Solved question paper for Math Mar-2018 (PSEB Class 12th)

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Math Mar-2018

PSEB • Class 12th • 1st • Mar-2018

Math previous year question papers on BRpaper for PSEB 12th Class Question Papers help students find PSEB Class 12 Maths papers in one place for revision and practice. This subject page is useful for checking how board exam questions are framed, what types of sums are asked, and which areas need more preparation before the exam. Students looking for Punjab Board 12th Maths old question papers can use this section to review question style, paper pattern, and important topics from earlier exams. It may also help with chapterwise practice, model paper-style revision, and understanding how Math or Maths questions are commonly presented in board-level exams. BRpaper is not the official website of Punjab School Education Board or any institution, and it does not publish official notices or academic updates.

1 Relations and Functions:

Types of relations: Reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations.

2 Inverse Trigonometric Functions:

Definition, Range, Domain, Principal value branches. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

3 Matrices:

Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and skew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication. Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

4 Determinants:

Determinant of a square matrix (up to 3×3matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equation by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

5 Continuity and Differentiability:

Continuity and Differentiability, derivative of composite functions, chain rule, derivative of inverse trigonometric functions, derivative of implicit function. Concepts of exponential and logarithmic functions. Derivatives of logex and ex. Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second order derivatives. Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretations.

6 Applications of Derivatives:

Applications of derivatives: rate of change, increasing/decreasing functions, tangents and normal, approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real life situations).

7 Integrals:

Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, only simple integrals of the type to be evaluated. Definite integrals as a limit of a sum. Fundamental Theorem of Calculus (without proof).Basic properties of definite integrals and evaluation of definite integrals.

8 Applications of the Integrals:

Applications in finding the area under simple curves, especially lines, areas of circles/parabolas/ellipses (in standard form only), area between the two above said curves (the region should be clearly identifiable).

9 Differential Equations:

Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables, homogeneous differential equations of first order and first degree.

10 Vectors:

Vectors and scalars, magnitude and direction of a vector. Direction cosines/ratios of vectors. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Scalar (dot) product of vectors, projection of a vector on a line. Vector (cross) product of vectors, scalar triple product.

11 Three-dimensional Geometry:

Direction cosines/ ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.

12 Linear Programming:

Introduction, definition of related terminology such as constraints, objectives function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constrains)

13 Probability:

Multiplication theorem on probability. Conditional probability, independent events, total probability, Baye’s theorem, Random variable and its probability distribution, mean and variance of haphazard variable. Repeated independent (Bernoulli) trials and Binomial distribution.

Note:- The subtopics which are printed in the books published by Punjab School Education Board but are not mentioned in syllabus, should be considered as part of syllabus

Question papers (year-wise) Solutions

Solved Questions

Solved

(i) If y = sin (sin^-1 x + cos^-1 x), x € [-1, 1] then dy/dx is

(a) ðœ‹/2 (b) −ðœ‹/2 (c) 0 d) 1

Very Short Answer Mar-2018 • PSEB Class 12th

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Mar 2018
If y = sin (sin^-1 x + cos^-1 x), x € [-1, 1] then dy/dx is
\r\n
\r\n\r\n
(a) ðœ‹/2 (b) −ðœ‹/2 (c) 0 d) 1
(int e^x ( log x {1over x}) ) dx is equal to

(a) e^x + c (b) e^xlogx + c (c) e^x/x + c (d) log x + c

Very Short Answer Mar-2018 • PSEB Class 12th

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Mar 2018
\\(\\int e^x ( log x {1\\over x}) \\) dx is equal to
\r\n\r\n
(a) e^x + c (b) e^xlogx + c (c) e^x/x + c (d) log x + c
If P(E) denotes probability of occurrence of event E then

(a) P (E) € [-1, 1] (b) P (E) € (1, 2) (c) P (E) € (0, 1) (d) P (E) € [0, 1]

