Let f(x)""=""x|x|""a n d""g(x)""=""s in ...

Let `f(x)""=""x|x|""a n d""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) 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

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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

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

Let f(x) = x|x| and g(x) = sin x Statement-1: gof is differentiable at x=0 and derivative is continous at that point. Statement-2: gof is twice differentiable at x=0

Let f(x)={x^n sin (1/x) , x!=0; 0, x=0; and n>0 Statement-1: f(x) is continuous at x=0 and AA n>0. and Statement-2: f(x) is differentiable at x=0 AA n>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: 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: 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.

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: 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

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