312301
23242
3 Hours / 70 Marks Seat No.
Instructions – (1) All Questions are Compulsory.
(2) Answer each next main Question on a new page.
(3) Illustrate your answers with neat sketches wherever
necessary.
(4) Figures to the right indicate full marks.
(5) Assume suitable data, if necessary.
(6) Use of Non-programmable Electronic Pocket
Calculator is permissible.
(7) Mobile Phone, Pager and any other Electronic
Communication devices are not permissible in
Examination Hall.
Marks
1. Solve any FIVE of the following: 10
a) Evaluate : # c 1 +1 x2 + 5 x n dx
b) Evaluate : ∫ tan2x dx
2
c) Evaluate : # dx
1
2x + 11
d) Find the order and degree of the following differential
equation.
d2 y dy 3
1 + c dx m
dx2 =
e) Show that there exist a root of the equation x2 – 2x – 1 = 0
in ( –1, 0 )
P.T.O.
23242
3 Hours / 70 Marks Seat No.
Instructions – (1) All Questions are Compulsory.
(2) Answer each next main Question on a new page.
(3) Illustrate your answers with neat sketches wherever
necessary.
(4) Figures to the right indicate full marks.
(5) Assume suitable data, if necessary.
(6) Use of Non-programmable Electronic Pocket
Calculator is permissible.
(7) Mobile Phone, Pager and any other Electronic
Communication devices are not permissible in
Examination Hall.
Marks
1. Solve any FIVE of the following: 10
a) Evaluate : # c 1 +1 x2 + 5 x n dx
b) Evaluate : ∫ tan2x dx
2
c) Evaluate : # dx
1
2x + 11
d) Find the order and degree of the following differential
equation.
d2 y dy 3
1 + c dx m
dx2 =
e) Show that there exist a root of the equation x2 – 2x – 1 = 0
in ( –1, 0 )
P.T.O.
