Let `S_1=sum_(j=1)^(10)j(j-1)^(10)C_j ,""S_2=sum_(j=1)^(10)j""^(10)C_j and S_3=sum_(j=1)^(10)j^2""^("10")"C"_"j"dot` Statement-1: `S_3=""55xx2^9` Statement-2: `S_1=""90xx2^8a n d""S_2=""10xx2^8` . (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

Let S_(1) = sum_(j=1)^(10) j(j-1).""^(10)C_(j), S_(2) = sum_(j=1)^(10)j.""^(10)C_(j) , and S_(3) = sum_(j=1)^(10) j^(2).""^(10)C_(j) . Statement 1 : S_(3) = 55 xx 2^(9) . Statement 2 : S_(1) = 90 xx 2^(8) and S_(2) = 10 xx 2^(8) .

S_(1)= sum_(j=1)^(10) j (j -1)""^(10)C_(j) and S_(2)= sum_(j=1)^(10)j.""^(10)C_(j) . Statement-1 S_(3) = 50xx2^(9) . Statement-2 S_(1) = 90xx2^(8) and S_(2) = 10 xx 2^(8)

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: 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: 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.

Four numbers are chosen at random (without replacement) from the set {1, 2, 3, ....., 20}. Statement-1: The probability that the chosen numbers when arranged in some order will form an AP Is 1/(85) . Statement-2: If the four chosen numbers form an AP, then the set of all possible values of common difference is {1, 2, 3, 4, 5}. (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: In naphthalene all C-C bonds are equal and Statement-2: Like benzene naphthalene is also aromatic. (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: p-Nitroaniline is more polar than nitrobenzene and Statement-2: Nitro group has -M effect. (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