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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^(2))dx=e^((x^2+1)/x^(2))+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.

Let A be a 2""xx""2 matrix Statement 1 : a d j""(a d j""A)""=""A Statement 2 : |a d j""A|""=""|A| (1) Statement1 is true, Statement2 is true, Statement2 is a correct explanation for statement1 (2) Statement1 is true, Statement2 is true; Statement2 is not a correct explanation for statement1. (3) Statement1 is true, statement2 is false. (4) Statement1 is false, Statement2 is true

Consider the function F(x)=intx/((x-1)(x^2+1))dx Statement-1: F(x) is discontinuous at x=1 ,Statement-2: Integrand of F(x) is discontinuous at x=1 (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 (1/2)^7lt(1/3)^4 implies 7log(1/2)lt4log(1/3)implies7lt4 Statement-2 If axltay , where alt0 ,x, ygt0 , then xgty . (a) Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1 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 value of the integral int_(pi//6)^(pi//3)(dx)/(1+sqrt(tanx)) is equal to pi/6 Statement 2: int_a^bf(x)dx=int_a^bf(a+b-x)dxdot Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true; Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true

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

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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),h(x) are polynomials in x of degree 2 and F(x)=|fghf'g' h...

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

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  6. If f(x)=prod(n=1)^(100)(x-n)^(n(101-n)),w h e r eprod(i=1)^k ai st...

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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: (1) ((d^2y)/(dx^2))^(-1) (2) -((d^2y)/(dx^2...

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  10. Find (dy)/(dx) in each of the following cases: y=tan^(-1)(4x)/(1+5x^2...

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  11. If f(x)=lim(n->oo)(3/2+[cosx](sqrt(n^2+1)-sqrt(n^2-3n+1))) whe...

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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 y=x/(a+x/(b+x/(a+oo))),t h e nfin d(dy)/(dx)

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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) and f^(prime)...

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  19. Find (dy)/(dx) if: x=a(cos t+1/2lntan^2t/2) and y=asintdot x=s in tsq...

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  20. If x^m y^n=(x+y)^(m+n), then (dy)/(dx) is (x+y)/(x y) (b) x y (c) x/...

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