, VD(DL, VD]D) [V3, V6Q.7Statement-1: The number of solution of the equations sec-( V-x? +6x – 8) = sin(3, 02exactly one.Statement-2: The domain of sec-' x is (–00,-1] [1,0)(A) Statement-I is true, statement-2 is true and statement-2 is correct explanatione

Statement-1: The number of solution of the equations sec^-1 (sqrt(-x^2+6x-8)=sin^-1((3-x)/4) is exactly one Statement-2: The domain of sec^-1 x is (-oo, -1] U[1,oo)

Statement-1: If N the number of positive integral solutions of x_(1)x_(2)x_(3)x_(4)=770 , then N is divisible by 4 distinct prime numbers. Statement-2: Prime numbers are 2,3,5,7,11,13, . . 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)=|x-2|+|x-5|,x in R . Statement 1: f'(4)=0 Statement 2: f is continuous in [2, 5] , differentiable in (2, 5) and f(2) = f(5) . (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

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

Statement-1 : The number of paired electrons in the following gaseouos ions Mn^(3+) , Cr^(3+) , V^(3+) and Ti^(3+) are 4,3,2 and 1 respectively. Statement-2 : Cr^(3+) is most stable in aqueous solution among these ions. (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

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

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

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.

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.

Let F(x) be an indefinite integral of sin2x . Statement- 1: The function F(x) satisfies F(x+pi)=F(x) for all real x . Statement- 2: sin2(x+pi)=sin2x for all real x . (A) Statement I is true, Statement II is also true, Statement II is the correct explanation of Statement I. (B)Statement I is true, Statement II is also true, Statement II is not the correct explanation of Statement I. (C) Statement I is true, Statement II is false. (D) Statement I is false, Statement II is ture.