# B.Sc in Mathematics Sample Paper for Allied Mathematics for Statics-I

** SAMPLE PAPER FOR B.SC IN ****MATHEMATICS, YEAR-2
**

**ALLIED- MATHEMATICS FOR STATISTICS-1**

**Time: 3 hours M.Marks:60**

Note: – Attempt any 5 questions.

All questions carry equal marks.

**Q1.** Choose the correct answers:

**1. **the middle term of X – 2 / X 12 is

**(a)** 12C6212

**(b)** 12C626

**(c)** 12 C6

**(d)** 1.2 1 3

**2.** The Rank of A = is

1 0 2

**(a) **2 **(b)** 3

**(c) **6 **(d)** 0.

**3.** The product of the roots of the equation

x^{5}-x^{3}+l = 0 is

**(a)** -1 **(b)** 1

**(c)** 1 / 5 **(d)** -1 / 5

**4. **x^{3} – 2x^{2} -3x – 4 = 0 has a root between

**(a)** 0 & 1 **(b)** 1 & 2

**(c)** 2 & 3 **(d)** 3 & 4.

sin0 5045

**5.** If = the value 01 6 is nearly

0 5046

**(a)** 1° **(b)** 3°

**(c)** 2° **(d)** 4°.

**6. **sinh 1(A:) is

**(a)** log/:*; + V*2-ll **(b)** loglx + V*2 +l)

**(c)** logx **(d)** log(l-*).

**Q2**. (a) Find the sum to infinity of the series, 357 I

1+ — + — + —- +. ..<*>. I

2! 3! 4!

**(b)** Examine the following equations are

consistent or not

x+y+z = 6 x + 2y – 2z = -3

2x + 3y + z = ll > I

**Q3.**

**(a)** Solve x4 + 2×2 -16x + 77 = 0 given that is a root.

**(b)** Find by Newton’s method, the positive root of (le equation x3 + 2×2 + 5x – 220 = 0.

**Q4.**

**(a)** Prove that sin5 0 = — (sin50 -5sin30 +lOsin0). 16V;

**(b)** Separate into real and imaginary parts of ian(x + iy).

**Q5.**

**(a)** Find the differential coefficient of (sinx)cosx .

**(b)** Find the radius of curvature at (x, y) for the curve a2y =x ~a .

**Q6.**

**(a)** Verify Euler’s theorem when

u = x3 +y3 +z3 + 3 xyz .

**(b)** Find the maximum or minimum value of |

2U2-/)-x4+/.

**Q7.**

**(a)** Find the sum to infinity of the since

2-3 3-5 4-7 5-9

+ + + +

3! 4! 5! 6!

**(b)** Find the eigen values and eigen vectors of

the matrix A =

I3 2,

**Q8.**

**(a)** Solve the reciprocal equation

x5 ~5×4 +9×3 -9×2 +5x-l = 0.

**(b)** Find by Horner’s method correct to three decimal places, the root of the equation

x3 +3×2-8x-6 = 0.

NOTE: Above sample paper for B.Sc in Mathematics, Allied Mathematics for Statics-I Year II has been created after reviewing few universities question papers.

We are not sure whether your university has same or similar question pattern. We always suggest you to go thoroughly with text books, teacher notes etc for better results.

We wish you best of luck for upcoming examinations.

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