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PPSC · PMS Punjab 2023

Mathematics, Paper I

100 marks · 3 hours · 6 questions
This paper Mathematics · all yearsQ. 2(a) · Discuss the validity of Rolle's…Q. 3(a) · Find the area of region…Q. 4(a) · Find the volume of the…Q. 6 · Prove that the function f(z)…Q. 7 · Transform x² + y² -…Q. 8 · Find the tangent line and…With this paper← 20222023 →
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Q. 2(a)
  1. (a)Discuss the validity of Rolle's theorem of f(x) = x(x+3)e -x/2 on [-3,0]. Find 'c' (if possible). [10]
  2. (b)f(a) = f
  3. (c)= 0 f'
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Q. 3(a)
  1. (a)Find the area of region bounded by the curve y = x² - 4x, the x-axis, and the lines x = 1 and x = 3. [10]
  2. (b)Using rectangular rule for n = 5, approximate the value of the definite integral ∫01dx1+x3\int_{0}^{1} \frac{dx}{1+x^3} [10]
Not yet checked
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Q. 4(a)
  1. (a)Find the volume of the tetrahedron bounded by the coordinate planes and the plane xa+yb+zc=1\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1 , where a, b, c are positive. [10]
  2. (b)The area in the first quadrant bounded by the parabola y² = 4ax and its latus rectum is revolved about the x-axis. Find the volume of the solid generated. [10]
Not yet checked
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Q. 6
  1. (a)Prove that the function f(z) = ∣ x y ∣ \sqrt{|xy|} ∣ x y ∣ ​ is not differentiable at origin although Cauchy- Riemann conditions are satisfied at origin. [10]
  2. (b)Evaluate ∮Cz(z−1)(z+2i)dz\oint_{C} \frac{z}{(z-1)(z+2i)}dz where (i) C:|z| = 2, (ii) C:|z| = 3/2. [10]
Not yet checked
(20)
Q. 7
  1. (a)Transform x² + y² - z = 9 into spherical coordinates. [10]
  2. (b)The tangent at any point on the curve x³ + y³ = 2a³ makes intercepts p and q on the coordinate axes respectively. Show that p -3/2 + q -3/2 = 2 -1/2 a -3/2 [10]
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Q. 8
  1. (a)Find the tangent line and normal plane to the curve x ⃗ = t e ^ 1 + t 2 e ^ 2 + t 3 e ^ 3 \vec{x} = t\hat{e}_1 + t^2 \hat{e}_2 + t^3 \hat{e}_3 x = t e ^ 1 ​ + t 2 e ^ 2 ​ + t 3 e ^ 3 ​ at t = 1. [10]
  2. (b)Find the curvature and torsion of $r⃗=(acos⁡θ,asin⁡θ,acot⁡α) \vec{r} = (a \cos \theta, a \sin \theta, a \cot \alpha) . [10]
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About this paper

The 2023 PMS Punjab Mathematics paper set by the PPSC. Question wording only; questions marked “Not yet checked” have not been compared with the official paper yet.

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