JEE Advanced2009MathematicsDefinite IntegrationActual
Match the statements/expressions in Column I with the open intervals in Column II.
Options
- A(A) p,q,t, (B) q,t, (C) r,s, (D) p,s
- B(A) p,q,s, (B) p,t, (C) p,q,r,t, (D) s
- C(A) p,q,s, (B) q,t, (C) r,s,t, (D) p,s
- D(A) p,q,t, (B) p,t, (C) p,q,r,t, (D) s
Correct answer
B. (A) p,q,s, (B) p,t, (C) p,q,r,t, (D) s
Step-by-step solution
(a) Given, (x-3)^2 y^ +y=0 array rlrl & d y d x & =- y (x-3)^2 & & d y y & =- d x (x-3)^3 & & y & = 1 (x-3) + C & & y & =C e^ 1 x-3 , C 0 array Domain of y is x R- 3 Aliter Given differential equation is homogeneous linear differential equation and has x=3 as a singular point, hence x=3 cannot be in domain of solution. (b) Let I= ₁^5(x-1)(x-2)(x-3)(x-4)(x-5) d x Let x-3=t d x=d t I= _ -2 ^2(t+2)(t+1) t(t-1)(t-2) d t Integrand is an odd function. I=0 Aliter Let I= ₁^5(x-1)(x-2)(x-3)(x-4)(x-5) d x Using, _a^b f(x) d