IIT-JEE 2009 Paper 1 Offline | Differential Equations Question 19 | Mathematics

IIT-JEE 2009 Paper 1 Offline

MCQ (Single Correct Answer)

-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 $${(x - 3)^2}y' + y = 0$$	(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)$$\to$$(P), (Q), (S); (B)$$\to$$(P), (T), (S); (C)$$\to$$(P), (Q), (R), (T); (D)$$\to$$(S)

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

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

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

IIT-JEE 2008 Paper 2 Offline

MCQ (Single Correct Answer)

-1

Let a solution $$y=y(x)$$ of the differential equation,

$$x\sqrt {{x^2} - 1} \,\,dy - y\sqrt {{y^2} - 1} \,dx = 0$$ satify $$y\left( 2 \right) = {2 \over {\sqrt 3 }}.$$

STATEMENT-1 : $$y\left( x \right) = \sec \left( {{{\sec }^{ - 1}}x - {\pi \over 6}} \right)$$ and

STATEMENT-2 : $$y\left( x \right)$$ given by $${1 \over y} = {{2\sqrt 3 } \over x} - \sqrt {1 - {1 \over {{x^2}}}} $$

STATEMENT-1 is True, STATEMENT-2 is True;STATEMENT-2 is a correct explanation for STATEMENT-1

STATEMENT-1 is True, STATEMENT-2 is True;STATEMENT-2 is NOT a correct explanation for STATEMENT-1

STATEMENT-1 is True, STATEMENT-2 is False

STATEMENT-1 is False , STATEMENT-2 is True

IIT-JEE 2008 Paper 2 Offline

MCQ (Single Correct Answer)

-1

Match the Statements/Expressions in Column I with the Statements/Expressions in Column II.

	Column I		Column II
(A)	The minimum value of $${{{x^2} + 2x + 4} \over {x + 2}}$$ is	(P)	0
(B)	Let A and B be 3 $$\times$$ 3 matrices of real numbers, where A is symmetric, B is skew-symmetric and (A + B) (A $$-$$ B) = (A $$-$$ B) (A + B). If (AB)$$^t$$ = ($$-1$$)$$^k$$ AB, where (AB)$$^t$$ is the transpose of the matrix AB, then the possible values of k are	(Q)	1
(C)	Let $$a=\log_3\log_3 2$$. An integer k satisfying $$1 < {2^{( - k + 3 - a)}} < 2$$, must be less than	(R)	2
(D)	If $$\sin \theta = \cos \varphi $$, then the possible values of $${1 \over \pi }\left( {\theta + \varphi - {\pi \over 2}} \right)$$ are	(S)	3