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Statement-1 Let f:[0,oo)vec[0,oo) be a f...

Statement-1 Let `f:[0,oo)vec[0,oo)` be a function defined by `y=f(x)=x^2,` then `((d^2y)/(dx^2))((d^2x)/(dy^2))=1` Statement-2 `(d^2y)/(dx^2)=-(d^2x)/(dy^2)dot((dy)/(dx))^3` Statement-1 is True, Statement-2 is True and Statement-2 is correct explanation for Statement-1 Statement-1 is True, Statement-2 is True and Statement-2 is not correct explanation for Statement-1 Statement-1 is True, Statement-2 is false Statement-2 is False, Statement-2 is true Both Statements are false

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Statement-1: int((x^2-1)/x^2)e^((x^2+1)/x)dx=e^((x^2+1)/x)+C Statement-2: intf(x)e^(f(x))dx=f(x)+C (A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1. (C) Statement-1 is True, Statement-2 is False. (D) Statement-1 is False, Statement-2 is True.

Statement-1: intsin^-1xdx+intsin^-1sqrt(1-x^2)dx=pi/2x+c Statement-2: sin^-1x+cos^-1x=pi/2 (A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1. (C) Statement-1 is True, Statement-2 is False. (D) Statement-1 is False, Statement-2 is True.

Statement-1: The function F(x)=intsin^2xdx satisfies F(x+pi)=F(x),AAxinR ,Statement-2: sin^2(x+pi)=sin^2x (A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1. (C) Statement-1 is True, Statement-2 is False. (D) Statement-1 is False, Statement-2 is True.

Statement-1: int(sinx)^x(xcotx+logsinx)dx=x(sinx)^x Statement-2: d/dx(f(x))^(g(x))=(f(x))^(g(x))d/dx[g(x)logf(x)] (A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1. (C) Statement-1 is True, Statement-2 is False. (D) Statement-1 is False, Statement-2 is True.

Statement-1: intdx/(x(1+logx)^2)=-1/(1+logx)+C , Statement-2: int(f(x))^nf\'(x)dx=(f(x))^(n+1)/(n+1)+C, n+1!=0 (A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1. (C) Statement-1 is True, Statement-2 is False. (D) Statement-1 is False, Statement-2 is True.

Statement-1: int(3-2x)/sqrt(4+2x-x^2)dx=2sqrt(4+2x-x^2)+sin^-1((x-1)/sqrt(5))+C ,Statement-2: intdx/sqrt(a^2-x^2)=x/2sqrt((a^2-x^2))+a^2/2sin^-1(x/a) (A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1. (C) Statement-1 is True, Statement-2 is False. (D) Statement-1 is False, Statement-2 is True.

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Statement-1: p-Nitroaniline is more polar than nitrobenzene and Statement-2: Nitro group has -M effect. (a) Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1 (b) Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement -1 (c) Statement -1 is true, Statement -2 is false (d) Statement -1 is false, Statement -2 is true

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RESONANCE DPP ENGLISH-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Let f:""(1,""1)vecR be a differentiable function with f(0)""=""-1""a...

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  2. If y=(sin^(-1)x)^2+(cos^(-1)x)^2 , then (1-x^2) (d^2y)/(dx^2)-x(dy)/(d...

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  3. Statement-1 Let f:[0,oo)vec[0,oo) be a function defined by y=f(x)=x^2,...

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  4. If f(x),g(x)a n dh(x) are three polynomial of degree 2, then prove t...

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  5. Let f(x) be a polynomial.Then, the second order derivative of f(e^x) i...

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  6. about to only mathematics

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  7. If the function f(x)=(x^2)/2+lnx+a x is always monotonically increasi...

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  8. fn(x)=e^(f(n-1)(x)) for all n in Na n df0(x)=x ,t h e n d/(dx){fn(x)}...

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  9. (d^2x)/(dy^2) equals: ((d^2y)/(dx^2))^(-1) (b) -((d^2y)/(dx^2))^(-1)(...

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  10. y=tan^(-1)""(4x)/(1+5x^(2))+tan^(-1)""(2+3x)/(3-2x)

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  11. If f (x) =lim (x to oo) x ((3)/(2) + [cos x)(sqrt(n^(2) +1)-sqrt(n ^(2...

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  12. If g(x)=(2h(x)+|h(x)|)/(2h(x)-|h(x)|) where h(x)=sinx-sin^n x ,n in R...

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  13. If f(x)=|"cos"(x+x^2)"sin"(x+x^2)-"cos"(x+x^2)"sin"(x-x^2)"cos"(x-x^2...

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  14. If If {:(" ""x"),(y=""),(" ""x"),(" ""a+")...

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  15. Find the sum of the series 1+2x+3x^2+(n-1)x^(n-2) using differentiatio...

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  16. If y=a^x^a^x^...^(((((oo))))) , then prove that (dy)/(dx)=(y^2(log)e ...

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  17. Let f(x)={s in2x ,0<xlt=pi//6a x+b ,pi//6<x<1 . If f(x)a n df^(prime)(...

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  18. If f is twice differentiable such that f''(x)=-f(x), f'(x)=g(x), h'(x...

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  19. Find (dy)/(dx) : x=a{cost+1/2logt a n^2t/2} and y=asint .

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  20. If x^m y^n=(x+y)^(m+n), prove that (dy)/(dx)=y/x .

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