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Statement 1: If f(x)={x ,\ if\ x\ i s\ i...

Statement 1: If `f(x)={x ,\ if\ x\ i s\ irr a t ion a l1-x ,\ if\ x\ i s\ r a t ion a l\ ,\ t h e n(lim)_(x->1//2)f(x)` does not exist. Statement 2: `x->1/2` can be rational or irrational value. 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

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Statement 1: The function f(x)=[[x]]-2[x-1]+[x+2] is discontinuous at all integers. Statement 2: [x] is discontinuous at all integral values of xdot 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

Statement 1: (lim)_(x->0)sin^(-1){x}\ does not exist (where {.} denotes fractional part function). Statement 2: {x} is discontinuous at x=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 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

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

Statement 1: (lim)_(x->0)[x]((e^(1//x)-1)/(e^(1//x)+1)) (where [.] represents greatest integer function) does not exist. Statement 2: (lim)_(x->0)((e^(1//x)-1)/(e^(1//x)+1)) does not exist. 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

Let f(x)=x|x| and g(x)=s in x Statement 1 : gof is differentiable at x=0 and its derivative is continuous at that point Statement 2: gof is twice differentiable at x=0 (1) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for statement 1 (2) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for statement 1. (3) Statement 1 is true, statement 2 is false. (4) 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: 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.

Consider the system of equations x-2y+3z=1;-x+y-2z=; x-3y+4z=1. Statement 1: The system of equations has no solution for k!=3. Statement2: The determinant |1 3-1-1-2k1 4 1|!=0,\ for\ k!=3. 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;2 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

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.

BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Statement 1:(lim)(x->0)sin^(-1){x}\ does not exist (where {.} denot...

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  2. Statement 1: lim(x->0) sqrt(1-cos 2x)/x does not existe . Statement 2...

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  3. Statement 1: If f(x)={x ,\ if\ x\ i s\ irr a t ion a l1-x ,\ if\ x\ i ...

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  4. Statement 1: (lim)(x->0)[x]((e^(1//x)-1)/(e^(1//x)+1)) (where [.] repr...

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  5. Statement 1: The function f(x)=[[x]]-2[x-1]+[x+2] is discontinuous ...

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  6. Let f(x)=-ax^2-b|x|-c, -alpha le x lt 0, ax^2+b|x|+c 0 le x le alpha ...

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  7. Let f(x)={1+(2x)/a ,0lt=x<1a x ,1lt=x<2dotIf("lim")(xvec1)f(x)e xi s t...

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  8. Given a real valued function f such that f(x)={(tan^2{x})/((x^2-[x]^2)...

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  9. Which of the following statement(s) is (are) INCORRECT ?. (A) If lim...

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  10. Each question contains statements given in two columns which have to b...

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  11. If L=+(lim)(x->1)((2x-3)(sqrt(x)-1))/(2x^2+x-3),\ t h e n\ 20\ L=

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  12. If L=(lim)(x->oo)(logx^n-[x])/([x]),\ w h e r e\ n in N ,\ t h e n-2L...

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  13. (lim)(x->0)([100(sin x)/x]+[100(tanx)/x])=

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  14. (lim)(x->0)([100 x/(sin\ x)]+[100(tanx)/x])=

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  15. (lim)(x->0)([100(sin^(-1)\ x)/x]+[100(tan^(-1)x)/x])=

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  16. (lim)(x->0)([100 x/(sin^(-1)x)]+[100(tan^(-1)x)/x])=

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  17. lim(x -> oo) (sqrt(x^2 - x - 1) - ax - b) = 0 where a > 0, then there ...

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  18. If lim(x->oo)((1+a^3)+8e^(1/ x))/(1+(1-b^3)e^(1/ x))=2, then there exi...

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  19. If (lim)(x->oo)(sqrt((x^4-x^2+1))-a x^2-b)=0 , then there exists at ...

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  20. If lim(x->-a) (x^7+a^7)/(x+a)=7, where a lt 0 then ,there exists at ...

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