Statement 1: For `-1

Statement 1: For every natural number ngeq2 , 1/(sqrt(1))+1/(sqrt(2))+...+1/(sqrt(n))>sqrt(n) . Statement 2: For every natural number ngeq2,""n(n+1)

Statement -1: if -1lexle1 then sin^(-1)(-x)=-sin^(-1)x and cos^(-1)(-x)=pi-cos^(-1)x Statement-2: If -1lexlex then cos^(-1)x=2sin^(-1)sqrt((1-x)/(2))= 2cos^(-1)sqrt((1+x)/(2))

Let A be an orthogonal square matrix. Statement -1 : A^(-1) is an orthogonal matrix. Statement -2 : (A^(-1))^T=(A^T)^(-1) and (AB)^(-1)=B^(-1)A^(-1)

Statement 1. cos^-1 x-sin^-1 (x/2+sqrt((3-3x^2)/2))=- pi/3, where 1/2 lexle1 , Statement 2. 2sin^-1 x=sin^-1 2x sqrt(1-x^2), where - 1/sqrt(2)lexle1/sqrt(2). (A) Both Statement 1 and Statement 2 are true and Statement 2 is the correct explanation of Statement 1 (B) Both Statement 1 and Statement 2 are true and Statement 2 is not the correct explanatioin of Statement 1 (C) Statement 1 is true but Statement 2 is false. (D) Statement 1 is false but Statement 2 is true

9, Let A be a 2 x 2 matrix with real entries. Let I be the 2 × 2 2identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that A2 -1 nvo bud o malai Statement 1: If A 1 and A?-1, then det A =-1. Statement 2: If A 1 and A?-I, then tr (A)?0 A. Statement 1 is false, statement 2 is true. B. Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 . C. Statement 1 is true, statement 2 is true; statement 2 is nota correct explanation for statement 1. D. Statement 1 is true, statement 2 is false.

Statement 1. 2^(sinx)+2^(cosx)ge 2^(1-1/sqrt(2)) for all real x , Statement 2. For positive numbers, AMgeG.M. (A) Both Statement 1 and Statement 2 are true and Statement 2 is the correct explanation of Statement 1 (B) Both Statement 1 and Statement 2 are true and Statement 2 is not the correct explanation of Statement 1 (C) Statement 1 is true but Statement 2 is false. (D) Statement 1 is false but 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: sin 1 lt sin 2 lt sin3 Statement-2: sin3 lt sin2 lt sin1 Statement-3: sinx_(1) lt sinx_(2), x_(1) , x_(2) in (0,pi/2)

Statement I : Focal length of a spherical mirror depends on the distances of object and image from the mirror. Statement II : (1)/(f ) = (1)/(v ) + (1)/(u)

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