NEW
New Website Launch
Experience the best way to solve previous year questions with mock tests (very detailed analysis), bookmark your favourite questions, practice etc...
1

IIT-JEE 1998

MCQ (Single Correct Answer)
If $${a_n} = \sum\limits_{r = 0}^n {{1 \over {{}^n{C_r}}},\,\,\,then\,\,\,\sum\limits_{r = 0}^n {{r \over {{}^n{C_r}}}} } $$ equals
A
$$\left( {n - 1} \right){a_n}$$
B
$$n{a_n}$$
C
$${1 \over 2}n{a_n}$$
D
None of the above
2

IIT-JEE 1992

MCQ (Single Correct Answer)
The expansion $${\left( {x + {{\left( {{x^3} - 1} \right)}^{{1 \over 2}}}} \right)^5} + {\left( {x - {{\left( {{x^3} - 1} \right)}^{{1 \over 2}}}} \right)^5}$$ is a polynomial of degree
A
5
B
6
C
7
D
8
3

IIT-JEE 1986

MCQ (Single Correct Answer)
If $${C_r}$$ stands for $${}^n{C_r},$$ then the sum of the series $${{2\left( {{n \over 2}} \right){\mkern 1mu} !{\mkern 1mu} \left( {{n \over 2}} \right){\mkern 1mu} !} \over {n!}}\left[ {C_0^2 - 2C_1^2 + 3C_2^2 - } \right......... + {\left( { - 1} \right)^n}\left( {n + 1} \right)C_n^2\mathop ]\limits^ \sim \,,$$
where $$n$$ is an even positive integer, is equal to
A
0
B
$${\left( { - 1} \right)^{n/2}}\left( {n + 1} \right)$$
C
$${\left( { - 1} \right)^{n/2}}\left( {n + 2} \right)$$
D
$${\left( { - 1} \right)^n}n$$
4

IIT-JEE 1983

MCQ (Single Correct Answer)
The coefficient of $${x^4}$$ in $${\left( {{x \over 2} - {3 \over {{x^2}}}} \right)^{10}}$$ is
A
$${{{405} \over {256}}}$$
B
$${{{504} \over {259}}}$$
C
$${{{450} \over {263}}}$$
D
none of these

Joint Entrance Examination

JEE Main JEE Advanced WB JEE

Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

Medical

NEET

CBSE

Class 12