Download PTU (I.K.Gujral Punjab Technical University (IKGPTU)) B-Tech (Bachelor of Technology) BT-Bio Technology 2020 December 2nd Sem 76258 Basic Mathematics Ii Previous Question Paper
Roll No.
Total No. of Pages : 03
Total No. of Questions : 18
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
INST RUCT IONS T O CANDIDAT ES :
1 .
SECT ION-A is COMPULSORY cons is ting of TEN questions carrying TWO marks
each.
2 .
SECT ION - B & C have FOUR questio ns eac h.
3 .
Attempt any FIVE questions from SECT ION B & C carrying EIGHT marks eac h.
4 .
Select atleast T WO que stions from SECT ION - B & C.
SECTION-A
Answer the following :
1.
Find domain and range of the relation R = {(x, y) : y = x + 5, x < 4, x, y N}.
2.
Examine, if the relation R = {(2, 1), (3, 1), (4, 2)} is a function or not?
3.
Draw the graph of exponential function f (x) = ex.
2
x
4
4.
Find the limit lim
.
3
2
x 2
x
4x
4x
z
5.
Find
given that z = x3 + y3 ? 3axy.
x
3
x 1
6.
Evaluate the integral
dx
.
2
x
7.
Evaluate the integral cosec x (cosec x + cot x) dx.
2 3
8.
Evaluate
2
xy dxdy
.
1 1
9.
Define order and degree of a differential equation.
2
dy
y 1
10. Solve
.
dx
4xy
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SECTION-B
2
kx ,
if x 2
11. a) Find the value of k, so that the function f (x)
is continuous at x = 2.
3, if x 2
b) Differentiate xsin x + (sin x)cos x.
12. a) Differentiate sin (tan?1 e?x).
dy
2
1 x
b) Find
, given that y = cos?1
,
0 < x < 1.
dx
2
1 x
13. a) Find local maximum and minimum values of f (x) = 3x4 + 4x3 ? 12x2 + 12.
b) Find absolute maximum and minimum values of f (x) = 2x3 ? 15x2 + 36x + 1, x [1,
5].
u
u
14. a) Show that x
y
2u log u where log u = (x3 + y3) / (3x + 4y).
x
y
y
2
x
u
b) If u = x2 tan?1
2
1
y tan
, then find the value of
.
x
y
x
y
SECTION-C
4
2
tan
x sec
x
15. a) Integrate
.
x
(3 sin 2) cos
b) Integrate
.
2
5 cos 4 sin
16. Using double integration, find area of plate in the form of a quadrant of the ellipse
2
2
x
y
1.
2
2
a
b
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1
17. a) Evaluate
4
5
5x
x 1 d .
x
1
b) Form a differential equation by eliminating the arbitrary constants a and b from y = a
sin (x + b).
dy
1 x
18. a) Find the general solution of the differential equation
, y 2.
dx
2 y
b) Rate of interest in a bank is 5% per year. An amount of Rs. 1000 is deposited with
this bank, how much it worth after 10 years. Solve using differential equations. Given
that e0.5 = 1.648).
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 13 February 2021