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 2003

Subjective
If a, b, c are in A.P., $${a^2}$$, $${b^2}$$, $${c^2}$$ are in H.P., then prove that either a = b = c or a, b, $${ - {c \over 2}}$$ form a G.P.

solve it
2

### IIT-JEE 2002

Subjective
Let a, b be positive real numbers. If a, $${{A_1},{A_2}}$$, b are in arithmetic progression, a, $${{G_1},{G_2}}$$, b are in geometric progression and a, $${{H_1},{H_2}}$$, b are in harmonic progression, show that $$\,{{{G_1},{G_2}} \over {{H_1},{H_2}}} = {{{A_1} + {A_2}} \over {{H_1} + {H_2}}} = {{(2a + b)\,(a + 2b)} \over {9ab}}$$.

solve it.
3

### IIT-JEE 2001

Subjective
Let $${a_1}$$, $${a_2}$$,.....,$${a_n}$$ be positive real numbers in geometric progression. For each n, let $${A_n}$$, $${G_n}$$, $${H_n}$$ be respectively, the arithmetic mean , geometric mean, and harmonic mean of $${a_1}$$,$${a_2}$$......,$${a_n}$$. Find an expression for the geometric mean of $${G_1}$$,$${G_2}$$,.....,$${G_n}$$ in terms of $${A_1}$$,$${A_2}$$,.....,$${A_n}$$,$${H_n}$$,$${H_1}$$,$${H_2}$$,........,$${H_n}$$.

$$G = {\left( {{A_1},{A_2}....{A_n}\,{H_1},\,{H_2}.....{H_n}} \right)^{{\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle {2n}}}}}$$
4

### IIT-JEE 2000

Subjective
The fourth power of the common difference of an arithmatic progression with integer entries is added to the product of any four consecutive terms of it. Prove that the resulting sum is the square of an integer.

solve it

### 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

NEET

Class 12