Download DBATU B-Tech 1st Year 2017 Oct Engineering Mathematics I Question Paper

Download DBATU (Dr. Babasaheb Ambedkar Technological University) B.Tech First Year 2017 Oct Engineering Mathematics I Question Paper

DR. BABASAHEB AMBEDKAR TECHNOLOGICAL UNIVERSITY, LONERE ?
RAIGAD -4021o3
Mid Semester Examination ? October - 2017
Branch: F.Y.B.Tech (Group A/Group B) Sem.:- I
Subject with Subject Code:- Engineering Mathematics ?I (MATH101)
Marks: 20
Date:-03/10/2017 Time:- 1 Hr.
Instructions: - 1. All questions are compulsory.
2. Use of nonprogrammable calculator is allowed.
3. Figures to the right indicate full marks.
(Marks)
Q.N0.1 Attempt the following 4 (06)
a. The maximum value of the rank of a non-zero matn'x (ALMS is
i) 0 ii) 1 iii) 4 iv) 5
b. If the rank ofmatrix A is 2, then the rank of matn'x AT is
i) 2 ii) 0 iii) 4 iv) 1
c. The eigen values of a tn'angular matrix are
i) The elements of its principle diagonal ii) 0, O, 0
iii) The elements of its non-principle diagonal iv) none
d. The two eigen vectors X1 and X2 are said to be orthogonal iff
i) X1X2 = I ii) X1X2 = 0 iii) XJLXZT = 0iv)X1TX2 = I
e. If y = e?5in_1x , then the value of (1 ? x2)y2 ? xy1 ? azy is
i) 1 ii) 21 iii) 0 iv) none
f. The Maclaurin?s series of tan?lx is
. x3 x5 .. x3 5
1)x+?3?+?+---....11)x??+??---....
iii) 1 ?x+x2 ?---...iv)1+x+x2 +-...
x

Q.No. 2 Attempt any one of the following: (06)
a. Find the eigen values and the corresponding eigenvectors for the Matrix
501
0?20
105
A:
b.1fy = (sin'1 x)2, then prove (1 -? x2)yn+2 ? (2n + 1)xyn+1 ? nzyn = 0, and
2 4 6
hence prove that (sin'1 x)2 = 2 :?l + 2.22 % + 222.42% + ......
Q.No 3. Attempt any two of the following (08)
21. Find for what value of k the set of equations
2x?3y+62?5t=3, y?4z+t=1, 4x?5y+82?9t=k
has (i) no solution (ii) In?nite number of solutions.
11
b. If cos?1 (2?,) = log (3) , then show that
(x2)Yn+2 + (271+ 1)x}?n+1 + 2nZYn = 0-
c. Find the approximate value of tan?1 (1.00 3) correctupto four decimal places
by using Taylor?s theorem.