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Roll No. 
ND-50/20
Total No. of Questions : 10
Total No. of Printed Pages : 04
RJ-114
B.Sc. B.Ed. (Secondary) Examination, 2024
(First Semester)
MATHEMATICS-DC-II
Calculus
Time : 3 Hours
[Maximum Marks : 60]
Note : There are two Sections. Each question in Section A carries 8 marks. There is internal choice with question in Section A. Each question in Section B carries 4 marks.
Section A
Note : Attempt all questions. All questions carry equal marks.
5×8=40
1.
Discuss the limit at x = 0 for the following function:
f : (0, ∞) → ℝ
f(x) = sin ¼
Or
With giving reasoning find the points of the Domain where the following function is continuous.
f: [0, 1] → R
| f(x) = | { | ¼ | x = p/q, q∈ℤ, q≠0 |
| 0 | x = (0)∪Qc |
State and prove Leibnitz's theorem.
Or
If y = cos (m sin-1 x) prove that :
(1 - x²)yn+2 - (2n + 1) xyn+1 + (m² - n²) yn = 0.
3.
Find the asymptotes of the curve :
x³ + 2x²y + xy² - x² - xy + 2 = 0.
Or
Trace the following function using the concept of concavity, convexity and point of inflexion :
f(x) = 3x&sup4; - 4x³ + 2.
4.
Trace the following curve :
x&sup6; + y&sup6; = 3axy
Or
Trace the conic :
36x² + 24xy + 29y² - 72x + 126y + 81 = 0
5.
Find the whole area of the curve :
a²y² = x² (2a - x).
Or
Find the perimeter of the loop of the curve :
3ay² = x² (a - x).
Section B
Note : Attempt all questions. All questions carry equal marks.
4×5=20
7.
Explain Hyperbolic function with proper diagram.
8.
Trace the following curve whose equation is given in Polar coordinate :
r = a(1 - cos θ)
9.
Give an example of a curve in parametric form.
10.
Explain Quadrature and rectification.