Very Short Answer Mar-2018 • PSEB Class 12th

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Mar 2018
If P(E) denotes probability of occurrence of event E then
\r\n
\r\n (a) P (E) € [-1, 1] (b) P (E) € (1, 2) (c) P (E) € (0, 1) (d) P (E) € [0, 1]
If is a binary operation such that a * b = a² +b² then 3 * 5 is

(a) 34 (b) 9 (c) 8 (d) 25

Very Short Answer Mar-2018 • PSEB Class 12th

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Mar 2018
(i) If is a binary operation such that a * b = a² +b² then 3 * 5 is
\r\n (a) 34 (b) 9 (c) 8 (d) 25

If f(x) = { ( {{{sinxover x}over k-1} , {x! = 0 over x=0}}) } ,ð‘¥ = 0 is continuous at x=0 then

(a) 2 (b) 0 (c) -1 (d) 1

Very Short Answer Mar-2018 • PSEB Class 12th

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Mar 2018
If
\r\nf(x) = { \\( {{{sinx\\over x}\\over k-1} , {x! = 0 \\over x=0}}\\) } ,ð‘¥ = 0 is continuous at x=0 then
\r\n\r\n

\r\n (a) 2 (b) 0 (c) -1 (d) 1
Distance between plane 3x +4y-20 = 0 and point (0, 0,-7) is

(a) 4 units (b) 3 units (c) 2 units (d) 1 unit

Very Short Answer Mar-2018 • PSEB Class 12th

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Mar 2018
Distance between plane 3x +4y-20 = 0 and point (0, 0,-7) is
\r\n
\r\n (a) 4 units (b) 3 units (c) 2 units (d) 1 unit
If cos^-1 x = y then

(a) −ðœ‹/2 <= y <= ðœ‹/2 (b) -π <=y <= π

(c) 0 <= y <= ðœ‹/2 (d) 0 <= y <= π

Very Short Answer Mar-2018 • PSEB Class 12th

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Mar 2018
If cos^-1 x = y then
\r\n
\r\n(a) −ðœ‹/2 <= y <= ðœ‹/2 (b) -π <=y <= π
\r\n\r\n
(c) 0 <= y <= ðœ‹/2 (d) 0 <= y <= π
Integrating factor of differential equation dy/dx + ð‘¦ = 3 is

(a) x (b) e (c) e^x (d) logx

Very Short Answer Mar-2018 • PSEB Class 12th

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Mar 2018
Integrating factor of differential equation dy/dx + ð‘¦ = 3 is
\r\n
\r\n(a) x (b) e (c) e^x (d) logx

Evaluate (intlimits_0^{x/2} sin^3X / sin^3X + cos^3X { sin^3x over sin^3x + cos^3x }dx)

Short Answer Mar-2018 • PSEB Class 12th

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Mar 2018
Evaluate \\(\\int\\limits_0^{x/2} sin^3X / sin^3X + cos^3X { sin^3x \\over sin^3x + cos^3x }dx\\)
Find particular solution of differential equation ({dy over dx} {1+y^2 over 1+x^2}) given that x=0 or y= 1

Short Answer Mar-2018 • PSEB Class 12th

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Mar 2018
Find particular solution of differential equation \\({dy \\over dx} {1+y^2 \\over 1+x^2}\\) given that x=0 or y= 1
Find the angle between the plane 2x+3 y-5z= 10 and the line passing from the points (2, 3,-1) Or (1, 2, 1)

Short Answer Mar-2018 • PSEB Class 12th

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Mar 2018
Find the angle between the plane 2x+3 y-5z= 10 and the line passing from the points (2, 3,-1) 2 Or (1, 2, 1)

Mar 2017
Find the angle between plane 3x + 4y - z = 8 and line \\({x-1\\over 2}\\) = \\({2-y\\over 7}\\) = \\({3z + 6\\over 12}\\)
If matrix A = [aij]_{3 x 2}, and aij = (3i-2j)² or matrix A find them

Short Answer Mar-2018 • PSEB Class 12th

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Mar 2018
If matrix A = [aij]_{3 x 2}, and aij = (3i-2j)² or matrix A find them

Form differential equation representing the family of lines making equal intercepts on the co-ordinate axes.

