1
IIT-JEE 1992
Subjective
+6
-0
Let $$p \ge 3$$ be an integer and $$\alpha $$, $$\beta $$ be the roots of $${x^2} - \left( {p + 1} \right)x + 1 = 0$$ using mathematical induction show that $${\alpha ^n} + {\beta ^n}.$$
(i) is an integer and (ii) is not divisible by $$p$$
2
IIT-JEE 1992
Fill in the Blanks
+2
-0
Let the harmonic mean and geometric mean of two positive numbers be the ratio 4 : 5. Then the two number are in the ratio .........
3
IIT-JEE 1992
MCQ (Single Correct Answer)
+2
-0.5
If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is
A
square
B
circle
C
straight line
D
two intersecting lines
4
IIT-JEE 1992
Subjective
+6
-0
Determine all values of $$\alpha $$ for which the point $$\left( {\alpha ,\,{\alpha ^2}} \right)$$ lies insides the triangle formed by the lines $$$\matrix{ {2x + 3y - 1 = 0} \cr {x + 2y - 3 = 0} \cr {5x - 6y - 1 = 0} \cr } $$$
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