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

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: 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

Statement I: If (log)_(((log)_5x))5=2,\ t h n\ x=5^(sqrt(5)) Statement II: (log)_x a=b ,\ if\ a >0,\ t h e n\ x=a^(1//b) 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

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)""=""sinx 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

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

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

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 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