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

Friday, 01 February 2013 09:05Web

B.Sc part2 mathematics

2008

iviii) The function ys 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

SL2

xut-yu* *.* + j,t/S

then find the value of

du , da x + y. dx dy

JO

3. If u=log(*3 + y3+23- 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'xL1'

\/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 dx=2P+ Y + a an(l a + P*

10

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

= cos mx; m ~ 0. 1,2.....

form orthogonal set of function on the interval

14. If

then find the value of L'xf[as).

10

10

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