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

First Semester B.E. exam
Engineering Mathematics- I (06MAT11)
Time:03 Hours Max Marks:100
Model ques. Paper
Note: 1. ans any 5 full ques. selecting at lowest 2 ques. from every
Part
2. ans all objective kinds ques. only in 1st and 2nd writing pages.
3. Objective kinds ques. should not be repeated.
PART - A
Q1. a ( i ) If y = xn log x, then yn+1 is
(A) (n-1)! / x (B) n! / x (C) n! / xn (D) -n! / xn
(ii) The angle ranging from radius vector & tangent is
(A) tan d r
dr
?
f= (B) tan dr r
d
f
?
= (C) one tan dr
r d
f
?
= (D) tan dr
d
f
?
=
(iii) The nth derivative of log (ax + b) is
(A)
1 ( 1) ( 1)!
( )
n n
n
n a
ax b
- - -
+
(B) 1
( 1) !
( )
n n
n
n a
ax b +
-
+
(C)
1
1
( 1) ( 1)!
( )
n n
n
n a
ax b
-
+
- -
+
(D)
2
1
( 1) ( 2)!
( )
n n
n
n a
ax b
-
+
- -
+
(iv) Angle ranging from the 2 curves r = sin? + cos? and r = two sin? is
(A) -3p / four (B) p / four (C) - p / four (D) p / two (1x four = 4)
b. obtain the nth derivative of e-2x cos32x (4)
c. If y = a cos (logx) + b sin(logx) prove that two 2
2 one (2 1) ( 1) 0 n n n x y n xy n y + + + + + + = (6)
d. obtain the pedal formula of the curve rn = an cosn? (6)
Q.2. a (i) If u = x2 + y2,then
2u
x y
?
? ?
is equal to
(A) -2 (B) two (C) 0 (D) two x + 2y
(ii) If ( ) ( ) u f x ay g x ay = + + - ,then the value
2 2
uy
? ?
is
(A)
2
2
u
x
? ?
(B)
2
2
u a
x
? ?
(C)
2
2
2
u a
x
? ?
(D)
2u
x y
?
? ?
(iii) If one 1 sin n x y u ta
y x
- - ? ? ? ? = + ? ? ? ?
? ? ? ?
then u u x y
x y
? ?
+
? ?
is
(A) -1 (B) one (C) 0 (D) -2
(iv) If u = x (1-y) and v = xy, then the value of JJ1
(A) two (B) -1 (C) one (D) 0 (1x four = 4)
b. If u is a homogeneous function of x & y with degree n, then
prove that u u x y nu
x y
? ?
+ =
? ?
(4)
c. If one 1 n sin y x u ta y
x y
- -? ? ? ? = + ? ? ? ?
? ? ? ?
then prove that
2 two 2
2 2
2 two 2 0 u u u x xy y
x xy y
? ? ?
+ + =
? ?? ?
(6)
d. If xy u
z
= , yz v
x
= , xz w
y
= then verify that JJ1 = one (6)

Earning:   Approval pending.