[" (ii) "f(x)=(x-1)(x-2)^(2)," ."],[" (Bihar "B.2014;H.B.2011;" A.I.C.B.S.E."2009C," ."]

If f(1)=2, f\'(x)=f(x) and h(x)=fof(x) then h'\(1) is equal to (A) 4e (B) 2e^2 (C) 4e^2 (D) e^2

If |[1 1 1];[a b c];[ a^3b^3c^3]|=(a-b)(b-c)(c-a)(a+b+c),w h e r ea ,b ,c are different, then the determinant |[1 1 1];[(x-a)^2(x-b)^2(x-c)^2];[(x-b)(x-c) (x-c)(x-a) (x-a)(x-b)| vanishes when a. a+b+c=0 b. x=1/3(a+b+c) c. x=1/2(a+b+c) d. x=a+b+c

If (lim)_(xvec0)(a e^x+bcos x+c e^(-x))/(e^(2x)-2e^x+1)=4,t h e n a. a=2 b. b=-4 c. c=2 d. a+b+c=-8

If (lim)_(xvec0)(a e^x+bcos x+c e^(-x))/(e^(2x)-2e^x=1)=4,t h e n a=2 b. b=-4 c. c=2 d. a+b+c=-8

If g(x)=(f(x))/((x-a)(x-b)(x-c)) ,where f(x) is a polynomial of degree <3 , then intg(x)dx=|[1,a,f(a)log|x-a|],[1,b,f(b)log|x-b|],[1,c,f(c)log|x-c|]|-:|[1,a, a^2],[ 1,b,b^2],[ 1,c,c^2]|+k (dg(x))/(dx)=|[1,a,-f(a)(x-a)^(-2)],[1,b,-f(b)(x-b)^(-2)],[1,c,-f(c)(x-c)^(-2)]|:-|[1,a,a^2],[1,b,b^2],[1,c,c^2]|

If g(x)=(f(x))/((x-a)(x-b)(x-c)) ,where f(x) is a polynomial of degree <3 , then intg(x)dx=|[1,a,f(a)log|x-a|],[1,b,f(b)log|x-b|],[1,c,f(c)log|x-c|]|-:|[1,a, a^2],[ 1,b,b^2],[ 1,c,c^2]|+k (dg(x))/(dx)=|[1,a,-f(a)(x-a)^(-2)],[1,b,-f(b)(x-b)^(-2)],[1,c,-f(c)(x-c)^(-2)]|:-|[1,a,a^2],[1,b,b^2],[1,c,c^2]|

If g(x)=(f(x))/((x-a)(x-b)(x-c)) ,where f(x) is a polynomial of degree <3 , then intg(x)dx=|[1,a,f(a)log|x-a|],[1,b,f(b)log|x-b|],[1,c,f(c)log|x-c|]|-:|[1,a, a^2],[ 1,b,b^2],[ 1,c,c^2]|+k (dg(x))/(dx)=|[1,a,-f(a)(x-a)^(-2)],[1,b,-f(b)(x-b)^(-2)],[1,c,-f(c)(x-c)^(-2)]|:-|[1,a,a^2],[1,b,b^2],[1,c,c^2]|

If g(x)=(f(x))/((x-a)(x-b)(x-c)),w h e r ef(x) is a polynomial of degree < 3, then prove that (dg(x))/(dx)=|{:(1,a, f(a)(x-a)^(-2)),(1,b,f(b)(x-b)^(-2)), (1,c,f(c)(x-c)^(-2)):}|/|{:(a^2,a,1),(b^2,b,1),(c^2,c,1):}|

If lim_(x to 1) (1 + ax + bx^(2))^((c )/(x - 1)) = e^(3) , then the value of a + b + bc + 2009 is…….

If lim_(x to 1) (1 + ax + bx^(2))^((c )/(x - 1)) = e^(3) , then the value of a + b + bc + 2009 is…….