# Vinoba Bhave University 2007 B.Sc Mathematics part2 - Question Paper

B.Sc part2 mathematics

2008

iviii) The function y^{s}tan* is (a) Continuous everywhere

(b) Nowhere continuous

(c) Continuous at some point

{d) Discontinuous ai some point or periodic point.

[lx ) The function defined by /t*) = x - 1*1,* is a positive variable, el*] denoies the integral part of x the

(a ) / ( a* ) is continuous <ii for all integral values of x

(b) Discontinuous for n\\ integral values of x

(c) Discontinuous for all other values id) Nnnc of these.

I*) Conditions of equilibrium, that is, the suns of moments of external fnrccs about any three perpendicular lines passing through the fixed point

(a) must be separately zero

(b) one of them be zero (cl none of these be/.cro id) None of these.

[d] Jf

SL^{2}

x^{ut}-y^{u}* *.* + j,t/S

then find the value of

du , da x + y. dx dy

JO

3. If u=log(*^{3} + y^{3}+2^{3}- 3 xyz), then prove that

^{1} 9

T - + - I U - -

dx

(A_{+}A_{+}A)

'A* 0/ dz^{}}

10

ix+ y + z)

4. Show that

r(_{n}+l) _U-l)Ufl-3)(2-S)...3,l_{>}0

^{2} 2" * 10

1. Choose the correct answer of any five of the following: -2x5

(/) In the equation of S.H.M. x 2 cos (Va/ t) the magnitude of oscillation is equal to

[a] VW {b) t IC) 3

(d) None of these, l/r) The periodic time of S.H.M. x=- - Mx is U) 2* __

\b) 2jtVA'

(Hi) if three component couples are L, M Bl N and C is the cnupk of moment then the direction cosines (Axis is along the line) are

U) L, M, N {) LG, MG, NO \c) LfG, A4/G.NfG M N

Wr'xL^{1}'

\/v) y- e cosh x;'c is (a ) intrinsic equation of catenary (>) Cartesian equation of catenary [c J Doth of the above (a) and (6) (d) None of ihcftc.

wa> The series E ^{+} is (a) Convergent {b) Absol ute convergent

(c) Oscillator)'

{d) Divergent.

t \

(c) -

VAf

7T

2. If u

id)

V

5. Show that + 1 IS. q- I -1
16. T(p+ q) 6. Define the Arithmetical definition of a limit. Find the 17. limit of the sequence whose n th from a 2 10 18. Which forces may be omitted in .forming the 7. What is the general convergence of sequence ? Show that every convergent sequence is a Cauchy 19. sequence. 10 8. Test the convergency of the infinite series 10 n 9. Determine the convergency of the series fi+ 1 10 10. Discuss the Eigenvalues of strum Liouville problem are all real. 10 11. Integrate the Bessel's in series and also find the Bessels function of zeroth order. 10 12. Prove that: |
Define Simple Harmonic Motion if p* {x be the displacement) be the acceleration then find the velocity at x- a. (a be any point in the point of motion). 10 Prove that s - c tan (The intrinsic equation of the catenary). 10 Discuss Descartes the rule of sign. 10 Find the condition that the roots of the equation x3 + px2 + qx + /= 0 be in Arithmetic Progression. 10 Or If a, + y > Y |

10

13. What do you mean by orthogonality of f unction show that the function

form orthogonal set of function on the interval

14. If

then find the value of L'^{x}f[as).

10

10

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