Name of the University : Alagappa University
Degree : B.Sc
Department : Mathematics
Subject Code/Name : Differential Calculus and Trigonometry
Semester : I
Document Type : Model Question Papers
Website : alagappauniversity.ac.in
Download Model/Sample Question Paper : NOV.2010 : https://www.pdfquestion.in/uploads/alagappauniversity.ac.in/3931.-B.Sc.MATHS%20CBCS.pdf
Alagappa University Differential Calculus Question Paper
Part A
1. Find the nth derivative of sin 3x cos 2x.
2. If x sin t = , and y = sin pt prove
Related : Alagappa University Topology II M.SC Model Question Papers : www.pdfquestion.in/3892.html
3. Find the length of the sub tangent and subnormal
4. Find the polar sub tangent and polar subnormal
5. Find the radius of curvature for y = ex at (0, 1).
6. Find the radius of curvature for pr = a2 at the point (p, r).
8. Expand sin2 – cos – in-terms of cosines of multiples of 0
Show that the curves.r = a (1 + sin – ) ; r = b (1 – sin – )
Find the slope of the curve r = ae- at – = 4.
Find the radius of curvature.
Expand cos5 – sin3 – is a series of series of multiples of –
If x + iy = sin (A + iB) prove thats
Prove that the rectangular solid of maximum volume
Find the evolute of x = a (- – sin – ) ; y = a (1 – cos – )
Prove that the equationa h sin – – bk cosec – = a2 – b2
sum of the values of – which satify it is equal to an odd
Find the direction cosine’s of the line
Find the distance of a point (3, 4, 5) from the point of
Find the angle between x – 2y – 3z – 4 – 0 and
Determine the constant ‘a’ so that the vector
Find the tangent plane to the sphere
State Stokes theorem.
Part B
Find the image of the point (1, 2, –3) on the plane
Find the bisector of the acute angle between the
Find the equation of the cone whose vertex is
Prove that div – u – v- – v. curl u – u. curl v.
Two system of rectangular axes have the same origin.
Find the unit normal to the surface xy3z2 = 4 at
Verify Gauss divergence theorem for f – yi – x j – z2 k
Define Half range Fourier series.
Find the Fourier coefficient ao for the functions
Prove that a monotonic sequence cannot be an
State Leibnitz test. Hence show that the series
Verify whether ey dx + (xey + 2y) d y = 0 is exact .
Verify the condition of integrability.
find partial differential equation.
Solve : (x2 + y2 + x) dx + xy dy = 0
Solve : x2 y ”- 3xy ‘- 5y – sin(log x)
Solve : (2x + 1)2 y ”- 2(2x – 1) y ‘- 12y – 6x
Solve by method of variation of parameter
Solve by Charpits method :
Part C
1. Give an example of a group.
2. Show that (N, +) is not a group.
3. State Lagrange’s theorem.
4. State Fermat’s theorem.
5. Define normal subgroup.
6. Write the quotient group Z/3Z.
7. Prove that f : (Z, – )- (2Z, – ) defined by f (x) – 2x is a homomorphism.
Prove that a group of prime order is cyclic.
Prove that the characteristic of an integral domain
Let A and B be two subgroups of a group. Then prove
State and prove Fundamental theorem of Hormomorphism.
Fuzzy Algebra
(CBCS—2008 onwards)
Time : 3 Hours
Maximum : 75 Marks
Part- A (10 × 2 = 20)
Answer all questions.
1. Define Normal and Subnormal fuzzy set.
2. Define support of fuzzy set with example.
3. Define fuzzy intersection with example.
4. State D’Morgan’s laws.
5. State the first Decomposition theorem.
6. State the boundary conditions on fuzzy complement.
7. State the monotonicity condi tion on fuzzy complement.
8. Define fuzzy ideal with example.
9. Define Fuzzy group and give an example.
Part- B : (5 × 5 = 25)
Answer all questions, choosing either (a) or (b).
10. (a) Write short notes on fuzzy sets and height of a fuzzy set with examlpes.
11. (a) Write any five properties of fuzzy intersection with suitable examples. (Or)
(b) Explain all standard fuzzy operations.
12. (a) Prove that every fuzzy complement has atmost one equilibrium. (Or)
(b) Explain fuzzy complement properties.
Part- C : (3 ×10 = 30)
Answer any three questions.
13. State D’Morgan’s laws and verify then with suitable examples.
14. State and prove the Second Decomposition theorem.
15. State and prove the first characterization theorem of fuzzy complement.