1
IIT-JEE 2009 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
An ellipse intersects the hyperbola $$2{x^2} - 2{y^2} = 1$$ orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinate axes then
A
equation of ellipse is $${x^2} + 2{y^2} = 2$$
B
the foci of ellipse are $$\left( { \pm 1,0} \right)$$
C
equation of ellipse is $${x^2} + 2{y^2} = 4$$
D
the foci of ellipse are $$\left( { \pm \sqrt 2 ,0} \right)$$
2
IIT-JEE 2009 Paper 2 Offline
Numerical
+3
-1

If the function $$f(x) = {x^3} + {e^{x/2}}$$ and $$g(x) = {f^{ - 1}}(x)$$, then the value of $$g'(1)$$ is _________.

Your input ____
3
IIT-JEE 2009 Paper 2 Offline
Numerical
+3
-1

Let ABC and ABC' be two non-congruent triangles with sides AB = 4, AC = AC' = 2$$\sqrt2$$ and angle B = 30$$^\circ$$. The absolute value of the difference between the areas of these triangles is ___________.

Your input ____
4
IIT-JEE 2009 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
For the function $$$f\left( x \right) = x\cos \,{1 \over x},x \ge 1,$$$
A
for at least one $$x$$ in the interval $$\left[ {1,\infty } \right)$$, $$f\left( {x + 2} \right) - f\left( x \right) < 2$$
B
$$\mathop {\lim }\limits_{x \to \infty } f'\left( x \right) = 1$$
C
for all $$x$$ in the interval $$\left[ {1,\infty } \right)f\left( {x + 2} \right) - f\left( x \right) > 2$$
D
$$f'(x)$$ is strictly decreasing in the interval $$\left[ {1,\infty } \right)$$
JEE Advanced Papers
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12