Mathematics 2024
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BS ZOOLOGY first semester Animal diversity ZOOL 101 - university of Punjab 2025
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Literary criticism
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this paper consists of 60 marks but now we have 35 marks paper.
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Can you please tell me more past papers please because my exams are starting from next week
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Did you provide the past papers of the science of society uos?
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Paper text
FEDERAL PUBLIC SERVICE COMMISSION
COMPETITIVE EXAMINATION-2024 FOR RECRUITMENT
TO POSTS IN BS-17 UNDER THE FEDERAL GOVERNMENT
APPLIED MATHEMATICS
TIME ALLOWED: THREE HOURS
MAXIMUM MARKS = 100
NOTE:
(i) Attempt only FIVE questions in all. ALL questions carry EQUAL marks.
(ii) All the parts (if any) of each Question must be attempted at one place instead of at different
places.
(iii) Write Q. No. in the Answer Book in accordance with Q. No. in the Q.Paper.
(iv) No Page/Space be left blank between the answers. All the blank pages of Answer Book must
be crossed.
(v) Extra attempt of any question or any part of the attempted question will not be considered.
(vi) Use of Calculator is allowed.
Q. No. 1
(a) Expand a fourier series of f(x) = x², 1 < x < 2
(b) Find equation of integral surface of the differential equation 2y(z - 3)p +
(2x - z)q = y(2x -
3) which passes through the circle x² + y² = 2x, z =
0.
Q. No. 2
(a) Solve the higher order differential equation y''' + y" = 3x² + 4Sinx - 2Cosx
(b) Solve the initial value problem y" - 8y' + 15y = 9xe²x, y(0) = 5, y'(0) = 10
Q. No. 3
(a) Solve the equation 4uxx + 5uxy + uyy + ux + uy = 2, also find its canonical
form.
(b) Prove that ∫₋₁¹ xⁿ Pₙ(x)dx = 2ⁿ⁺¹(n!)² / (2n+1)! where Pₙ(x) = 1 / 2ⁿn! dⁿ/dxⁿ (x² - 1)ⁿ is
Legender polynomial of degree n.
Q. No. 4
(a) Verify the divergence theorem for A = 4xi - 2y²j + z²k taken over the region
bounded by x² + y² = 4, z = 0 and z =
3.
(b) State and prove Stoke's theorem.
Q. No. 5
(a) Using the modified Euler's method, obtain the solution of the differential equation
dy/dt = t + √y = f(t,y)
with initial condition y₀ = 1 at t₀ = 0 for the range 0 ≤ t ≤ 0.6 in step of 0.2.
(b) Find the real roots of equation 4x + Cosx + 2 = 0 by using Newton Raphson
method, correct to four decimal places.
Q. No. 6
(a) Solve the system of linear equations by Guass-Seidel iterative method and perform
the first three iterations of
20x + y - 2z = 17
3x + 20y - z = -18
2x - 3y + 20z = 25
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