Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech Bio-Technology (Biotechnology Engineering) 2020 March 2nd Sem BTAM 207 Basic Mathematics Ii Previous Question Paper
Roll No. Total No. of Pages : 03
Total No. of Questions : 09
B.Tech. (Bio Tech) (2018 & Onwards) (Sem.?2)
BASIC MATHEMATICS-II
Subject Code : BTAM-207-18
M.code : 76258
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION - B & C have FOUR questions each.
3. Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
4. Select atleast TWO questions from SECTION - B & C.
SECTION-A
l. Answer the following :
a) Define an onto function, also give an example of an onto function.
b) Find the domain of the function f (x) = log (sin x), ? 0 ? x ? 2 ?.
c) Give an example of a function which is continuous but not differentiable.
d) Find the derivative of e
x sin x
with respect to x.
e) Find partial derivative of f w.r.t. x, if f (x, y) =
cos
xy
xy x ?
.
f) Solve ? log x dx.
g) Evaluate the integral ? e
x
sin x dx.
h) Form a differential equation representing the family of curves y = mx where, m is
arbitrary constant.
i) Form a differential equation whose order is 2 and degree is 3.
j) Define a homogeneous function of degree n also give one example of a homogeneous
function of degree 2.
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1 | M-76258 (S1)-2039
Roll No. Total No. of Pages : 03
Total No. of Questions : 09
B.Tech. (Bio Tech) (2018 & Onwards) (Sem.?2)
BASIC MATHEMATICS-II
Subject Code : BTAM-207-18
M.code : 76258
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION - B & C have FOUR questions each.
3. Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
4. Select atleast TWO questions from SECTION - B & C.
SECTION-A
l. Answer the following :
a) Define an onto function, also give an example of an onto function.
b) Find the domain of the function f (x) = log (sin x), ? 0 ? x ? 2 ?.
c) Give an example of a function which is continuous but not differentiable.
d) Find the derivative of e
x sin x
with respect to x.
e) Find partial derivative of f w.r.t. x, if f (x, y) =
cos
xy
xy x ?
.
f) Solve ? log x dx.
g) Evaluate the integral ? e
x
sin x dx.
h) Form a differential equation representing the family of curves y = mx where, m is
arbitrary constant.
i) Form a differential equation whose order is 2 and degree is 3.
j) Define a homogeneous function of degree n also give one example of a homogeneous
function of degree 2.
2 | M-76258 (S1)-2039
SECTION-B
2. a) Find all points of discontinuity of the function defined by
| |
, 0
( )
0, 0
x
if x
f x x
if x
?
?
?
?
?
?
?
?
b) Differentiate tan
?1
sin
. . .
1 cos
x
w r t x
x
? ?
? ?
?
? ?
.
3. Differentiate the function x
sin x
+ (sin x)
x
w.r.t. x.
4. a) Find the interval in which the function f (x) = x
4/3
? 4x
1/3
is increasing and decreasing.
b) Find maxima and minima, if any, of the function f (x) = sin x + cos x, 0 < x < ?/2.
5. a) Show that the function
3
6 2
( , ) (0,0)
( , )
0 ( , ) (0,0)
x y
x y
f x y
x y
x y
?
? ?
? ?
?
?
?
is not continuous at (0, 0),
also check whether its partial derivatives f
x
and f
y
exist at (0, 0).
b) Find the local extreme values of the function
f (x, y) = 4x
2
? 6xy + 5y
2
? 20x + 26y
SECTION-C
6. a) Find the area lying above x-axis and included between the circle x
2
+ y
2
= 8x and
inside of the parabola y
2
= 4x.
b) Solve the integral
2
6
1
x
dx
x ?
?
.
7. a) Evaluate
2
0
sin
1 cos
x x
dx
x
?
?
?
.
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Roll No. Total No. of Pages : 03
Total No. of Questions : 09
B.Tech. (Bio Tech) (2018 & Onwards) (Sem.?2)
BASIC MATHEMATICS-II
Subject Code : BTAM-207-18
M.code : 76258
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION - B & C have FOUR questions each.
3. Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
4. Select atleast TWO questions from SECTION - B & C.
SECTION-A
l. Answer the following :
a) Define an onto function, also give an example of an onto function.
b) Find the domain of the function f (x) = log (sin x), ? 0 ? x ? 2 ?.
c) Give an example of a function which is continuous but not differentiable.
d) Find the derivative of e
x sin x
with respect to x.
e) Find partial derivative of f w.r.t. x, if f (x, y) =
cos
xy
xy x ?
.
f) Solve ? log x dx.
g) Evaluate the integral ? e
x
sin x dx.
h) Form a differential equation representing the family of curves y = mx where, m is
arbitrary constant.
i) Form a differential equation whose order is 2 and degree is 3.
j) Define a homogeneous function of degree n also give one example of a homogeneous
function of degree 2.
2 | M-76258 (S1)-2039
SECTION-B
2. a) Find all points of discontinuity of the function defined by
| |
, 0
( )
0, 0
x
if x
f x x
if x
?
?
?
?
?
?
?
?
b) Differentiate tan
?1
sin
. . .
1 cos
x
w r t x
x
? ?
? ?
?
? ?
.
3. Differentiate the function x
sin x
+ (sin x)
x
w.r.t. x.
4. a) Find the interval in which the function f (x) = x
4/3
? 4x
1/3
is increasing and decreasing.
b) Find maxima and minima, if any, of the function f (x) = sin x + cos x, 0 < x < ?/2.
5. a) Show that the function
3
6 2
( , ) (0,0)
( , )
0 ( , ) (0,0)
x y
x y
f x y
x y
x y
?
? ?
? ?
?
?
?
is not continuous at (0, 0),
also check whether its partial derivatives f
x
and f
y
exist at (0, 0).
b) Find the local extreme values of the function
f (x, y) = 4x
2
? 6xy + 5y
2
? 20x + 26y
SECTION-C
6. a) Find the area lying above x-axis and included between the circle x
2
+ y
2
= 8x and
inside of the parabola y
2
= 4x.
b) Solve the integral
2
6
1
x
dx
x ?
?
.
7. a) Evaluate
2
0
sin
1 cos
x x
dx
x
?
?
?
.
3 | M-76258 (S1)-2039
b) Solve the integral Evaluate
2
(3sin 2)cos
5 cos 4sin
d
? ? ?
?
? ? ? ?
?
.
8. Solve the differential equation
(x dy ? y dx) y sin
y
x
= (y dx + x dy) x cos
y
x
.
9. a) Find general solution of the following differential equation
2
cos tan
dy
x y x
dx
? ? (0 ? x ? ?/2)
b) Form the differential equation representing the family of curves y = ae
3x
+ be
?2x
,
where a and b are arbitrary constants.
NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.
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This post was last modified on 21 March 2020