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Let S1=sum(j=1)^(10)j(j-1)^(10)Cj ,""S2=...

Let `S_1=sum_(j=1)^(10)j(j-1)^(10)C_j ,""S_2=sum_(j=1)^(10)j""^(10)C_i("andS")_"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

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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

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

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) .

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) .

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)

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 A be a 2""xx""2 matrix Statement 1 : a d j""(a d j""A)""=""A Statement 2 : |a d j""A|""=""|A| (1) Statement1 is true, Statement2 is true, Statement2 is a correct explanation for statement1 (2) Statement1 is true, Statement2 is true; Statement2 is not a correct explanation for statement1. (3) Statement1 is true, statement2 is false. (4) Statement1 is false, Statement2 is true