Assertion (A): Equation `(x-a)(x-b)-2=0, altb` has one root less than a and other root greater than b. , Reason (R): A polynomial equation `f\'(x)=0` has even number of roots between a and b if `f(a) and f(b)` have opposite signs. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion (A): Equation (x-p)(x-q)-r=0 where p,q,r epsilon R and 0ltpltqltr has roots in (p,q) , Reason(R): A polynomial equation f(x)=0 has odd number of roots between a and b (altb) if f(a) and f(b) have opposite signs (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion : A^-1 exists, Reason: |A|=0 (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion: Tr(A)=0 Reason: |A|=1 (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) both A and R is false.

Assertion: r=15 Reason : ^nC_x=^InC_yrarrx+y=n (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion: |A A^T|=0 , Reason : A is a skew symmetric matrix (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion (A): Quadratic equation f(x)=0 has real and distinct roots. Reason (R): quadratic equation f(x)=0 has even number of roots between p and q(pltq) if f(p) and f(q) have same sign. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Let alpha be the root of the equation ax^2+bx+c=0 and beta be the root of the equation ax^2-bx-c=0 where alphaltbeta Assertion (A): Equation ax^2+2bx+2c=0 has exactly one root between alpha and beta ., Reason(R): A continuous function f(x) vanishes odd number of times between a and b if f(a) and f(b) have opposite signs. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion: |M|=0 , Reason: Determinant of a skew symmetric matrix is 0. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion: adj(adjA)=(det A)^(n-2)A Reason: |adjA|=|A|^(n-1) (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion: f(n) is divisible by 961, Reason : 2^(5n)=(1+31)^n (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.