W.B. Joint Entrance- 2011 Mathematics Paper (English Version)

WEST BENGAL JOINT ENTRANCE EXAMINATION,2011

MATHEMATICS

( English Version )

1.  4 boys and 2 girls occupy seats in a row at random. Then the probability that the two girls occupy seats side by side is

A. ${1 \over 2}$      B. ${1 \over 4}$      C. ${1 \over 3}$     D. ${1 \over 6}$

2. A coin is tossed again and again. If tail appears on first three tosses, then the chance that head appears on fourth toss is

A. ${1 \over 16}$      B.  ${1 \over 2}$      C.  ${1 \over 8}$     D.  ${1 \over 4}$

3. The coefficient of xn in the expansion of xⁿ in the expansion of ${{{e^{7x}} - {e^x}} \over {{e^{3x}}}}$

A. ${{{4^{n - 1}} - {{( - 2)}^{n - 1}}} \over {n!}}$   B. ${{{4^{n - 1}} - {2^{n - 1}}} \over {n!}}$  C. ${{{4^n} - {2^n}} \over {n!}}$   D. ${{{4^n} + {{( - 2)}^n}} \over {n!}}$

4. The sum of the series ${1 \over {1.2}} - {1 \over {2.3}} + {1 \over {3.4}} -  \cdots \infty$

A. $2{\log _e}2 + 1$  B. $2{\log _e}2$    C. $2{\log _e}2 - 1$   D. ${\log _e}2 - 1$