1
IIT-JEE 1983
Subjective
+2
-0
Find three numbers $$a,b,c$$ between $$2$$ and $$18$$ such that
(i) their sum is $$25$$
(ii) the numbers $$2,$$ $$a, b$$ are consecutive terms of an A.P. and
(iii) the numbers $$b,c,18$$ are consecutive terms of a G.P.
2
IIT-JEE 1983
MCQ (Single Correct Answer)
+1
-0.25
The rational number, which equals the number $$2\overline {357} $$ with recurring decimal is
A
$${{2355} \over {1001}}$$
B
$${{2379} \over {997}}$$
C
$${{2355} \over {999}}$$
D
none of these
3
IIT-JEE 1983
Subjective
+2
-0
m men and n women are to be seated in a row so that no two women sit together. If $$m > n$$, then show that the number of ways in which they can be seated is $$\,{{m!(m + 1)!} \over {(m - n + 1)!}}$$
4
IIT-JEE 1983
Subjective
+2
-0
Use mathematical Induction to prove : If $$n$$ is any odd positive integer, then $$n\left( {{n^2} - 1} \right)$$ is divisible by 24.
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