IIT-JEE 2008 Paper 1 Offline | Differential Equations Question 22 | Mathematics

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

If $$y=y(x)$$ and it follows the relation $$x\cos \,y + y\,cos\,x = \pi $$ then $$y''(0)=$$

$$1$$

$$-1$$

$${\pi - 1}$$

$$ - \pi $$

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

$$3$$

$$2$$

$$1$$

$$5$$

IIT-JEE 2005 Screening

MCQ (Single Correct Answer)

-0.5

The solution of primitive integral equation $$\left( {{x^2} + {y^2}} \right)dy = xy$$
$$dx$$ is $$y=y(x),$$ If $$y(1)=1$$ and $$\left( {{x_0}} \right) = e$$, then $${{x_0}}$$ is equal to

$$\sqrt {2\left( {{e^2} - 1} \right)} $$

$$\sqrt {2\left( {{e^2} + 1} \right)} $$

$$\sqrt 3 \,e$$

$$\sqrt {{{2\left( {{e^2} + 1} \right)} \over 2}} $$

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