# 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. $${\log _e}2 - 1$$

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