1
IIT-JEE 1982
Subjective
+5
-0
$$mn$$ squares of equal size are arranged to from a rectangle of dimension $$m$$ by $$n$$, where $$m$$ and $$n$$ are natural numbers. Two squares will be called ' neighbours ' if they have exactly one common side. A natural number is written in each square such that the number written in any square is the arithmetic mean of the numbers written in its neighbouring squares.Show that this is possible only if all the numbers used are equal.
2
IIT-JEE 1982
Fill in the Blanks
+2
-0
The coeffcient of $${x^{99}}$$ in the polynomial (x -1) (x - 2)...(x - 100) is ..............
3
IIT-JEE 1982
Fill in the Blanks
+2
-0
If $$2 + i\sqrt 3 $$ is root of the equation $${x^2} + px + q = 0$$, where p and q are real, then (p, q) = (..........,....................).
4
IIT-JEE 1982
MCQ (Single Correct Answer)
+2
-0.5
The number of real solutions of the equation $${\left| x \right|^2} - 3\left| x \right| + 2 = 0$$ is
A
4
B
1
C
3
D
2
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