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Model Question Paper (CBCS) with effect from 2018-19
USN 17MATDIP31
Third Semester B.E.Degree Examination
Additional Mathematics-I
(Common to all Branches)
Time: 3 Hrs Max.Marks: 100
Note: Answer any FIVE full questions, choosing at least ONE question from each module.
Module-I
1. Define dot product between two vectors A and B.Find the sine of the angle between
A i j k

2 2 and B i j k

2 2 . (08 Marks)
Express 5 2i in the polar form and hence find its modulus and amplitude. (06 Marks)
Find the real part of
1
1
i
(06 Marks)
OR
2. Show that cos sin cos sin 2 cos 1 i i n n n (08 Marks)
If A i j k

2 2 and B i j k

2 2 show that

and

are orthogonal. (06 Marks)
Find the value of so that the vectors A i j k

3 5 3 B i j k

2 and (06 Marks)
C i j k

2 2 are coplanar.
Module-II
3. If x tanlog prove that 0. 1 1
2 n x y nx y n n y (08 Marks)
Find the angle between the curves r a n n cos and r b n n sin .
(06 Marks)
Using Euler's theorem, prove that xu yu u x y sin 2 ,where u y 3 3 tan . (06 Marks)
OR
4. Obtain the Maclaurin's series expansion of logsec x up to the terms containing . 6 x (08 Marks)
Find the pedal equation of the following curve 2a . (06 Marks)
If u f y z show that 0 x y z u u u
(06 Marks)
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17MATDIP31
Module-III
Obtain a reduction formula for sin
2
0


xdx n n (08 Marks)
Evaluate:


0
2 3
2
1 x
x dx
(06 Marks)
Evaluate: y zdydxdz
z x z
x z





1
1 0
(06 Marks)
OR
6. Obtain a reduction formula for
2
0
cos 0

xdx n n
(08 Marks)
Evaluate x ax x dx
a
2
2
0
3 2
(06 Marks)
Evaluate
R
xydxdy where R is the first quadrant of the circle 0. 2 2 2 x y a x y (06 Marks)
Module-IV
7. A particle moves along a curve x e y t z t t 2cos3 2sin3 where t is the time variable. Determine
the components of velocity and acceleration vectors at t 0 in the direction of i j k

. (08 Marks)
Find the directional derivative of 2 3 xy yz at the point the direction of the vector
i 2 j 2k.

(06 Marks)
Find the values of the constants c such that F y y j cy

2 2
is irrotational. (06 Marks)
OR
8. If F y j

show that F 0

(08 Marks)
If 3 3 3 3 x y z x y z xyz find at (06 Marks)
Show that vector field 2 2 F xi yj x y

is solenoidal. (06 Marks)
Module-V
9. Solve: 2 2 0 2 2 2 2 x xy y dx y xy x dy (08 Marks)
Solve: cos log x xsin 0 (06 Marks)
Solve: y y 2 1 tan (06 Marks)
OR
10. Solve: 2y y 0 (08 Marks)
Solve: 4 3 0 2 3 2 2 2
y e x dx xye y dy xy xy (06 Marks)
Solve: cos y xsin dy 3 2 (06 Marks)