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Statement-1 : Solution of (1 + xsqrt(x^2...

Statement-1 : Solution of `(1 + xsqrt(x^2+y^2) ) dx + y (-1 +sqrt(x^2+y^2)) dy = 0` is `x-y^2/2+1/3(x^2 + y^2)^(3/2) +c=0` Statement-2 : Solution of `(1 + xy) y dx + (1-xy) x dy = 0` is `ln (x/y)-1/(xy)=c` (A) STATEMENT-1 is true, STATEMENT-2 is true and STATEMENT-2 is correct explanation for (B) STATEMENT-1 is true, STATEMENT-2 is true and STATEMENT-2 is not correct explanation of STATEMENT-1 for STATEMENT-1 C) STATEMENT-1 is true, STATEMENT-2 is false D)STATEMENT-1 is false, STATEMENT-2 is true

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STATEMENT-1 : The graph of y=[sqrt(1-cos2x)] consists of only two line segments. where [.] represent greatest integer function. AND STATEMENT-2: The graph of sqrt(y=1-cos2x) is STATEMENT-1 is true, STATEMENT-2 is true and STATEMENT-2 is correct explanation for STATEMENT-1 STATEMENT-1 is true, STATEMENT-2 is true and STATEMENT-2 is not correct explanation for STATEMENT-1 STATEMENT-1 is true, STATEMENT-2 is false STATEMENT-1 is false, STATEMENT-2 is true Both STATEMENTS are false

STATEMENT-1 : The graph of y=[sqrt(1-cos2x]) consists of only two line segments. where [.] represent greatest integer function. AND STATEMENT-2: The graph of sqrt(y=1-cos2x) is STATEMENT-1 is true, STATEMENT-2 is true and STATEMENT-2 is correct explanation for STATEMENT-1 STATEMENT-1 is true, STATEMENT-2 is true and STATEMENT-2 is not correct explanation for STATEMENT-1 STATEMENT-1 is true, STATEMENT-2 is false STATEMENT-1 is false, STATEMENT-2 is true Both STATEMENTS are false

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: 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.

Let a solution y=y(x) of the differential equation xsqrt(x^2-1)dy-ysqrt(y^2-1)dx=0 satisfy y(2)=2/sqrt(3) Statement-1: y(x)=sec(sec^-1x-pi/6) Statement-2: y(x) is given by 1/y=(2sqrt(3))/x-sqrt(1-1/x^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.

Let a solution y=y(x) of the differential equation xsqrt(x^2-1)dy-ysqrt(y^2-1)dx=0 satisfy y(2)=2/sqrt(3) Statement-1: y(x)=sec(sec^-1x-pi/6) Statement-2: y(x) is given by 1/y=(2sqrt(3))/x-sqrt(1-1/x^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: 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: int((x^2-1)/x^2)e^((x^2+1)/x)dx=e^((x^2+1)/x)+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: 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.