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. [tex]{1 \over 2}[/tex] B. [tex]{1 \over 4}[/tex] C. [tex]{1 \over 3}[/tex] D. [tex]{1 \over 6}[/tex]
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. [tex]{1 \over 16}[/tex] B. [tex]{1 \over 2}[/tex] C. [tex]{1 \over 8}[/tex] D. [tex]{1 \over 4}[/tex]
3. The coefficient of xn in the expansion of xn in the expansion of [tex]{{{e^{7x}} - {e^x}} \over {{e^{3x}}}}[/tex]
A. [tex]{{{4^{n - 1}} - {{( - 2)}^{n - 1}}} \over {n!}}[/tex] B. [tex]{{{4^{n - 1}} - {2^{n - 1}}} \over {n!}}[/tex] C. [tex]{{{4^n} - {2^n}} \over {n!}}[/tex] D. [tex]{{{4^n} + {{( - 2)}^n}} \over {n!}}[/tex]
4. The sum of the series [tex]{1 \over {1.2}} - {1 \over {2.3}} + {1 \over {3.4}} - \cdots \infty[/tex]
A. [tex]2{\log _e}2 + 1[/tex] B. [tex]2{\log _e}2[/tex] C. [tex]2{\log _e}2 - 1[/tex] D. [tex]{\log _e}2 - 1[/tex]
