Visvesvaraya Technological University (VTU) 2007 B.E MATHS1 - Question Paper

Q3.a. (i) The value of
1
2 23/2
0
(1 ) x x dx - ? is
(A) p/32 (B) - p/32 (C) 0 (D) 1/32
(ii) The formula of the asymptote of x3 + y3 = 3axy is
(A) x + y -a=0 (B) x - y + a =0 (C) x + y + a = 0 (D) x – y – a = 0
(iii) A curve r = a (1+cos?) has a maximum value
(A) a (B) 2a (C) -2a (D ) 0
(iv) If In = ? tann ? d? ,then which of the subsequent is actual
(A) one 1 ( ) n n n I I + - + =1 (B) one 1 n n I I + - + = one (C) one 1 ( ) n n n I I + - - = one (D) one n n I I + + =1
(1x four = 4)
b. 0btain the reduction formula for ? cosnx dx (4)
c. Evaluate
2 2
2
0 2
a x dx
ax x - ? (6)
d. Trace the curve r2 = a2 cos2? (6)
Q.4 a. (i) The complete area of the curve 2/3 2/3 2/3 x y a + = is
(A) 2a (B) -a (C) 0 (D) 6a
(ii) The length of the loop of the curve two 2 three ( ) ay x x a = - is
(A) two / three a (B) four / three a (C) three / a (D) three / 4a -
(iii) The quantity of the curve r = a( 1+ cos?) about the initial line is
(A)
3 4
3
a p
(B)
3 2
3
a p
(C)
3 8
3
a p
(D)
3
3
a p
(vi) The surface area of the sphere of radius ‘a’ is
(A) two pr2 (B) four pa2 (C) four pr (D) four pa (1x four = 4)
b. obtain the length of the arc of the curve y =log secx ranging from the
points x = 0 to x= p/3 (4)
c. obtain the area bounded by the curve r2 =a2 cos2? (6)
d. Evaluate
0
log (1 cos ) x dx
p
a + ? , using differentiation under integral sign (6)
PART -B
Q5 a. (i) The solution of the differential formula tan dy y y
dx x x
? ? = + ? ?
? ?
is
(A) cos(x/y) = c (B) sin(y/x) = c (C) sin -1(x/y)=cx (D) cos(y/x)=cx
(ii) The solution of the differential formula dy y
dx x xy
=
+
is
(A) two log y y c
x
+ = (B) two log x y c
y
= + (C) three log x x c

Earning:   Approval pending.