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Exam Review

Key Facts: MET Exam

60

Questions

MAHE

120 min

Exam Time

MAHE

INR 2,000

Exam Fee

MAHE

The Manipal Entrance Test (MET) consists of 60 questions to be completed in 120 minutes. The registration fee is INR 2,000, and it is the pathway to B.Tech programs at MAHE campuses.

Sample MET Practice Questions

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

1If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^2 - 5x + 6 = 0$, what is the value of $\alpha^3 + \beta^3$?
A.35
B.65
C.95
D.125
Explanation: From the given equation, the sum of roots is $\alpha + \beta = 5$ and the product of roots is $\alpha\beta = 6$. Using the algebraic identity, we have $\alpha^3 + \beta^3 = (\alpha + \beta)^3 - 3\alpha\beta(\alpha + \beta)$. Substituting the values gives $5^3 - 3(6)(5) = 125 - 90 = 35$.
2Find the sum of the infinite geometric series $1 + 1/3 + 1/9 + 1/27 + \dots$.
A.4/3
B.3/2
C.2
D.5/3
Explanation: The given series is an infinite geometric progression with first term $a = 1$ and common ratio $r = 1/3$. Since $|r| < 1$, the sum of the infinite series is given by $S = a / (1 - r)$. Substituting the values yields $S = 1 / (1 - 1/3) = 1 / (2/3) = 3/2$.
3What is the number of terms in the expansion of $(x + y + z)^{10}$?
A.55
B.66
C.11
D.121
Explanation: The number of terms in the multinomial expansion of $(x_1 + x_2 + \dots + x_r)^n$ is given by the formula $^{n+r-1}C_{r-1}$. For $(x + y + z)^{10}$, we have $n = 10$ and $r = 3$. The number of terms is $^{10+3-1}C_{3-1} = ^{12}C_2 = (12 \times 11) / 2 = 66$.
4If $^nC_8 = ^nC_2$, find the value of $n$.
A.6
B.8
C.10
D.12
Explanation: Using the combination property $^nC_x = ^nC_y \implies x = y$ or $x + y = n$, we compare the subscripts. Since $8 \neq 2$, we must have $8 + 2 = n$. Therefore, $n = 10$.
5Solve for the sum of the series $1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \dots + n(n+1)$.
A.$n(n+1)(n+2)/3$
B.$n(n+1)(2n+1)/6$
C.$n(n+1)(n+2)(n+3)/4$
D.$n^2(n+1)^2/4$
Explanation: The $r$-th term of the series is $T_r = r(r+1) = r^2 + r$. The sum of the series is $S_n = \sum T_r = \sum r^2 + \sum r = [n(n+1)(2n+1)/6] + [n(n+1)/2]$. Factoring out $n(n+1)/2$, we get $[n(n+1)/2] \cdot [(2n+1)/3 + 1] = [n(n+1)/2] \cdot [(2n+4)/3] = n(n+1)(n+2)/3$.
6Find the coefficient of $x^4$ in the expansion of $(1 + x - 2x^2)^6$.
A.-15
B.-45
C.15
D.45
Explanation: The general term in the trinomial expansion of $(1 + x - 2x^2)^6$ is given by $T = [6! / (p! q! r!)] \cdot (1)^p (x)^q (-2x^2)^r$, where $p + q + r = 6$. For the power of $x$ to be 4, we must have $q + 2r = 4$. Possible non-negative integer solutions are: (1) $r=0, q=4 \implies p=2$, term is $[6! / (2!4!0!)] \cdot (-2)^0 = 15$; (2) $r=1, q=2 \implies p=3$, term is $[6! / (3!2!1!)] \cdot (-2)^1 = -120$; (3) $r=2, q=0 \implies p=4$, term is $[6! / (4!0!2!)] \cdot (-2)^2 = 60$. The sum of these coefficients is $15 - 120 + 60 = -15$.
7What is the value of $\sin(75^\circ)$?
A.$(\sqrt{3} - 1)/(2\sqrt{2})$
B.$(\sqrt{3} + 1)/(2\sqrt{2})$
C.$(\sqrt{3} + 1)/2$
D.$(\sqrt{3} - 1)/2$
Explanation: We can write $\sin(75^\circ)$ as $\sin(45^\circ + 30^\circ)$. Using the angle sum identity $\sin(A + B) = \sin(A)\cos(B) + \cos(A)\sin(B)$, we have $\sin(75^\circ) = \sin(45^\circ)\cos(30^\circ) + \cos(45^\circ)\sin(30^\circ) = (1/\sqrt{2})(\sqrt{3}/2) + (1/\sqrt{2})(1/2) = (\sqrt{3} + 1)/(2\sqrt{2})$.
8If $\tan(A) = 1/2$ and $\tan(B) = 1/3$, what is the value of $A + B$?
A.$\pi/6$
B.$\pi/4$
C.$\pi/3$
D.$\pi/2$
Explanation: We use the tangent sum identity $\tan(A + B) = [\tan(A) + \tan(B)] / [1 - \tan(A)\tan(B)]$. Substituting the given values gives $\tan(A + B) = (1/2 + 1/3) / [1 - (1/2)(1/3)] = (5/6) / (1 - 1/6) = (5/6) / (5/6) = 1$. Therefore, $A + B = \pi/4$ (or $45^\circ$).
9Find the general solution of the trigonometric equation $\cos(x) = -1/2$.
A.$2n\pi \pm \pi/3$
B.$2n\pi \pm 2\pi/3$
C.$n\pi + (-1)^n (2\pi/3)$
D.$n\pi \pm 2\pi/3$
Explanation: The principal value of $x$ for which $\cos(x) = -1/2$ is $2\pi/3$. The general solution for $\cos(x) = \cos(\alpha)$ is $x = 2n\pi \pm \alpha$, where $n \in \mathbb{Z}$. Thus, the general solution is $x = 2n\pi \pm 2\pi/3$.
10What is the limit of $(\sin(x) - x) / x^3$ as $x \to 0$?
A.0
B.-1/6
C.1/6
D.Does not exist
Explanation: Using the Taylor series expansion of $\sin(x) = x - x^3/6 + x^5/120 - \dots$, the expression becomes $[(x - x^3/6 + \dots) - x] / x^3 = -x^3/(6x^3) + O(x^2) = -1/6 + O(x^2)$. Taking the limit as $x \to 0$, the value is $-1/6$. Alternatively, applying L'Hopital's rule three times yields the same result.

