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

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DR. BABASAHEB AMBEDKAR TECHNOLOGICAL UNIVERSITY, LONERE - RAIGAD - 402 103

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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.

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2. Use of nonprogrammable calculator is allowed.

3. Figures to the right indicate full marks.

Q.No.1 Attempt the following (06 Marks)

1. The maximum value of the rank of a non-zero matrix (4) is
   1. 0
   2. 1

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   3. 4
   4. 5
2. If the rank of matrix A is 2, then the rank of matrix A^T is
   1. 2
   2. 0

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   3. 4
   4. 1
3. The eigen values of a triangular matrix are
   1. The elements of its principle diagonal
   2. 0,0,0

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   3. The elements of its non-principle diagonal
   4. none
4. The two eigen vectors X₁ and X₂ are said to be orthogonal iff
   1. X₁ X₂ =1
   2. X₁ X₂ =0

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   3. X₁ X^T=0
   4. X^TX₁ =1
5. If y = e ^ax then the value of (1—x²)y₂ —xy₁ —a²y is
   1. 1
   2. a

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   3. 0
   4. none
6. The Maclaurin’s series of tan^-1x is
   1. x + x³/3 + x⁵/5 + ...
   2. x - x³/3 + x⁵/5 - ...

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   3. 1 —x+x²—...
   4. 1+ x+x² +...

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Q.No.2 Attempt any one of the following: (06 Marks)

1. Find the eigen values and the corresponding eigenvectors for the Matrix
   A=[5 0 1
   0 -2 0
   1 0 5]

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hence prove that (sin^-1 x)² = 2 [x²/2! + 2²x⁴/4! + 2².4²x⁶/6! + ...]

Q.No 3. Attempt any two of the following (08 Marks)

1. Find for what value of k the set of equations
   2x—3y+6z—5t=3, y—4z+t=1, 4x—-5y+8z—9t=k
   has (i) no solution (ii) Infinite number of solutions.

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2. If cos^-1 (x/a) = log (y/b) , then show that
   (x² + a²)y_n+2 + (2n+1)xy_n+1 + (n²)y_n = 0.
3. Find the approximate value of tan^-1(1.003) correct upto four decimal places by using Taylor’s theorem.

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