Thapar University 2006 M.Tech Mechanical Engineering Basic Mathematics (MA 502) - Question Paper
Thapar Institute Of Engineering & Technology, Patiala
End Semester Examination, 2006
Mechanics of Deformed Bodies
Thapar Institute of Engineering & Technology End semester Examination Dec. 09, 2006 Time: 3 hrs Subject: Basie Mathematics ( MA-502) MM : 45
Note: Attempt any five questions. Do all questions in sequence.
Ql(a) If the sum of the roots of equation x2 -px + q = 0 be m times their 3
difference, then prove that p2{m2 -1) = 4nrq.
Solve the equation jt(.y + 3) + 3-v/(2;r + 6,v + $) = 25 3
(c) Find the coefficients of *10 and x6 in the expansion of I 2x2 I .
Q2(a) Show that the coefficient of mid term of (1 + j)2" is equal to the sum of 3 the coefficient of the two mid terms of((1 + x)2*~].
If (jc + j)1 3 ~a + ib. Prove that 4(a2 -b2) = + .
a b
<c) Find the square root of-2 + 2V3/. 3.5
|
Q3(a) |
a |
y a |
a3 -1 |
|
If |
b |
b2 |
by-1 |
|
c |
c2 |
c3 -1 |
3.5
= 0, in which a,b and c are different, show that abc = 1.
(b) Apply the Cramer's rule to solve the equations 2.5 3-v + y + 2z - 3, 2.v - 3y - z = -3, x + 2y + r = 4
(c) Find n if 2""' Pn :2n_1 = 22:7. 3
Q4(a) Find the intervals on which f{x) = -x} + 12.v + 5, -3<.v<3is 2.5
increasing and decreasing. Where does the function assume extreme values and what are these values?
(b) .. 2 i(5
4.5
Graph the function v = x~' \ ~~x
(c) ln how many ways four books of physics three books of chemistry and 2 two hooks of mathematics can be arrange in a shelf so that books of the same subjects are put together.
Q5(a) v2 xi 2.5+
Evaluate the integrals (i) ,, ,ax (n) -1-dx
0JV(37m] J(*-2)(* + 1)(2.v + 3)
(b) Find the general solution of the following differential equation 3
(.v3 + 3*y2 )dx + (3 x2y + v3 )dy = 0
Q6(a) Find the solution of 2y" - 4y + 8y = 0, y(0) = 1, y(Q) = 1 4.5
(b) The vertices of a quadrilateral are (6,3), (-3,5), (4,-2) and (x,3x) denoted 4.5 by A. B, C and D respectively. Find the values of x so that the area of triangle ABC is double the area of triangle DBC
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Attachment: |
| Earning: Approval pending. |
