15. for legendre's polynomial, p,(-1) is equal to (b) 1 (c) 0 (d 16. if p(r) is legendre's polynomial, then the value of pa()ps()dx is equal (a) 0 3! 2 17. the

15. For Legendre's polynomial, P,(-1) is equal to (b) 1 (c) 0 (d 16. If P(r) is Legendre's polynomial, then the value of Pa()Ps()dx is equal (a) 0 3! 2 17. The value of ) 1s b) 1 c) (d) 18. The value of H2(x) is (a) x- 1 (b) 2x (d)x 19. The Fourier series expansion of x* in the interval -TS*STis *=-4- }then the value of i+ is (a) 20. For a halt wave rectilier, current 1s given by I= 0Sts 2 '/2 f(ot)==2+ 2na1 Gy COS tot + 21 by sin not, then the value of ag is fc (d) ni 21. fg(o) is the Fourier transform of f), then the Fourier transform of f(at) is. a ag) (b)9)) (c)g(aw) (d)9 22. Fourier transform of etl is (a) 23. The finite Fourier sine transtorms of in the interval (0, T) 1s (a) +1 24. The value of integral J O-4)dx is (c) v2T (d 25. f f) is the laplace transform of F€), the laplace transform of F(at) is (a)f) (b) af ( (c) af (d)f 26. Laplace transtorms of t",n20 1s anT (b)T rn+1) (d) Tm 2 L1s1n ar) +a hen the Laplace transtorms ot tsinat 1s a +a) -a) 28. It f6) 1s the Laplace transtorm of F(t), then f(S ~ a)] 1s c) eatf (t 29. f A6) = sta and fs) = s4 then £"lA)£)is (a) -e (d)ba 30. The integral třet sin tdt is equal to (D