STATEMENT-1: `log(2 + sin 2x) (x^4+x^2+1)e^(sinx) gt0` STATEMENT-2: Product of non-negative expressions can not assume negative value (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: 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.

Statement-1: int((x^2+1)/x^2)e^((x^2+1)/x^(2))dx=e^((x^2+1)/x^(2))+C Statement-2: intf(x)e^(f(x))dx=f(x)+C (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: intdx/(x(1+logx)^2)=-1/(1+logx)+C , Statement-2: int(f(x))^nf\'(x)dx=(f(x))^(n+1)/(n+1)+C, n+1!=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 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:If sin ((3x)/2) cos ((5y)/3) =k^8-4k^4+5 where x,y in R , then exactly four distinct real values of k are possible Statement -2 : If sin ((3x)/2) and cos ((5y)/3) both are less than or equal to 1 and greater than or equal to -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: int(sinx)^x(xcotx+logsinx)dx=x(sinx)^x Statement-2: d/dx(f(x))^(g(x))=(f(x))^(g(x))d/dx[g(x)logf(x)] (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 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(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.

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: Yield of R-Br follows the order 1^(@) gt 2^(@) gt 3^(@) in Hundsdicker reaction Statement -2: Hundsdicker reaction follows free redical mechanism.