1
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 ______.
2
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 $$n$$
3
IIT-JEE 1991
Subjective
+4
-0
Using induction or otherwise, prove that for any non-negative integers $$m$$, $$n$$, $$r$$ and $$k$$ ,
$$\sum\limits_{m = 0}^k {\left( {n - m} \right)} {{\left( {r + m} \right)!} \over {m!}} = {{\left( {r + k + 1} \right)!} \over {k!}}\left[ {{n \over {r + 1}} - {k \over {r + 2}}} \right]$$
4
IIT-JEE 1991
Subjective
+4
-0
Eighteen guests have to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on the other side. Determine the number of ways in which the sitting arrangements can be made.
JEE Advanced Papers
EXAM MAP