[BA 1st Sem Question Papers, Dibrugarh University, 2014, Mathematics, General]
1. (a) Write the range set of the sequence 
1
1
(b) Prove that every convergent sequence is bounded. 4
(c) State and prove Cauchy’s general principle of convergence. 1+4=5
Or
Define monotonic sequence. Prove that 
is convergent, when
is convergent, when 
2. (a) State the Cauchy’s root test for convergence.
(b) Prove that a necessary condition for a infinite series 
to be convergent that 
to be convergent that
(c) Test for convergence: 3
(d) Discuss the convergency or divergency of the following (any one): 5
3. (a) Write the fundamental theorem of algebra. 1
(b) Show that 
has at least two imaginary roots. 2
has at least two imaginary roots. 2
(c) Solve the equation
Where the sum of two roots is zero 3
(d) Solve by Cardan’s method (any one):
(e) If 
is a factor of 
then show that 
is a factor of then show that
GROUP – B
(Trigonometry)
4. (a) Express
in De Moivre’s form.
in De Moivre’s form.
(b) Find the values of
.
.
(c) If n is a positive integer, prove that
Or
If 
then prove that
then prove that
.
5. If 
then prove that 5
then prove that 5
6. Prove that 4
7. (a) Find the sum of the series:
(b) Find the sum of the series (any one):
GROUP – C
(Vector Calculus)
8. (a) Define space curve.
(b) A particle moves along a curve 
where 
time is. Find the velocity and acceleration at 
where time is. Find the velocity and acceleration at
(c) If 
, then find the unit normal vector to the surface of 
at 
. 3
, then find the unit normal vector to the surface of at . 3
(d) If 
then prove that 
2
then prove that 2
(e) Prove any one of the following: 4
- grad
(f) Prove that
Also Read: Dibrugarh University Question Papers
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