Download AKTU B-Tech 1st Sem 2015-2016 BT 101 Engineering Mathematics I Question Paper

Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU)) B-Tech 1st Semester (First Semester) 2015-2016 BT 101 Engineering Mathematics I Question Paper

Printed Pages: 4 171 BT-101
(Following Paper ID and Roll No. to be filled in your
Answer Book)
Roll No.
B.Tech.
(SEM. I) THEORYEXAMINATION, 2015-16
ENGINEERIN G MATHEMATICS - I
[Time:3 hours] [Total Marks:100]
SECI'ION?A
Note : Attempt all parts. All parts can'y equal marks. Write
answer of each part in short. (2 ><10=20)
. Sin 6x
1. (a) Evaluate 11m? 0 .
5x
. . . 1 1
(b) Fmd the denvatlve of + .
tan x cot x
(c) State lagrange?s mean value theorem.
((1) Find the critical points of f(x)=9x2+12x+2.
(6) Evaluate: [(1 ? x)?/; dx .
71'
(0 Evaluate: J03 coszx dx.
300 (1) P.T.O.

(g) F ind the order and degree of the given differential
equation y"+2y'+ sin y = 0 .
(h) Form the differential equation representing the
family of curves y=mx, where m is the arbitrary
constant.
(i) If 2/11 is the probability of an event, what is the
probability of the event ?notA?.
(i) If P(A)=7/l3, P(B) and P(Pn B) = 4/13, ?nd
P(A/B).
SECTION?B
Note: Attempt any ?ve questions from this sections.
(10 X 5=5 O)
b ? ax, if x > 1
For the ?mction f(x), given by f(x)= 4, if x =1
a+bx ifx<1
?\
. E"
if x 1: 1 f(x) = f(l) , ?nd the value of a and b.
t d
3. If y=a sint, x=a (cost+logtan?) ?nd 3y .
- 4. If y=3 cos(log x)+4 sine(log x), show that
X?y2+xyl+y=0.
5. Integrate : eJr (Sin x + cos x)
6. Solve xg+2y=leogx
300 (2) BT-101
.L _ M?A ~
_> -k?hz?. _
_. ~ f?..-?\..?.?w:m;wmmwmgu?-?-??g?: - -'
7. solve sec2 x tanydx+sec2 ytanxdy = 0
8. Bag I contains 3 red and 4 black balls while another bag
11 contains 5 red and 6 black balls. One ball is drawn at
random from one of the bags and it is found to be red.
F ind the probability that it was drawn from bag 11.
s
9. Evaluate limx?n x 3? 32
x ? 8
SECTION-C
Note: Attempt any two questions from this section.
( l 5 X2=30)
10. (a) Differentiate the functions (sin x)? +sin?1J;
with respect to x.
in t epomt atw 1c e tan ent tot e curve
(b) F' d h ' h' hth g h
y = ?/4x?3 ?1 has its slope 2/3.
2
11. (a) Integrate the function (logx) .
x
(b) Solve (x3+x2+x+1)gxy?=2xz+x;y=l when x=0-
(c) F ind the integration, the area of the region bounded
by curves, y2 = 4ax and x2 = 4ay -
300 (3) P.T.O.

12. (a)
(b)
(0)
In class XI of a school 40% of the student study
Mathematics and 30% study Biology. If a student
is selected at random from the class, ?nd the
probability that he will be studying Mathematics
or Biology.
In a school, there are 1000 students, out of which
430 are girls. It is know that out of 430,10% of
the girls study in class XII. What is the probability
that a student chosen randomly studies in class XII
given that the chosen student is a girl?
Let X denote the no of hours you study during a
randomly selected college day, the probability that
X can take the value x, has the following form,
where k some unknown constant:
0.1, ifx=0
PX Iocifleorx=2
( ?x)? k(5?x), ifx=3or4
0, otherwise
Find the value of k and what is the probability that you
study at least two hours? Exactly two hours? At most
two hours?
300
(4) BT?lOl