AP EAPCET Maths Important Questions 2027: Important Topics & Weightage

Mathematics carries the highest number of questions in the AP EAPCET Engineering paper, making it an important section for improving your overall score. However, trying to give equal attention to every chapter can make your preparation difficult. Focusing on important topics, practising exam-level questions and solving previous year questions can help you use your preparation time effectively.

In the latest official AP EAPCET Engineering pattern, Mathematics had 80 questions carrying 80 marks out of 160 questions. Each question carried one mark, and there was no negative marking. The AP EAPCET 2027 pattern will be confirmed through the official notification. Until then, you can use the latest syllabus and previous year questions to plan your Maths preparation.

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AP EAPCET Maths Important Questions 2027

Practising important questions can help you understand how concepts are applied in the examination. Give particular attention to questions based on Complex Numbers, Coordinate Geometry, Algebra, Calculus, Matrices, Probability, Vectors and Trigonometry.

Complex Numbers

Q1. If z1=3 +i3 and z2=3+i then in which quadrant  ( z1z2)Does it lie?

• (A) I

• (B) II

• (C) III

• (D) IV

Answer: A

Q2. If α,β,γ\alpha,\beta,\gamma and a,b,ca,b,c are complex numbers such that

αa+βb+γc=1+i\frac{\alpha}{a}+\frac{\beta}{b}+\frac{\gamma}{c}=1+i

and

aα+bβ+cγ=0,\frac{a}{\alpha}+\frac{b}{\beta}+\frac{c}{\gamma}=0,

then the value of

α2a2+β2b2+γ2c2\frac{\alpha^2}{a^2}+\frac{\beta^2}{b^2}+\frac{\gamma^2}{c^2}

is equal to:

• (A) −1-1

• (B) 22

• (C) 00

• (D) +1+1

Answer: The given options need verification. The direct algebraic result is 2i2i.

Q3. If z=x+iyz=x+iy is a variable complex number such that

arg⁡(z−1z+1)=π4,\arg\left(\frac{z-1}{z+1}\right)=\frac{\pi}{4},

then the corresponding equation is:

• (A) x2−y2−2x=1x^2-y^2-2x=1

• (B) x2+y2−2x=1x^2+y^2-2x=1

• (C) x2+y2−2y=1x^2+y^2-2y=1

• (D) x2+y2+2x=1x^2+y^2+2x=1

Answer: C

Algebra and Complex Number Operations

Q4. Evaluate

(11−2i+31+i)(3+4i2−4i).\left(\frac{1}{1-2i}+\frac{3}{1+i}\right) \left(\frac{3+4i}{2-4i}\right).

• (A) 12+92i\frac12+\frac92i

• (B) 12−92i\frac12-\frac92i

• (C) 14−94i\frac14-\frac94i

• (D) 14+94i\frac14+\frac94i

Answer: D

Q5. Find the equation of the perpendicular bisector of the line segment joining the points 7+7i7+7i and 7−7i7-7i in the Argand plane.

• (A) x=0x=0

• (B) y=0y=0

• (C) y=xy=x

• (D) x+y=0x+y=0

Answer: B

Q6. If

(2x−y+1)+i(x−2y−1)=2−3i,(2x-y+1)+i(x-2y-1)=2-3i,

then the multiplicative inverse of x−iyx-iy is:

• (A) 1541+1241i\frac{15}{41}+\frac{12}{41}i

• (B) 629+1529i\frac{6}{29}+\frac{15}{29}i

• (C) 1529+629i\frac{15}{29}+\frac{6}{29}i

• (D) 1241+1541i\frac{12}{41}+\frac{15}{41}i

Answer: D

Q7. If the point (x,y)(x,y) satisfies

x+i(x−2)3+i−i=2y+i(1−3y)i−3,\frac{x+i(x-2)}{3+i}-i = \frac{2y+i(1-3y)}{i-3},

then x+y=x+y=

• (A) 4

• (B) 2

• (C) 0

• (D) -2

Answer: B

Coordinate Geometry

Q8. If z∈Cz\in C, then the minimum value of

∣z∣+∣2z−3∣+∣z−1∣|z|+|2z-3|+|z-1|

is:

• (A) 2

• (B) 0

• (C) 1

• (D) 3

Answer: A

Q9. The real part of

(cos⁡4+isin⁡4+1)2020(\cos4+i\sin4+1)^{2020}

is:

• (A) 22020cos⁡20202cos⁡20202^{2020}\cos^{2020}2\cos2020

• (B) 22020cos⁡20202cos⁡40402^{2020}\cos^{2020}2\cos4040

• (C) 21020cos⁡20202cos⁡40402^{1020}\cos^{2020}2\cos4040

• (D) 22020cos⁡20201cos⁡20202^{2020}\cos^{2020}1\cos2020

Answer: B

Q10. The smallest positive integer nn for which

(1+i)2n=(1−i)2n(1+i)^{2n}=(1-i)^{2n}

is:

• (A) 1

• (B) 2

• (C) 3

• (D) 4

Answer: B

Circle

Q11. If the length of the tangent from (5,4)(5,4) to the circle

x2+y2+2ky=0x^2+y^2+2ky=0

is 1, then find kk.

• (A) 5

• (B) 6

• (C) 7

• (D) -5

Answer: D

Q12. If 4x−3y+7=04x-3y+7=0 is a tangent to the circle

x2+y2−6x+4y−12=0,x^2+y^2-6x+4y-12=0,

then find its point of contact.

• (A) (−1,2)(-1,2)

• (B) (−1,8)(-1,8)

• (C) (−1,1)(-1,1)

• (D) (2,3)(2,3)

Answer: C

Q13. Find the length of the chord formed by

x2+y2=a2x^2+y^2=a^2

on the line

xcos⁡α+ysin⁡α=p.x\cos\alpha+y\sin\alpha=p.

• (A) 2a2+p22\sqrt{a^2+p^2}

• (B) 2a2−p22\sqrt{a^2-p^2}

• (C) a2−p2\sqrt{a^2-p^2}

• (D) 2acos⁡p2a\cos p

Answer: B

Q14. Find the equation of the normal to the circle

x2+y2−4x−6y+11=0x^2+y^2-4x-6y+11=0

at (3,2)(3,2). Also find the other point where the normal meets the circle.

• (A) Normal: y=−x+5y=-x+5; Other point: (1,4)(1,4)

• (B) Normal: y=x+5y=x+5; Other point: (1,−4)(1,-4)

• (C) Normal: y=−x+2y=-x+2; Other point: (4,1)(4,1)

• (D) Normal: y=x−1y=x-1; Other point: (−1,4)(-1,4)

Answer: A

Q15. If a circle passes through the point (a,b)(a,b) and cuts the circle

x2+y2=4x^2+y^2=4

orthogonally, then the locus of its centre is:

• (A) 2ax−2by−(a2+b2+4)=02ax-2by-(a^2+b^2+4)=0

• (B) 2ax+2by−(a2+b2+4)=02ax+2by-(a^2+b^2+4)=0

• (C) 2ax−2by+(a2+b2+4)=02ax-2by+(a^2+b^2+4)=0

• (D) 2ax+2by+(a2+b2+4)=02ax+2by+(a^2+b^2+4)=0

Answer: B

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AP EAPCET Maths Important Questions 2027 PDF

Download the AP EAPCET Maths Important Questions 2027 PDF to practise important concepts and exam-level questions in one convenient resource. Use it for regular practice, revision and quick preparation before mock tests.