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Key Facts: PERA CET Exam

100

Questions

PERA India

120 mins

Time Limit

PERA India

INR 1,500

Exam Fee

PERA India

Online

Mode

Remote-proctored

PERA CET 2026 is an online remote-proctored entrance exam for admissions to private universities in Maharashtra. The B.Tech exam consists of 100 MCQs (200 marks total) with no negative marking and a 2-hour duration. The registration fee is INR 1,500.

Sample PERA CET Practice Questions

Try these sample questions to review concepts for the PERA CET exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1What is the conjugate of the complex number z = (3 - 4i) / (1 + 2i)?
A.-1 + 2i
B.-1 - 2i
C.1 - 2i
D.1 + 2i
Explanation: Multiplying the numerator and denominator by the conjugate of the denominator (1 - 2i) yields z = (3 - 4i)(1 - 2i) / (1^2 + 2^2) = (3 - 8 - 6i - 4i) / 5 = (-5 - 10i) / 5 = -1 - 2i. Therefore, the complex conjugate of z is -1 + 2i.
2If the roots of the equation x^2 - px + q = 0 differ by unity, which of the following relations is correct?
A.p^2 = 4q + 1
B.p^2 = 4q - 1
C.q^2 = 4p + 1
D.q^2 = 4p - 1
Explanation: Let the roots be alpha and beta. Given |alpha - beta| = 1, squaring both sides gives (alpha + beta)^2 - 4*alpha*beta = 1. Since alpha + beta = p and alpha*beta = q, substituting these gives p^2 - 4q = 1, or p^2 = 4q + 1.
3What is the sum of the first 20 terms of an arithmetic progression whose first term is 5 and the common difference is 4?
A.860
B.840
C.880
D.900
Explanation: The sum of the first n terms of an AP is given by S_n = (n/2) * [2a + (n-1)d]. Substituting n = 20, a = 5, and d = 4, we get S_20 = 10 * [10 + 19 * 4] = 10 * [10 + 76] = 860.
4For a geometric progression, if the 3rd term is 12 and the 6th term is 96, what is the 1st term?
A.3
B.4
C.2
D.6
Explanation: The n-th term of a GP is a*r^(n-1). Given a*r^2 = 12 and a*r^5 = 96, dividing the two equations gives r^3 = 8, which means the common ratio r is 2. Substituting r = 2 into a*r^2 = 12 gives a*4 = 12, so the first term a is 3.
5What is the coefficient of x^4 in the expansion of (1 + x + x^2 + x^3)^10?
A.705
B.715
C.695
D.725
Explanation: The expression can be written as [(1 - x^4) / (1 - x)]^10 = (1 - x^4)^10 * (1 - x)^-10. Expanding both parts, the term containing x^4 is 1 * (coefficient of x^4 in (1-x)^-10) + (-10x^4) * (coefficient of x^0 in (1-x)^-10) = 13C4 - 10 = 715 - 10 = 705.
6If z = cos(theta) + i*sin(theta), what is the value of (z^2n - 1) / (z^2n + 1) where n is an integer?
A.i*tan(n*theta)
B.i*cot(n*theta)
C.tan(n*theta)
D.cot(n*theta)
Explanation: Using De Moivre's Theorem, z^2n = cos(2n*theta) + i*sin(2n*theta). The expression simplifies to [cos(2n*theta) - 1 + i*sin(2n*theta)] / [cos(2n*theta) + 1 + i*sin(2n*theta)] = [-2*sin^2(n*theta) + 2i*sin(n*theta)*cos(n*theta)] / [2*cos^2(n*theta) + 2i*sin(n*theta)*cos(n*theta)] = i*tan(n*theta).
7What is the sum of the roots of the quadratic equation 3x^2 - 9x + 5 = 0?
A.3
B.-3
C.5/3
D.-5/3
Explanation: For any quadratic equation ax^2 + bx + c = 0, the sum of the roots is given by -b/a. Substituting a = 3 and b = -9 gives -(-9)/3 = 3.
8What is the sum of an infinite geometric series with first term 10 and common ratio 0.6?
A.25
B.20
C.16
D.30
Explanation: The sum of an infinite geometric series is given by S = a / (1 - r), where a is the first term and r is the common ratio (|r| < 1). Substituting a = 10 and r = 0.6 yields S = 10 / (1 - 0.6) = 10 / 0.4 = 25.
9What is the number of terms in the expansion of (x + y + z)^15?
A.136
B.120
C.153
D.105
Explanation: The number of terms in the multinomial expansion of (x1 + x2 + ... + xr)^n is given by the combination formula (n + r - 1)C(r - 1). For (x + y + z)^15, n = 15 and r = 3, so the number of terms is (15 + 3 - 1)C(3 - 1) = 17C2 = (17 * 16) / 2 = 136.
10What is the modulus of the complex number z = (1 + 3i)(2 - i)?
A.5*sqrt(2)
B.sqrt(10)
C.sqrt(5)
D.10
Explanation: The modulus of a product of complex numbers is the product of their individual moduli: |z1 * z2| = |z1| * |z2|. Here, |1 + 3i| = sqrt(1^2 + 3^2) = sqrt(10) and |2 - i| = sqrt(2^2 + (-1)^2) = sqrt(5). Thus, |z| = sqrt(10) * sqrt(5) = sqrt(50) = 5*sqrt(2).

About the PERA CET Exam

The PERA CET (Preeminent Education and Research Association Common Entrance Test) is a state-level entrance exam for admission into various undergraduate and postgraduate programs (including B.Tech, B.Pharmacy, MBA, and MCA) at participating private universities in Maharashtra, India. The engineering exam is based on the 10+2 curriculum covering Physics, Chemistry, and Mathematics/Biology.

Exam sponsor: Preeminent Education and Research Association (PERA). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

100 MCQs (50 Mathematics, 25 Physics, 25 Chemistry)

Time Limit

2 hours

Passing Score

Based on participating university cut-offs

Exam / Certification Fees

₹1,500

Exam sponsor website

Reported exam pass rate: Not published. Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

50%

Mathematics

Calculus, vectors, 3D geometry, coordinate geometry, matrices, determinants, and algebra.

25%

Physics

Mechanics, thermodynamics, electrostatics, magnetism, current electricity, optics, and modern physics.

25%

Chemistry

Physical chemistry, chemical kinetics, coordination compounds, chemical bonding, and organic chemistry.

Preparing for the PERA CET Exam

What You Need to Know

  • Passing score: Based on participating university cut-offs
  • Assessment: 100 MCQs (50 Mathematics, 25 Physics, 25 Chemistry)
  • Time limit: 2 hours
  • Exam / certification fees: ₹1,500 Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

PERA CET: Suggested Study Strategy

1Practice basic calculus, vectors, and matrices which form 50% of the exam weight.
2Focus on NCERT and Maharashtra State Board textbooks for Class 12 concepts.
3Attempt all questions since there is no negative marking.
4Test your system and webcam beforehand since the exam is home-based and remote-proctored.

Frequently Asked Questions

What is the exam fee for PERA CET 2026?

The exam fee for PERA CET 2026 is INR 1,500 for all categories.

How many questions are on the PERA CET B.Tech exam?

The exam consists of 100 multiple-choice questions (MCQs) carrying 2 marks each, for a total of 200 marks.

What is the time limit for the exam?

The exam duration is 120 minutes (2 hours).

Is there negative marking in PERA CET?

No, there is no negative marking for incorrect answers in PERA CET.

What is the exam format?

The exam is administered online as a remote-proctored (home-based) test.