1
IIT-JEE 2007 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-0

Match the crystal system/unit cells mentioned in Column I with their characteristic features mentioned in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 $$\times$$ 4 matrix given in the ORS.

Column I Column II
(A) Simple cubic and face-centred cubic (P) have these cell parameters $$a=b=c$$ and $$\alpha=\beta=\gamma$$
(B) cubic and rhombohedral (Q) are two crystal systems
(C) cubic and tetragonal (R) have only two crystallographic of 90$$^\circ$$
(D) hexagonal and monoclinic (S) belong to same crystal system

A
$$\mathrm{A-(s);B-(q);C-(q);(d)-(q,r)}$$
B
$$\mathrm{A-(p,s);B-(p);C-(q);(d)-(r)}$$
C
$$\mathrm{A-(p,s);B-(p,q);C-(q);(d)-(q,r)}$$
D
$$\mathrm{A-(s);B-(q);C-(q);(d)-(q)}$$
2
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
$$P\left( E \right) - P\left( {{F^c}} \right)$$
3
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
$$\left(\frac{4}{3}, \frac{2}{3}\right)$$
4
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

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