1

IIT-JEE 1984

Subjective

+2

-0

If $$n$$ is a natural number such that

$$n = {p_1}{}^{{\alpha _1}}{p_2}{}^{{\alpha _2}}.{p_3}{}^{{\alpha _3}}........{p_k}{}^{{\alpha _k}}$$ and $${p_1},{p_2},\,\,......,\,{p_k}$$ are distinct primes, then show that $$In$$ $$n \ge k$$ $$in$$ 2

$$n = {p_1}{}^{{\alpha _1}}{p_2}{}^{{\alpha _2}}.{p_3}{}^{{\alpha _3}}........{p_k}{}^{{\alpha _k}}$$ and $${p_1},{p_2},\,\,......,\,{p_k}$$ are distinct primes, then show that $$In$$ $$n \ge k$$ $$in$$ 2

2

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.

(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.

3

IIT-JEE 1982

Subjective

+3

-0

Does there exist a geometric progression containing $$27, 8$$ and $$12$$ as three of its terms? If it exits, how many such progressions are possible ?

4

IIT-JEE 1980

Subjective

+3

-0

The interior angles of a polygon are in arithmetic progression. The smallest angle is $${120^ \circ }$$, and the common difference is $${5^ \circ }$$, Find the number of sides of the polygon.

Questions Asked from Sequences and Series (Subjective)

Number in Brackets after Paper Indicates No. of Questions

JEE Advanced Subjects

Physics

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