Bi- (c) 1x) (d) jo ) 15. for legendre's polynomial, pa(-1) is equal too a )0 1f p,x) is legendre's polynomial, then the value of j. pa)p3p)dx is equal 6. (aj 31

bi- (c) 1X) (d) Jo ) 15. For Legendre's polynomial, Pa(-1) is equal too a )0 1f P,x) is Legendre's polynomial, then the value of J. Pa)P3P)dx is equal 6. (aj 31 c) 17. The value of 4G) is (a) 0 D) d) 18. The value of H2) is [c) - 2 (a)gOx 19. The Fourier series expansion of x* in the interval fcoxcos2x coscst then the value of 4-4 15 T is 20. For a half wave rectiter, Current l5 gven oy o T/2 : f f(ut) = l =+n=14n COS not + 2n=1 Da Sin not, then the value of dag is 21. Ifg(o) is the Fourier transform of f), then the Fourier transform of f(at) is. (a) a g) (b)o) ()o(aw) 22. Fourier transform of e d js (a) d) . Ine nte Fourer sine ranstorms O7 n the interva (0,71) 1S (a) (b) d(-1)n+1 The value ot integral * dx - 4)dx is b) 4 (aE 25. f(6) 1s the laplace transtorm ot F(t), the laplace transtorm ot F(a (a) / (b) af ) (c) af ) 26. Laplace transforms of r",n 2 0 is (a) (c) r(n+1) (d 27. 1f £[sin at] = then the Laplace transforms of t sin at is (b) -a c) s2+a) 8. If f() is the Laplace transform of FO), then £-f-a)] is (a) eF(t) d) et FC) 29. If AG) sia and fels) = s then £ Ii6)f6)| is -at_bt t-e-b (ab-a 50. The integral J, tfe"" sin tdt is equal to a), d- -;