IIT-JEE 2008 Paper 2 Offline | Differential Equations Question 20 | Mathematics

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

A - iii; B - ii, iv; C - iii, iv; D - i, iii

A - iii; B - ii; C - iii, iv; D - i, iii

A - ii; B - ii, iv; C - iii, iv; D - i

A - ii; B - ii, iv; C - iii, iv; D - i, iii

IIT-JEE 2008 Paper 1 Offline

MCQ (Single Correct Answer)

-1

Let a and b be non-zero real numbers. Then, the equation

$$(a{x^2} + b{y^2} + c)({x^2} - 5xy + 6{y^2}) = 0$$ represents :

four straight lines, when c = 0 and a, b are of the same sign

two straight lines and a circle, when a = b, and c is of sign opposite to that of a

two straight lines and a hyperbola, when a and b are of the same sign and c is of sign opposite to that of a

a circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a

IIT-JEE 2005 Screening

MCQ (Single Correct Answer)

-0.5

For the primitive integral equation $$ydx + {y^2}dy = x\,dy;$$
$$x \in R,\,\,y > 0,y = y\left( x \right),\,y\left( 1 \right) = 1,$$ then $$y(-3)$$ is

$$3$$

$$2$$

$$1$$

$$5$$

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