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Key Facts: NEB Class 12 Mathematics Exam

75

Theory Marks

25

Internal Assessment Marks

3 hours

Theory Paper Duration

35%

Minimum Theory Score

NEB

Conducting Board

The NEB Class 12 Mathematics examination is conducted by the National Examinations Board (NEB) of Nepal. It consists of a 75-mark written theory paper (3 hours) plus 25 marks of internal assessment, and students need at least 35% in theory to avoid a Non-Graded (NG) result. OpenExamPrep offers free independent practice questions on algebra, trigonometry and coordinate geometry, calculus, vectors and mechanics, and probability and statistics. OpenExamPrep's questions are an independent English-language multiple-choice study adaptation of the curriculum topics. They are not an official translation of the board paper or a simulation of its written format.

Sample NEB Class 12 Mathematics Practice Questions

Try these sample questions to review concepts for the NEB Class 12 Mathematics exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1What are the modulus and the principal argument of the complex number z = -1 + i*sqrt(3)?
A.Modulus = 2, Argument = pi/3
B.Modulus = 4, Argument = 2*pi/3
C.Modulus = 2, Argument = -2*pi/3
D.Modulus = 2, Argument = 2*pi/3
Explanation: The modulus is |z| = sqrt((-1)^2 + (sqrt(3))^2) = sqrt(1 + 3) = sqrt(4) = 2. Since the real part x = -1 is negative and the imaginary part y = sqrt(3) is positive, z lies in the second quadrant. The principal argument is theta = pi - arctan(|y/x|) = pi - arctan(sqrt(3)) = pi - pi/3 = 2*pi/3.
2If omega is a non-real complex cube root of unity, what is the value of the product (1 - omega + omega^2)(1 + omega - omega^2)?
A.-4
B.1
C.4
D.2
Explanation: The cube roots of unity satisfy 1 + omega + omega^2 = 0 and omega^3 = 1. Therefore, 1 + omega^2 = -omega, so the first factor is (1 - omega + omega^2) = -omega - omega = -2*omega. Similarly, 1 + omega = -omega^2, so the second factor is (1 + omega - omega^2) = -omega^2 - omega^2 = -2*omega^2. Their product is (-2*omega) * (-2*omega^2) = 4*omega^3 = 4 * 1 = 4.
3By de Moivre's theorem, what is the exact value of [cos(pi/6) + i*sin(pi/6)]^6?
A.1
B.i
C.-i
D.-1
Explanation: By de Moivre's theorem, (cos(theta) + i*sin(theta))^n = cos(n*theta) + i*sin(n*theta). Here n = 6 and theta = pi/6, so n*theta = 6 * (pi/6) = pi. Thus, [cos(pi/6) + i*sin(pi/6)]^6 = cos(pi) + i*sin(pi) = -1 + i*0 = -1.
4What are the square roots of the complex number 7 + 24i?
A.+-(3 + 4i)
B.+-(4 - 3i)
C.+-(4 + 3i)
D.+-(5 + 2i)
Explanation: Let (x + iy)^2 = 7 + 24i. Expanding gives x^2 - y^2 = 7 and 2xy = 24 (so xy = 12 > 0). The modulus is |z| = sqrt(7^2 + 24^2) = sqrt(49 + 576) = sqrt(625) = 25. Thus, x^2 + y^2 = 25. Adding equations: 2x^2 = 32 => x^2 = 16 => x = +-4. Subtracting equations: 2y^2 = 18 => y^2 = 9 => y = +-3. Since xy > 0, x and y have the same sign, yielding +-(4 + 3i).
5In the complex plane, which geometric curve or line is represented by the equation |z - 2| = |z + 2i|?
A.A circle with center at the origin and radius 2
B.An ellipse with foci at (2, 0) and (0, -2)
C.A straight line with equation x - y = 0
D.A straight line with equation x + y = 0
Explanation: Let z = x + iy. Then |(x - 2) + iy| = |x + i(y + 2)|. Squaring both sides: (x - 2)^2 + y^2 = x^2 + (y + 2)^2. Expanding both sides: x^2 - 4x + 4 + y^2 = x^2 + y^2 + 4y + 4. Canceling common terms: -4x = 4y => x + y = 0. This is the perpendicular bisector of the line segment joining (2, 0) and (0, -2), which is a straight line through the origin with equation x + y = 0.
6If alpha and beta are the roots of x^2 - 5x + 6 = 0, which quadratic equation has roots alpha^2 and beta^2?
A.x^2 - 13x + 36 = 0
B.x^2 - 25x + 36 = 0
C.x^2 + 13x + 36 = 0
D.x^2 - 13x + 6 = 0
Explanation: From the given equation, alpha + beta = 5 and alpha*beta = 6. The new roots have sum alpha^2 + beta^2 = (alpha + beta)^2 - 2*alpha*beta = 25 - 12 = 13 and product alpha^2 * beta^2 = (alpha*beta)^2 = 36. The required equation is x^2 - (sum)x + (product) = 0, that is, x^2 - 13x + 36 = 0. (Check: the roots of the original are 2 and 3, and 4 and 9 are the roots of x^2 - 13x + 36 = 0.)
7What is the inverse of the 2x2 matrix A = [[3, 2], [7, 5]]?
A.[[5, 2], [7, 3]]
B.[[-5, 2], [7, -3]]
C.[[3, -2], [-7, 5]]
D.[[5, -2], [-7, 3]]
Explanation: The determinant of A is det(A) = (3)(5) - (2)(7) = 15 - 14 = 1. For a 2x2 matrix [[a, b], [c, d]], the inverse is (1/det(A)) * [[d, -b], [-c, a]]. Substituting a = 3, b = 2, c = 7, d = 5 gives A^-1 = (1/1) * [[5, -2], [-7, 3]] = [[5, -2], [-7, 3]].
8If A is a square matrix of order 3 with det(A) = 4, what is the value of det(2A)?
A.8
B.16
C.32
D.64
Explanation: For an n x n matrix, det(kA) = k^n * det(A), because each of the n rows is multiplied by k. Here n = 3, so det(2A) = 2^3 * 4 = 8 * 4 = 32.
9Using Cramer's rule, what is the value of x in the system of linear equations: x + y + z = 6, x - y + z = 2, and 2x + y - z = 1?
A.1
B.2
C.3
D.-1
Explanation: Compute the coefficient determinant D = |[1, 1, 1], [1, -1, 1], [2, 1, -1]| = 1*(1 - 1) - 1*(-1 - 2) + 1*(1 + 2) = 0 - (-3) + 3 = 6. Now compute Dx by replacing the first column with constant terms [6, 2, 1]^T: Dx = |[6, 1, 1], [2, -1, 1], [1, 1, -1]| = 6*(1 - 1) - 1*(-2 - 1) + 1*(2 + 1) = 0 - (-3) + 3 = 6. By Cramer's rule, x = Dx / D = 6 / 6 = 1.
10For what value of k does the system of linear equations x + y + z = 2, x + 2y + 3z = 5, and x + 3y + kz = 8 possess infinitely many solutions?
A.k = 3
B.k = 4
C.k = 5
D.k = -5
Explanation: The coefficient matrix has determinant D = |[1, 1, 1], [1, 2, 3], [1, 3, k]|. Applying row operations R2 -> R2 - R1 and R3 -> R3 - R1 gives |[1, 1, 1], [0, 1, 2], [0, 2, k - 1]| = 1 * (1*(k - 1) - 2*2) = k - 5. For infinitely many solutions, D must vanish, so k = 5. Checking consistency with k = 5: the augmented matrix reduces to row 2: y + 2z = 3 and row 3: 2y + 4z = 6, which are identical (0 = 0). Thus rank(A) = rank(A|B) = 2 < 3, ensuring infinitely many solutions.

