IIT-JEE 2009 Paper 2 Offline | Differential Equations Question 23 | Mathematics

1

IIT-JEE 2009 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-0

Match the statements/expressions in Column I with the values given in Column II:

	Column I		Column II
(A)	The number of solutions of the equation $$x{e^{\sin x}} - \cos x = 0$$ in the interval $$\left( {0,{\pi \over 2}} \right)$$	(P)	1
(B)	Value(s) of $$k$$ for which the planes $$kx + 4y + z = 0,4x + ky + 2z = 0$$ and $$2x + 2y + z = 0$$ intersect in a straight line	(Q)	2
(C)	Value(s) of $$k$$ for which $$\|x - 1\| + \|x - 2\| + \|x + 1\| + \|x + 2\| = 4k$$ has integer solution(s)	(R)	3
(D)	If $$y' = y + 1$$ and $$y(0) = 1$$ then value(s) of $$y(\ln 2)$$	(S)	4
		(T)	5

A

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

B

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

C

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

D

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

2

IIT-JEE 2009 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-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

(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)

3

IIT-JEE 2008 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-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 $${1 \over y} = {{2\sqrt 3 } \over x} - \sqrt {1 - {1 \over {{x^2}}}} $$

A

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

B

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

C

STATEMENT-1 is True, STATEMENT-2 is False

D

STATEMENT-1 is False , STATEMENT-2 is True

4

IIT-JEE 2007 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-1

The differential equation $$\frac{d y}{d x}=\frac{\sqrt{1-y^{2}}}{y}$$ determines a family of circles with :

A

variable radii and a fixed centre at $$(0,1)$$

B

variable radii and a fixed centre at $$(0,-1)$$

C

fixed radius 1 and variable centres along the $$x$$-axis

D

fixed radius 1 and variable centres along the $$y$$-axis

JEE Advanced Subjects