1
IIT-JEE 2007 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Let $${E^c}$$ denote the complement of an event $$E.$$ Let $$E, F, G$$ be pairwise independent events with $$P\left( G \right) > 0$$ and $$P\left( {E \cap F \cap G} \right) = 0.$$ Then $$P\left( {{E^c} \cap {F^c}|G} \right)$$ equals
A
$$P\left( {{E^c}} \right) + P\left( {{F^c}} \right)$$
B
$$P\left( {{E^c}} \right) - P\left( {{F^c}} \right)$$
C
$$P\left( {{E^c}} \right) - P\left( F \right)$$
D
$$P\left( E \right) - P\left( {{F^c}} \right)$$
2
IIT-JEE 2007 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1

Let $$\mathrm{O(0,0), P(3,4), Q(6,0)}$$ be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR, OQR are of equal area. The coordinates of R are

A
$$\left(\frac{4}{3}, 3\right)$$
B
$$\left(3, \frac{2}{3}\right)$$
C
$$\left(3, \frac{4}{3}\right)$$
D
$$\left(\frac{4}{3}, \frac{2}{3}\right)$$
3
IIT-JEE 2007 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1

If $$|z|=1$$ and $$z \neq \pm 1$$, then all the values of $$\frac{z}{1-z^{2}}$$ lie on

A
a line not passing through the origin
B
$$|z|=\sqrt{2}$$
C
the X-axis
D
the Y-axis
4
IIT-JEE 2007 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1

$$\frac{d^{2} x}{d y^{2}}$$ equals :

A
$$\left(\frac{d^{2} y}{d x^{2}}\right)^{-1}$$
B
$$-\left(\frac{d^{2} y}{d x^{2}}\right)^{-1}\left(\frac{d y}{d x}\right)^{-3}$$
C
$$\left(\frac{d^{2} y}{d x^{2}}\right)\left(\frac{d y}{d x}\right)^{-2}$$
D
$$-\left(\frac{d^{2} y}{d x^{2}}\right)\left(\frac{d y}{d x}\right)^{-3}$$

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