Q.
Match the following:
Column I
Column II
A
$2 \cot \left(\cot ^{-1}(3)+\cot ^{-1}(7)+\cot ^{-1}(13)+\cot ^{-1}(21)\right)$ has the value equal to
P
3
B
If $\tan \left(\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{13}\right)+\ldots+\tan ^{-1}\left(\frac{1}{381}\right)\right)=\frac{m}{n}$ where $m, n \in N$, then the least value of $(m+n)$ is divisible by
Q
4
C
Number of integral ordered pairs $(x, y)$ satisfying the equation $\arctan \frac{1}{x}+\arctan \frac{1}{y}=\arctan \frac{1}{10}$, is
R
5
D
The smallest positive integral value of $n$ for which $( n -2) x ^2+8 x + n +4>\sin ^{-1}(\sin 12)+\cos ^{-1}(\cos 12) \forall x \in R$, is
S
8
T
10
| Column I | Column II | ||
|---|---|---|---|
| A | $2 \cot \left(\cot ^{-1}(3)+\cot ^{-1}(7)+\cot ^{-1}(13)+\cot ^{-1}(21)\right)$ has the value equal to | P | 3 |
| B | If $\tan \left(\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{13}\right)+\ldots+\tan ^{-1}\left(\frac{1}{381}\right)\right)=\frac{m}{n}$ where $m, n \in N$, then the least value of $(m+n)$ is divisible by | Q | 4 |
| C | Number of integral ordered pairs $(x, y)$ satisfying the equation $\arctan \frac{1}{x}+\arctan \frac{1}{y}=\arctan \frac{1}{10}$, is | R | 5 |
| D | The smallest positive integral value of $n$ for which $( n -2) x ^2+8 x + n +4>\sin ^{-1}(\sin 12)+\cos ^{-1}(\cos 12) \forall x \in R$, is | S | 8 |
| T | 10 | ||
Inverse Trigonometric Functions
Solution: