exam 2016

1) Construct the switching circuit for the following statement

i)  [p V (~pɅq) ]V[(~qɅr) V~p]         ii) (pɅqɅr )V[~pV (qɅ ~r)]

iii) [p V (~pɅq)] V [(~qɅr) V ~p]        iv)  [( pɅr) V (~qɅ~r)]V (~pɅ~r)

v)    (pɅq) V [(~pɅ (~q V p V r)]

2) Find the volume of tetrahedron whose vertices are A(-1,2,3),    B( 3,-2,1) , C(2,1,3) & D(-1,-2,4)

3) Find the inverse of matrix   

4) Solve the equations by reduction

            x + y + z=1,  2x + 3y + 2z=2,   x + y + 2z=4

5) Show that the points A(2,1,--1), B(0,--1,0), C(4,0,4)&D(2,0,1) are coplanar

6) Find the direction cosine of the line which  is perpendicular to the lines with d.r.s  --1,2, 2   & 0,  2,  1

7) Find the acute angle between the lines           =   =                    &                               =  =

8) Solve the equations by the method of inversion

x - y  + z = 4;    2x + y -3z =  0;      x + y +z  = 2

9) If A =     find   by adjoint  method

1)  Find approximate value of

2) Find the area of region bounded by the curve =16x, y=1, y=4 & the y-axis.

3)  Verify Rolle's  theorem for the function

            f(x) = --4x +10   on  [0,4]

4) Find the maximum & minimum value of the function   

f(x) =  -- 27x + 15

5) Given below is the probability distribution of a random variable

X            1        2          3          4          5          6

p(x)     k          0          2k       5k       k          3k

6) Evaluate the integral as a limit of sum  dx

7) A fair coin is tossed 3 times . Let X be the number of heads obtained . Find E(X)               & V(X) 

8)  Find the approximate value of  given that= 0.4343    

9) Given X ~B(n, p) .  If n= 20,  E(x) = 10. Find p, Var (X) &  S.D.(X)

10) Verify LMVT for the function  f(x) = logx   on [1,e]

11) Divide the number 84 in to two parts such that the product of one part & the square of other is maximum

12)  Evaluate the following integrals as a limit of sum

 i)       ii) dx

13) find k if the following is p.d.f. of a r.v.x

  f(x)