Consider : Statement I : `(phat~""q)hat(~""phatq)` is a fallacy. Statement II : `(pvecq)harr(~""qvec~""p)` is a tautology. (1) Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I (2) Statement -I is True; Statement -II is False. (3) Statement -I is False; Statement -II is True (4) Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I

Statement - I : The value of the integral int_(pi//6)^(pi//3)(dx)/(1+sqrt(tanx)) is equal to pi/6 . Statement - II : int_a^bf(x)dx=int_a^bf(a+b-x)dxdot (1) Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I (2) Statement -I is True; Statement -II is False. (3) Statement -I is False; Statement -II is True (4) Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I

Given : A circle, 2x^2+""2y^2=""5 and a parabola, y^2=""4sqrt(5)""x . Statement - I : An equation of a common tangent to these curves is y="x+"sqrt(5) Statement - II : If the line, y=m x+(sqrt(5))/m(m!=0) is their common tangent, then m satisfies m^4-3m^2+""2""=0. (1) Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I (2) Statement -I is True; Statement -II is False. (3) Statement -I is False; Statement -II is True (4) Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I

Let A be a 2xx2 matrix with non-zero entries and let A^2=""I , where I is 2xx2 identity matrix. Define Tr(A) = sum of diagonal elements of A and |A| = determinant of matrix A. Statement-1: T r(A)""=""0 Statement-2: |A|""=""1 (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Let f: R R be a continuous function defined by f(x)""=1/(e^x+2e^(-x)) . Statement-1: f(c)""=1/3, for some c in R . Statement-2: 0""<""f(x)lt=1/(2sqrt(2)), for all x in R . (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Statement-1: The point A(3, 1, 6) is the mirror image of the point B(1, 3, 4) in the plane x""""y""+""z""=""5 . Statement-2: The plane x x""""y""+""z""=""5 bisects the line segment joining A(3, 1, 6) and B(1, 3, 4). (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Consider : Statement I: (p^^~q)^^(~p^^q) is a fallacy Statement II: (ptoq)harr(~q to ~p) is a tautology

If A is 2 x 2 invertible matrix such that A=adjA-A^-1 Statement-I 2A^2+I=O(null matrix) Statement-II: 2|A|=1 (i) Statement-I is true, Statement-II is true; Statement-II is a correct explanation for Statement-I (2) Statement-I is true, Statement-II is true; Statement-II is not a correct explanation for Statement-I. 3) Statement-I is true, Statement-II is false. (4) Statement-I is false, Statement-II is true.

Each question has 5 choices (a) ,(b) ,(c ) (d) and (e ) out of which ONLY ONE is correct. (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. (e) Statement -1 and Statement -2 both are False. Statement -1: Statement -2: Migratory aptitude of p-methoxyphenyl group is greater than migratory aptitude p-nitrophenyl of group during carbrocation rearrangements.