Short Answer Mar-2018 • PSEB Class 12th

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Mar 2018
Form differential equation representing the family of lines making equal intercepts on the co-ordinate axes.
If P (A) = 7/13, P (B) = 9/13 and P (AUB) = 12/13 then find (A|B)

Short Answer Mar-2018 • PSEB Class 12th

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Mar 2018
If P (A) = 7/13, P (B) = 9/13 and P (AUB) = 12/13 then find P(A|B)
Check whether Lagrange's mean value theorem is applicable on f(x) = sin x + cos x Interval [0, ðœ‹/2]

Short Answer Mar-2018 • PSEB Class 12th

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Mar 2018
Check whether Lagrange's mean value theorem is applicable on f(x) = sin x + cos x Interval [0, ðœ‹/2 ]
Evaluate (int {7dx over x(x^7-1)})

Short Answer Mar-2018 • PSEB Class 12th

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Mar 2018
Evaluate \\(\\int {7dx \\over x(x^7-1)}\\)

If y = (x)^tanx + (tanx)^x then find ð‘‘ð‘¦/ð‘‘ð‘¥

Short Answer Mar-2018 • PSEB Class 12th

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Mar 2018
If y = (x)^tanx + (tanx)^x then find ð‘‘ð‘¦/ð‘‘ð‘¥
\r\n\r\n
Using differentials find approximate value of (0.37)^1/2

Short Answer Mar-2018 • PSEB Class 12th

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Mar 2018
Using differentials find approximate value of (0.37)^1/2
Evaluate (int {x^2 +1 over x^4 +1}) dx

Or

Evaluate (int {dx over x^2+1})

Long Answer Mar-2018 • PSEB Class 12th

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Mar 2018
Evaluate \\(\\int {x^2 +1 \\over x^4 +1}\\) dx
13 If à = 2í-3j+4k à¨…à¨¤à©‡ 6 = 5i +j-k represents sider parallelogram then find both diagonals and a unit vector perpendicular to both dingonals.

Long Answer Mar-2018 • PSEB Class 12th

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Mar 2018
If à = 2í-3j+4k à¨…à¨¤à©‡ 6 = 5i +j-k represents sider parallelogram then find both diagonals and a unit vector perpendicular to both dingonals

Two cards are drawn (without replacement from a well shulle distribution table and mean of number of kings.

Long Answer Mar-2018 • PSEB Class 12th

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Mar 2018
Two cards are drawn (without replacement from a well shulle distribution table and mean of number of kings.
Find the particular solution of differential equation [x sin2 (y/x)-y] dx +xdy = 0;y(1)=ðœ‹/4

Or

Find the particular solution of differential equation " given that tanx ð‘‘ð‘¥/ð‘‘ð‘¥ +y = 2x tan x + x² , x != 0 given that y=0 when x = ðœ‹/2

Long Answer Mar-2018 • PSEB Class 12th

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Mar 2018
Find the particular solution of differential equation [x sin2 (y/x)-y] dx +xdy = 0;y(1)=ðœ‹/4
Prove that function f : R --> R, f(x) = (3âˆ’2ð‘¥ over 7) in one-one and onto. Also find f^-1

Long Answer Mar-2018 • PSEB Class 12th

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Mar 2018
10 Prove that function f : R --> R, f(x) = \(3âˆ’2ð‘¥ \over 7\) in one-one and onto. Also find f^-1
Express ( egin{matrix} 2 & 5 & -1 \ 3 & 1 & 5 \ 7 & 6 & 9 end{matrix}) as sum of symmetric and skew-symmetric matrices.

