]^{2}$, where $f(\theta)=\sqrt{a^{2} \cos ^{2} \theta+b^{2} \sin ^{2} \theta}$ $+\sqrt{a^{2} \sin ^{2} \theta+b^{2} \cos ^{2} \theta}$. Then $M-m=$

$a^2 + b^2$
$(a -b)^2$
$a^2 b^2$
$(a + b)^2$

View Solution

Categories	State
General	600
sc	500

AP ECET 2025 May 6 Shift 1 Question Paper (Available): Download Solutions with Answer Key

AP ECET 2025 Question Paper with Solution PDF

AP ECET 2025 Difficulty Level

AP ECET 2025 Expected Category-Wise Cut-off

AP ECET Questions

1.
The curvature of the straight line \( y = 2x + 3 \) at \( (1, 5) \) is:

2.
Let $A, G, H$ and $S$ respectively denote the arithmetic mean, geometric mean, harmonic mean and the sum of the numbers $a_1 , a_2 , a_3 ....., a_n$ . Then the value of at which the function $f(x) =\displaystyle \sum^n_{k =1} (x -a_k)^2$ has minimum is

3.
A parallel plate capacitor consists of two circular plates each of radius $2 \,cm$, separated by a distance of $0.1 \,mm$. If the potential difference across the plates is varying at the rate of $5 \times 10^{6} Vs ^{-1}$, then the value of displacement current is

4.
The equation of the circle with extremities \( (1, 3) \) and \( (5, 7) \) of the diameter is:

6.
Let $M$ and $m$ respectively denote the maximum and the minimum values of $[f(\theta)]^{2}$, where $f(\theta)=\sqrt{a^{2} \cos ^{2} \theta+b^{2} \sin ^{2} \theta}$ $+\sqrt{a^{2} \sin ^{2} \theta+b^{2} \cos ^{2} \theta}$. Then $M-m=$

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AP ECET 2025 Question Paper with Solution PDF

AP ECET 2025 Difficulty Level

AP ECET 2025 Expected Category-Wise Cut-off

AP ECET Questions

1.The curvature of the straight line \( y = 2x + 3 \) at \( (1, 5) \) is:

2.Let $A, G, H$ and $S$ respectively denote the arithmetic mean, geometric mean, harmonic mean and the sum of the numbers $a_1 , a_2 , a_3 ....., a_n$ . Then the value of at which the function $f(x) =\displaystyle \sum^n_{k =1} (x -a_k)^2$ has minimum is

3.A parallel plate capacitor consists of two circular plates each of radius $2 \,cm$, separated by a distance of $0.1 \,mm$. If the potential difference across the plates is varying at the rate of $5 \times 10^{6} Vs ^{-1}$, then the value of displacement current is

4.The equation of the circle with extremities \( (1, 3) \) and \( (5, 7) \) of the diameter is:

6.Let $M$ and $m$ respectively denote the maximum and the minimum values of $[f(\theta)]^{2}$, where $f(\theta)=\sqrt{a^{2} \cos ^{2} \theta+b^{2} \sin ^{2} \theta}$ $+\sqrt{a^{2} \sin ^{2} \theta+b^{2} \cos ^{2} \theta}$. Then $M-m=$

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1.
The curvature of the straight line \( y = 2x + 3 \) at \( (1, 5) \) is:

2.
Let $A, G, H$ and $S$ respectively denote the arithmetic mean, geometric mean, harmonic mean and the sum of the numbers $a_1 , a_2 , a_3 ....., a_n$ . Then the value of at which the function $f(x) =\displaystyle \sum^n_{k =1} (x -a_k)^2$ has minimum is

3.
A parallel plate capacitor consists of two circular plates each of radius $2 \,cm$, separated by a distance of $0.1 \,mm$. If the potential difference across the plates is varying at the rate of $5 \times 10^{6} Vs ^{-1}$, then the value of displacement current is

4.
The equation of the circle with extremities \( (1, 3) \) and \( (5, 7) \) of the diameter is:

6.
Let $M$ and $m$ respectively denote the maximum and the minimum values of $[f(\theta)]^{2}$, where $f(\theta)=\sqrt{a^{2} \cos ^{2} \theta+b^{2} \sin ^{2} \theta}$ $+\sqrt{a^{2} \sin ^{2} \theta+b^{2} \cos ^{2} \theta}$. Then $M-m=$