About the NEB Class 12 Mathematics Exam

The Nepal NEB Class 12 Mathematics Board Examination is the national secondary school leaving examination conducted by the National Examinations Board (NEB) under the curriculum developed by the Curriculum Development Centre (CDC). The syllabus tests Algebra, Coordinate Geometry, Trigonometry, Calculus, Vectors, Mechanics, and Probability & Statistics through a 3-hour 75-mark written paper.

Exam sponsor: National Examinations Board (NEB), Sanothimi, Bhaktapur. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Written board examination: a 75-mark written theory paper (3 hours) plus 25 marks of internal assessment.

Time Limit

3 hours (theory paper)

Passing Score

At least 35% in the theory paper (below that: Non-Graded, NG)

Exam / Certification Fees

Set annually by NEB; paid through the school

Exam sponsor website

Reported exam pass rate: Not published by subject. Under NEB's letter-grading rules, a theory score below 35% is recorded as Non-Graded (NG) for that subject. 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.

25% of practice bank

Algebra

Complex numbers, sequences and series, matrices and determinants, and the binomial theorem.

20% of practice bank

Trigonometry and Coordinate Geometry

Inverse trigonometric functions, conic sections and three-dimensional geometry.

35% of practice bank

Calculus

Limits, derivatives and their applications, integration, and differential equations.

10% of practice bank

Vectors and Mechanics

Vector products and their applications, and statics and dynamics.

10% of practice bank

Probability and Statistics

Probability, correlation and regression, and probability distributions.

Preparing for the NEB Class 12 Mathematics Exam

What You Need to Know

  • Passing score: At least 35% in the theory paper (below that: Non-Graded, NG)
  • Assessment: Written board examination: a 75-mark written theory paper (3 hours) plus 25 marks of internal assessment.
  • Time limit: 3 hours (theory paper)
  • Exam / certification fees: Set annually by NEB; paid through the school 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

NEB Class 12 Mathematics: Suggested Study Strategy

1Master high-weight calculus methods: focus on standard integration substitutions, integration by parts, definite integral area calculations, and separating variables in differential equations.
2Practise matrix inversion and determinant expansions thoroughly, as they appear in multi-step questions.
3Memorize standard formulas and properties for conic sections (eccentricity, foci, directrix, vertex) and 3D coordinate geometry (angle between planes, shortest distance).
4Pay attention to probability distributions and regression coefficient relations (r = sqrt(b_yx * b_xy)) to secure quick, dependable marks on both objective and short-answer sections.

Frequently Asked Questions

What is the format of the NEB Class 12 Mathematics examination?

The official assessment is a 75-mark written theory paper (3 hours) plus 25 marks of internal assessment. It is a written board examination, not a multiple-choice test.

What score is needed to pass NEB Class 12 Mathematics?

Under NEB's letter-grading rules, students need at least 35% of the theory marks. A lower theory score is recorded as Non-Graded (NG) for the subject.

What happens if a student is Non-Graded (NG) in Mathematics?

Students who are NG in up to two subjects can sit the grade-increment (supplementary) examination announced by NEB after the results; others take the subject again in a later regular examination.

Are these practice questions official NEB papers?

No. OpenExamPrep's questions are an independent English-language multiple-choice study adaptation of the curriculum topics. They are not an official translation of the board paper or a simulation of its written format. OpenExamPrep is independent and is not affiliated with or endorsed by NEB or the Curriculum Development Centre (CDC).