Or

If x,y,z are different and ( egin{matrix} x & x^2 & 1 + x^3 \ y & y^2 & 1 + y^3 \ z & z^2 & 1 + z^3 end{matrix}) = 0 then prove that xyz =-1

Long Answer Mar-2018 • PSEB Class 12th

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Prove that : sin^-1 ( (5over13) ) +cos^-1 ((4over 5)) = (1over 2) sin^-1 (3696 over 4225)

Long Answer Mar-2018 • PSEB Class 12th

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Mar 2018
Prove that : sin^-1 ( \\(5\\over13\\) ) +cos^-1 (\\(4\\over 5\\)) = \\(1\\over 2\\) sin^-1 \\(3696 \\over 4225\\)
Find the area of region bounded by the ellipse ({x^2 over 9 } + {y^2 over 4} = 1)

Long Answer Mar-2018 • PSEB Class 12th

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Mar 2018
Find the area of region bounded by the ellipse \\({x^2 \\over 9 } + {y^2 \\over 4} = 1\\)
A window is in the form of rectangle surmounted by a semi-circular opening. The perimeter of window is 30 m. Find the dimensions of window so that it can admit maximum light through the whole opening.

Or

Prove that volume of largest cone, which can be inscribed in a sphere, is 8/27 part of sphere.

Long Answer Mar-2018 • PSEB Class 12th

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Maximise and minimise : Z=15x + 30y Subject to the constraints : x+y <= 8, 2x +y >= 28, x - 2y >=0, x, y >= 0
Or

Maximise and minimize Z = 4x + 3y -7 Subject to the constraints : x+y <= 10, x +y >= 3, x<=8, y <= 9 , x , y >-0

Long Answer Mar-2018 • PSEB Class 12th

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Mar 2018
Maximise and minimise : Z=15x + 30y Subject to the constraints : x+y <= 8, 2x +y >= 28, x - 2y >=0, x, y >= 0

Solve the following system oflincar equations by matrix mehord:

x - 2y +3z = -5, 3 x +y +c= 8, 2x –y +2z = 1

Or

Using elementary transformations find inverse of ( egin{matrix} 2 & 4 & 1 \ 1 & 2 & 3 \ 1 & -3 & 0 end{matrix})

Long Answer Mar-2018 • PSEB Class 12th

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Mar 2017
Solve the following sysJeur oflinear equations by matrix method :
\r\n\r\n
3 x+y +z=10, 2x-y-z=0, x-y + 2z = 1
\r\n\r\n
or
\r\n\r\n
Using elementary transformation find the inverse of \\(\\begin{bmatrix} 3 & 2 & 1 \\\\[0.3em] 2 & 4 & 3 \\\\[0.3em] 2 & -1 & 2 \\end{bmatrix}\\)

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Frequently Asked Questions

Answers about this subject, solved papers, and preparation.

Updated regularly

01 Where can I find PSEB 12th Class Math previous year question papers for 1st semester on BRpaper?

This Math subject page is meant to help students find PSEB Class 12 previous year Math question papers in one place. You can use it to access subject-wise paper links for revision and to review how board-level Math questions are presented.

02 Are the PSEB 12th Math papers on BRpaper arranged subject-wise?

Yes, this page is focused on Math for PSEB 12th Class Question Papers, so it helps students navigate previous year papers by subject. That makes it easier to revise Maths separately instead of searching across all subjects.

03 How should I use previous year Math papers for PSEB board exam revision?

Use old Math papers to practice question selection, step-based solving, and time management. They can also help you spot repeated topic areas, understand common question styles, and check which chapters need more revision before the exam.

04 What is the difference between previous year Math papers and sample or model papers?

Previous year papers show questions asked in earlier board exams, while sample or model papers are practice papers used to understand the current paper style. For best revision, students often use previous year Math papers for real exam trends and the latest official model paper for updated pattern guidance.

05 Can PSEB 12th Math previous year papers help me understand the exam pattern and marks distribution?

They can help you understand the general paper pattern, question types, and level of presentation commonly seen in Math exams. For exact sections or marks distribution for your session, it is better to also check the latest official sample or model paper because patterns can change.

06 How many previous year PSEB 12th Math papers should I practice?

Students often try to solve multiple recent papers so they can compare question style, difficulty, and recurring topics. A practical approach is to start with the latest available papers first, then use older ones for extra revision and self-assessment.

Solved question paper for Math Mar-2018 (PSEB Class 12th)

Math Mar-2018

Solved Questions

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