About the MET Exam

The Manipal Entrance Test (MET), formerly known as MU-OET, is a university-level entrance examination conducted by the Manipal Academy of Higher Education (MAHE) for admission to various undergraduate engineering (B.Tech) and other professional programs. The exam is computer-based and tests candidates on Mathematics, Physics, Chemistry, and English.

Exam sponsor: Manipal Academy of Higher Education (MAHE). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Questions

60 questions

Time Limit

120 minutes

Passing Score

Cutoff-based

Exam / Certification Fees

₹2,000

Exam sponsor website

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

Official sources

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.

33%

Mathematics

Algebra, Trigonometry, Coordinate Geometry, Calculus, Vectors, Probability, Matrices

25%

Physics

Mechanics, Thermodynamics, Electrostatics, Magnetism, Optics, Modern Physics

25%

Chemistry

Physical Chemistry, Inorganic Chemistry, Organic Chemistry

17%

English

Grammar, Vocabulary, Sentence Correction

Preparing for the MET Exam

What You Need to Know

  • Passing score: Cutoff-based
  • Exam length: 60 questions
  • Time limit: 120 minutes
  • Exam / certification fees: ₹2,000 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

MET: Suggested Study Strategy

1Focus heavily on Mathematics as it carries the highest weightage (33%)
2Practice speed and accuracy with Numerical Answer Type (NAT) questions
3Review NCERT concepts for Physics and Chemistry as they form the core of the syllabus
4Do not neglect the English section which can boost your overall score

Frequently Asked Questions

What is the fee for MET 2026?

The application fee is INR 600 and the test fee is INR 1,400, making the total MET registration fee INR 2,000.

What is the duration of the MET B.Tech exam?

The exam is 120 minutes (2 hours) long.

How many questions are there on the MET exam?

The B.Tech exam consists of 60 questions, including 50 Multiple Choice Questions (MCQs) and 10 Numerical Answer Type (NAT) questions.