Match the statements/expressions in Column I with the open intervals in Column II: Column I Column II (A) Interval contained in the domain of definition of non-zero solutions of the differential equation (x – 3)^2 y′ + y = 0 (P) (*\pi/4,\pi/2) (B) Interval containing the value of the integral \int^{5}_{1} (x - 1) (x - 3) (x - 4) (x - 5) dx (Q) (0,\pi/2) (C) Interval in which at least one of the points of local maximum of \cos^2 x + \sin x lies (R) (\pi/8,{5\pi}/4) (D) Interval in which \tan^{-1} (\sin x + \cos x) isincreasing (S) (0,\pi/8) (T) (-π ,π ) [JEE Adv 2009 P1]

Correct Answer is : (A)→(P), (Q), (S); (B)→(P), (T), (S); (C)→(P), (Q), (R), (T); (D)→(S)

(A)→(P), (R), (S); (B)→(P), (T), (S); (C)→(P), (Q), (R), (T); (D)→(S)

(A)→(P), (Q), (S); (B)→(P), (T), (S); (C)→(P), (Q), (R), (T); (D)→(S)

(A)→(P), (Q), (S); (B)→(R), (T), (S); (C)→(P), (Q), (R), (T); (D)→(Q)

(A)→(P), (Q), (S); (B)→(R), (T), (S); (C)→(P), (Q), (R), (T); (D)→(P)

Differential Equations

Section: Mathematics

Question : 22 of 23

Marks: +1, -0

Match the statements/expressions in Column I with the open intervals in Column II:

Column I

Column II

(A) Interval contained in the domain of definition of non-zero solutions of the differential equation (x–3)2y′+y=0

(P) (*

)

(B) Interval containing the value of the integral

∫

(x - 1) (x - 3) (x - 4) (x - 5) dx

(Q) (0,

)

(R) (

5π

)

(D) Interval in which tan−1(sinx+cosx) isincreasing

(S) (0,

)

(T) (-π ,π )

[JEE Adv 2009 P1]

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