#1
22nd November 2014, 10:31 AM
| |||
| |||
North Gujarat University question paper
Hi I want the question paper of B.Sc Computer Science of Advance Mathematics of North Gujarat University?
|
#2
22nd November 2014, 11:01 AM
| |||
| |||
Re: North Gujarat University question paper
Ok, as you want the question paper of B.Sc Computer Science of Advance Mathematics of North Gujarat University so here I am providing you. North Gujarat University B.Sc Computer Science Advance Mathematics question paper 1 (a) Write the De-Morgan’s lows and prove 3 any 1 of them . (b) If A = {1,2,3}, B = {2,4} and C = {3,4} 4 then prove that A × ( B ? C) = (A × B) ? (A × C). (c) (i) If f : Z ->Z , x ? Z , f(x) = 4x + three 3 Is it one-one ? Is it onto? Is it even ? (ii) If f : R -> R ,f(x) =5x + four and g : R->R, 4 g(x) = 4x + k and fog=gof then obtain k and fog (-2). OR one (a) describe the subsequent terms : 3 (i) Intersection of 2 sets (ii) Disjoint sets (iii) Cartesian product of 2 sets (b) If n(U)=100, n(A)=60, n(B)=50 and 4 n(A U B) = 90, then obtain n(A’ U B’), n(A’ n B’) and n(A n B’). (c) (1) If f : R -> R , x ? R, f(x) = 2x +3 then 3 prove that f has it’s inverse function and find it. (2) A company sells its product for Rs.5 4 per unit. Fixed cost for the company are Rs.3500 and variable costs are estimates to run 30% of the total revenue . Determine : (i) The total revenue functions (ii) The total cost function (iii) The break-even point. two (a) (1) describe limit of a function . 2 _________ (2) Evaluate : lim v n2 + n + one – n 2 n->8 (b) explain the continuity of a function 2 F(x) = { 2/5-x : x < three , five – x ; x = three at point x = three (c) Find dy /dx 6 _______ (1) y = log(x + v x two - a two ) (2) y = (sin x)x (2) y = e 3x – x sin x + x two /4 (d) obtain the maximum value of f(x) = x + 4/x. 2 OR 2 (a) Evaluate : 4 (1) lim x(ex - one ) x->0 ----------- 1-cos x (2) lim (1+ x)5 – one x->0 -------------- x (b) explain the continuity of a function : 2 F(x) = { |x| / x ; x ? 0 , one ; x = 0 at point x=0. C(x) = x3 /3=3 x2-7z+16, where x is the Output. obtain the output at which the total Cost is minimum. 3 (a) (1) If every element of a row is multiplied 3 with K and added to the corresponding element of a different row then prove that the value of determinant is not changed. (2) one a a2 Prove that one b b2 =(a-b) (b-c) (c-a). 3 one c c2 one two two (b) (1) If A = two one two then prove that one two one a2 -4A-5I=0 seven four (2) If A = five three then prove that A + AT + A-1 3 (c) Solving usimg matrix method. 3 2x – 3y + 5= 0 3x +y -9 = 0 OR 3 (a) (1) Solving the formula by Cramer’s rule 3 x + 6y = 2xy 3x + 2y = 2xy X p 3x – 5p 3 (2) Prove that y q 3y – 5q =0 Z r 3z – 5r 0 four three (b) (1) IF A = one -1 -3 Prove that 2 -1 four four A2 = I (2) IF A = one two and B = four 0 three four two one Prove that (AB)T = B2 AT (c) describe every with example : 3 (1) Row matrix (2) Null matrix (3) Skew-symetrix metrix. 4 (a) obtain : 6 __ __ (1) ? (v x + 1/ v x )2 (2) x log x dx two (3) ? 2x + five / x2 +5x +3 dx 1 (b) Find tht area of region bounded by 3 Y = x2 and the line y=x +2 (c) describe differential formula . Determine the 3 degree and the order of the differential ___________ formula v d2 y/d x2 +2y=dy/dx (d) Solve tany 1 : 2 (1) dy/dx = ex-y + x2 xey (2) dy/dx +y = ex OR 4 (a) obtain : 6 (1) ? x ex dx (2) ? ex (sin x+ cos x) dx two (3) ? logx / x dx one (b) obtain the quantity of sphere of radius r 3 using the definite integral (c) discuss the method of solving a linear three formula dy/dx+Py = Q where P and Q are the function of x only. (d) Solve any 1 : 2 (1) (x+5) dy + y dx=0 (2) ( x2 + y2 ) dy/dx xy . 5 (a) (1) Derive the formula to obtain the area of 3 A triangle ?ABC whose vertices are A(x1,y1), B(x2,y2) and C= (x3,y3) (2) A( 0 , 0 ) ,B( four , two ), C( three , -3 ) and 3 D( k , -2 ) are provided points. obtain k if <-----> <-----> <-----> <-----> AB || CD and AB | CD (b) (1) Prove that points ( four , three ) ,( seven , one ) and two ( 9, three ) are the vartices of an isoseceles triangle. (2) If P( four , k ) divides the line segement 2 joining A( 2, 3) and B(5, -1). obtain the ratio of division from A and value of k . (c) obtain the formula of a line passing through 4 The point ( two , five ) and marking an angle of 45o with line x – 3y + two = 0 OR 5 (a) (1) find the formula of line of the 3 From x/a + y/b = one where ab ? 0 (2) If the area of the triangle with 3 Varitices (k ,3) ,(4,5) and (3,1) is six unites ,find k. (b) (1) Show that the 3 points 2 A(1,4), B(3,-2) and C(-3,16) are Collinear. (2) If (-3,4) is the centroid of the triangle 2 whose certices are (6,2),(x,3) and (0,y) then obtain x,y. (c) obtain the formula of line parallel to 4 3x + y + five = 0 and pass through the point of intersection of lines x + y – three =0 and x – y -5=0. |
|