Download AKTU B-Tech 2nd Sem 2016-17 RBT203 Elementary Mathematics II Question Paper

Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU)) B-Tech 2nd Semester (Second Semester) 2016-17 RBT203 Elementary Mathematics II Question Paper

PrintedPages :2 Roll No.| l l l l I l l l l l RBT203
B. TECH.
THEORY EXAMINATION (SEM?II) 2016-17
ELEMENTARY MATHEMATICS - II
Time : 3 Hours Max. Marks : 70
Note : Be precise in your answer.
SECTION ? A
1. Attempt all parts of the following questions: 7 x 2 = 14
(3) Evaluate I(xz + 1) dx.
. . . . d 2y d)? 2 dy
(b) F1nd the order and degree of the d1fferent1al equatlon x?Z + (?) ? ? = 0.
dx dx dx
6
(c) Find unit vector in the direction of the vector a 2 2i + 3 j + k.
(d) If a line has direction ratios 2, ?1, -2, determine its direction cosines.
(e) Find magnitude of the vector ; = i + j + k.
1
(f) j ede.
0
(g) Write formula for equation of line passing through a given point and parallel to a given
vector.
SECTION ? B
2. Attempt any three parts of the following questions: 3 x 7 = 21
(3) Find the area of a triangle having the points A(1, 1, 1), B(1, 2, 3) and C(2, 3, 1) as its
vertices.
2
(b) Find the solution of the differential equation d?y = ?3/2.
dx 1+x
1 ?1
t
(c) Evaluate I an 2x dx.
O1+x
(d) ((1) Find the vector equations of the plane passing through the points R(2, 5, ?3), S(?2, -
3, 5) and T(5, 3, ?3).
4)
(e) Show that the vectors a 2 2i _ 3j + 4k and b 2 4? + W _ 81?
are collinear.
SECTION ? C
3. Attempt any two parts of the following: ( 3% x 2 = 7)
1 3
(3) Evaluate I(xz + e" + sin x)dx.
O
(b) Evaluate leog xdx.
(c) Find the area enclosed by the circle X2 + y2 = a2.
4. Attempt any two parts of the following: ( 3% X 2 = 7)
. .3, . . . . . d 2 y dy
(a) Verlfy that y = e 1s a solutlon 0f the dlfferentlal equatlon dx2 + a ? 6y = 0.
(b) Find the general solution of the differential equation 2?: = g.

(c) Find the general solution of the differential equation x 2?: + 2 y = x2.
Attempt any two parts of the following: ( 3% X 2 = 7)
(3) Find projection of the vector a = 21' + 3 j + 2k 0n the vector 17 = i+ 2 j + k.
9?
(b) Find axbifZ=2i+j+3k and Z=3i+5j?2k.
(c) Find angle between the vectors a = i+ j ? k and b = i? j +k.
Attempt any two parts of the following: ( 3% x 2 = 7)
(3) Find the vector equation for the line passing through the points (?1, 0, 2) and (3, 4, 6).
(b) Find the equation of the plane with intercepts 2, 3 and 4 on the X, y and z?aXis
respectively.
(c) Find the angle between the two planes 2x + y ?2z = 5 and 3x ? 6y -2z = 7 using vector
method.
Attempt any two parts of the following: ( 3% X 2 = 7)
(a) If P(A) = % P(B) = 19?3 and P(A?B) = % evaluate P(A|B) and P(AUB).
(b) Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card
is drawn randomly. If it is known that the number on the drawn card is more than 3,
what is the probability that it is an even number?
(c) An unbiased die is thrown twice. Let the event A be ?odd number on the first throw?
and B the event ?odd number on the second throw?. Check the independence of the
events A and B.