1
IIT-JEE 2000
Subjective
+4
-0
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.
2
IIT-JEE 1999
Subjective
+10
-0
Let a, b, c, d be real numbers in G.P. If u, v, w, satisfy the system of equations
u + 2v + 3w = 6
4u + 5v + 6w = 12
6u + 9v = 4

then show that the roots of the equation $$\left( {{1 \over u} + {1 \over v} + {1 \over w}} \right){x^2}$$
$$+ [{(b - c)^2} + {(c - a)^2} + {(d - b)^2}]x + u + v + w = 0$$ and $$20{x^2} + 10{(a - d)^2}x - 9 = 0$$ are reciprocals of each other.

3
IIT-JEE 1996
Subjective
+3
-0
The real numbers $${x_1}$$, $${x_2}$$, $${x_3}$$ satisfying the equation $${x^3} - {x^2} + \beta x + \gamma = 0$$ are in AP. Find the intervals in which $$\beta \,\,and\,\gamma$$ lie.
4
IIT-JEE 1991
Subjective
+4
-0
Let p be the first of the n arithmetic means between two numbers and q the first of n harmonic means between the same numbers. Show that q does not lie between p and $$\,{\left( {{{n + 1} \over {n - 1}}} \right)^2}\,p$$.
EXAM MAP
Medical
NEET