1
IIT-JEE 1991
Fill in the Blanks
+2
-0
If the mean and the variance of binomial variate $$X$$ are $$2$$ and $$1$$ respectively, then the probability that $$X$$ takes a value greater than one is equal to ...............
2
IIT-JEE 1991
Fill in the Blanks
+2
-0
The value of
$$\sin {\pi \over {14}}\sin {{3\pi } \over {14}}\sin {{5\pi } \over {14}}\sin {{7\pi } \over {14}}\sin {{9\pi } \over {14}}\sin {{11\pi } \over {14}}\sin {{13\pi } \over {14}}$$ is equal to ______.
3
IIT-JEE 1991
MCQ (Single Correct Answer)
+2
-0.5
The product of $$n$$ positive numbers is unity. Then their sum is
A
a positive integer
B
divisible by $$n$$
C
equal to $$n + {1 \over n}$$
D
never less than $$n$$
4
IIT-JEE 1991
Subjective
+4
-0
Using induction or otherwise, prove that for any non-negative integers $$m$$, $$n$$, $$r$$ and $$k$$ ,
$$\sum\limits_{m = 0}^k {\left( {n - m} \right)} {{\left( {r + m} \right)!} \over {m!}} = {{\left( {r + k + 1} \right)!} \over {k!}}\left[ {{n \over {r + 1}} - {k \over {r + 2}}} \right]$$
JEE Advanced Papers
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