1
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
The sum of the series $$1 + {1 \over {4.2!}} + {1 \over {16.4!}} + {1 \over {64.6!}} + .......$$ ad inf. is
A
$${{e - 1} \over {\sqrt e }}\,$$
B
$${{e + 1} \over {\sqrt e }}$$
C
$${{e - 1} \over {2\sqrt e }}$$
D
$${{e + 1} \over {2\sqrt e }}$$
2
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
Let $${{T_r}}$$ be the rth term of an A.P. whose first term is a and common difference is d. If for some positive integers m, n, $$m \ne n,\,\,{T_m} = {1 \over n}\,\,and\,{T_n} = {1 \over m},\,$$ then a - d equals
A
$${1 \over m} + {1 \over n}$$
B
1
C
$${1 \over {m\,n}}$$
D
0
3
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
The sum of the first n terms of the series $${1^2} + {2.2^2} + {3^2} + {2.4^2} + {5^2} + {2.6^2} + ....\,is\,{{n{{(n + 1)}^2}} \over 2}$$ when n is even. When n is odd the sum is
A
$${\left[ {{{n(n + 1)} \over 2}} \right]^2}$$
B
$${{{n^2}(n + 1)} \over 2}$$
C
$${{n{{(n + 1)}^2}} \over 4}$$
D
$$\,{{3n(n + 1)} \over 2}$$
4
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
The sum of series $${1 \over {2\,!}} + {1 \over {4\,!}} + {1 \over {6\,!}} + ........$$ is
A
$${{\left( {{e^2} - 2} \right)} \over e}\,$$
B
$${{{{\left( {e - 1} \right)}^2}} \over {2e}}$$
C
$${{\left( {{e^2} - 1} \right)} \over {2e}}\,$$
D
$${{\left( {{e^2} - 1} \right)} \over 2}$$
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