Differential Equations PYQ — JEE Advanced 2009 · Shift 1 · Q36 with Solution

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)	$\left( { - {\pi \over 2},{\pi \over 2}} \right)$
(B)	Interval containing the value of the integral $\int\limits_1^5 {(x - 1)(x - 2)(x - 3)(x - 4)(x - 5)dx}$	(Q)	$\left( {0,{\pi \over 2}} \right)$
(C)	Interval in which at least one of the points of local maximum of ${\cos ^2}x + \sin x$ lies	(R)	$\left( {{\pi \over 8},{{5\pi } \over 4}} \right)$
(D)	Interval in which ${\tan ^{ - 1}}(\sin x + \cos x)$ is increasing	(S)	$\left( {0,{\pi \over 8}} \right)$
		(T)	$( - \pi ,\pi )$

A
(A) $\to$ (P), (Q), (S); (B) $\to$ (P), (T), (S); (C) $\to$ (P), (Q), (R), (T); (D) $\to$ (S)
B
(A) $\to$ (P), (Q), (S); (B) $\to$ (P), (T), (R); (C) $\to$ (P), (Q), (R), (T); (D) $\to$ (R)
C
(A) $\to$ (P), (Q), (S); (B) $\to$ (P), (T), (S); (C) $\to$ (S), (Q), (R), (T); (D) $\to$ (S)
D
(A) $\to$ (P), (T), (S); (B) $\to$ (P), (T), (S); (C) $\to$ (P), (Q), (R), (T); (D) $\to$ (S)

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