PSEB 12th Sample Paper 2025 Maths

Punjab Board

Sample Academic Year
2025

Paper

MODEL TEST PAPER 2024-25
TIME ALLOWED: 3 hours MATHEMATICS(10+2) MAX. MARKS:80
Instructions:
1. All the questions are compulsory.
2. The question paper consists of 19questions divided into 4sections A,B,C and D.
3. Section A comprises of 2 questions:
(0 Q.NO.I consists of 15Multiple Choice GQuestions carrying Imark each.
(ii) Q.NO.2 consists of 5 Fill in the Blank type questions carrying Imark each.
4. Section Bcomprises of 7 questions of 2 markseach.
5. Section Ccomprises of 7 questions of 4 marks each.
6. Section D comprises of 3questions of 6 marks each.
7. Internal choice has been provided in three questiorns of 2marks, three questions of 4 marksand
three questions of 6marks each. You have to attempt only one of the alternatives in allsuch
questions.
8. Use of calculatorisnot permitted.
SECTION - A
Q1 Choose the correct options in thefollowing questions:
(i) Function f:N ’N, f(x) =x? + 1 is: 1
(AJone-one only (B)onto only (C)one-one and onto (D)neither one-one nor onto

(ii) Relation given by R= {(6,(B)symmetric
(A)reflexive only
b), (g. g). (g, s),only
(s. g)(C)tran
in thesitive
set only
A=(b.g.s)
(D) isequivalence
: relation

(ii) , then value of x is: 1
(A)8 (B)-4 (C)3 (D)-8
matrix B'A is:
(iv) If order of matrix A' is 2 x3 and order of matrix B is 3 x5 then order of 1

(A)5 x 2 (B) 2 x 5 (C) 5 x3 (D) 3x 2
(v) If y = log x, then y" is equal to: 1
(A)1 (B) (C), (D)
Critical point of the function f(x) = x'-10x +2 is: 1
(vi) (C)x =5 (D)x = 2
(A)x = 4 (B)x = 6

(vii) [e2iogx dx is equal to: 1
(A)x + c (C+c (D+c
(vii) x2024 dx is equal to: 2
1
(D) 2025
(A)0 (B) 2024
(C)202S
(ix) Degree of differential equation dx?
(B) 2
d'y2()
+3 siny= 0 is:
(C)1 (D) not defined
1
(A)3
given by:
(x) y= e2* is solution of differential equation + y' = 0 (D) y" - 2y' = 0
1
(A)y"- y' = 0 (B) y" - 4y' = 0 (Cly"
b) then angle between vector å and vector b is:
(xi) If å.b=-låx
V3 271 1
(B) (C)# (D) 3
(A) ;
(xii) If å.b=0then angle between vectors åand b is :
(B) (C) (D) ;
(A) 2 x-1_2y+6 are: 1
(xiii) Direction ratios of line given by 3 12
(C) < 3,6,7 > (D)< 3,6, -7 >
(A) < 3,12,-7 > (B) < 3,-6,7 >
1
(xiv) Common area for each constraint is called: (D)main region
(B)feasible region (C)useless region
(A)infeasible region
(xv) If P(A) = 2 P(B) = 2 and P(An B) = then P(A/B) is equal to:
8
(B) 15 (c): (D):

Q2 Fill in the blanks:
(i) cos(cos) =
(ü) If A= [a,l2x3 Such that a,, = 1
-|i-j| then a2 =
(ii) Jn/4 COtx dx = 1
If a line makes angles
(iv) 135,90',45 with X,V,Z axes respectively, then its direction 1
are
cosines
(v) If Aand B are independent events such 1
that P(B) = 0.3, P(An B) = 0.12, then P(A) = 1

SECTION - B
Q3 If the area of triangle is 3 square units with
vertices(2,0), (0,0) and (1,k), then find k. 2
Q4 Ify= sin' (cos). then fnd ydx
Q5 Find the interval in which function f() =x+ 4x +7 is 2
decreasing. 2
OR
An edge of a variable cube is increasing at the rate of 4 cm/s. How
fast is the volume of the
cube increasing when the edge is 20cm long? 2
dx
Q6 Evaluate
1+Vtanx 2
OR
Evaluate Sdx
V16-9r2
2
Q7 Find the general solution of the differential equation dy = (4 + y?)(1 + 3x²)
dx
2
Q8 Using integration find the area bounded by the parabolay' = 8x straight lines x = 2,x =5 in
the first quadrant. 2
Q9 Find the value of Aif the vectors d= 2i-j- Ak and b=5i-j +2k are
other. perpendicular to each
2
OR

Find the angle between the lines: 1
== 2
and +5 =Y2
3 2
Z-6

4
2

SECTION -C

Q10 Prove that cos-112 + sin-13 sin-1 56
13
4
65

Q11 If 2X +3Y = 4 and 3X +2Y = | , then findXand Y 4

Q12 Differentiate xog x + (log x)* w.r.t. x 4
OR

If x= 3 (cos + log tan ), y =5 sin 0, then find dx 4

Q13 Evaluate S(x-2|+ |x) dx 4
OR
Evaluate f[log(log x) t dx 4

Q14 Find the particular solution of the differential equation dx +2y tan x= sinx :y=0 4
when x = "
Q15 Solve the following linear programming problem graphically:
Maximize and minimize Z= 4x +3y subject to the constraints
4
X +y S 10, 5x +2y 10, 3y >x, X0, y0

Q16 Probability of solving a specific problem independently by A and B are 1/3 and 1/2
4
respectively. If both try to solve the problem independently, find the probability that:
(i)the problem is solved (ii)exactly one of them solves the problem
OR
An insurance company insures 2000 scooter drivers, 4000 car drivers and 6000 truck
drivers. The probability of accidents is 0.01, 0.03 and 0.15 respectively. One of the 4
insured persons meets with an accident. What is the probability that he is a truck
driver ?

SECTION -D

2 -3
Express the matrix A -7 as a sum of a symmetric matrix and a skew 4
Q17(a) -6 5 -4J
symmetric matrix.
If A
then find k so that A + 2/ = kA 2
(b) OR
by matrix method:
Solve the following system of linear2xequations
+ 5y- 3z = -39 4x +2z-2y = 30
6
3x 7y- 2z = 29,
inscribed ina sphere of
Q18 Findthe height of the cone of greatest volume that can be 6
radius 30 cm.
OR
x 6
Solve f dx
+ -2k 2
Q19(a) Find the projection of the vector å= 3- 2î +7k on the vector b = 6
Find any diagonal of the parallelogram whose adjacent sides are given by the vectors 4
(b)
d= 5i + 2j +k and b = î+9j +2k. Alsofindthe area of the parallelogram.
OR
Find the shortest distance between the lines 6
y+23-z z+1
x-1 and
2 2 -2

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