The value of $\cot \left( {\sum\limits_{n = 1}^{50} {{{\tan }^{ - 1}}\left( {{1 \over {1 + n + {n^2}}}} \right)} } \right)$ is :
Previous 10 Questions — JEE Main 2022 (27 June Evening Shift)
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If a point A(x, y) lies in the region bounded by the y-axis, straight lines 2y + x = 6 and 5x $-$ 6y = 30, then the pro…
Topic: JEE Main 2022 (27 June Evening Shift)
The mean and variance of the data 4, 5, 6, 6, 7, 8, x, y, where x < y, are 6 and ${9 \over 4}$ respectively. Then ${x^4…
Topic: JEE Main 2022 (27 June Evening Shift)
Let $\overrightarrow a $ and $\overrightarrow b $ be the vectors along the diagonals of a parallelogram having area $2\…
Topic: JEE Main 2022 (27 June Evening Shift)
The shortest distance between the lines ${{x - 3} \over 2} = {{y - 2} \over 3} = {{z - 1} \over { - 1}}$ and ${{x + 3} …
Topic: JEE Main 2022 (27 June Evening Shift)
The set of values of k, for which the circle $C:4{x^2} + 4{y^2} - 12x + 8y + k = 0$ lies inside the fourth quadrant and…
Topic: JEE Main 2022 (27 June Evening Shift)
If the equation of the parabola, whose vertex is at (5, 4) and the directrix is $3x + y - 29 = 0$, is ${x^2} + a{y^2} +…
Topic: JEE Main 2022 (27 June Evening Shift)
If the solution curve of the differential equation $(({\tan ^{ - 1}}y) - x)dy = (1 + {y^2})dx$ passes through the point…
Topic: JEE Main 2022 (27 June Evening Shift)
The integral $\int\limits_0^1 {{1 \over {{7^{\left[ {{1 \over x}} \right]}}}}dx} $, where [ . ] denotes the greatest in…
Topic: JEE Main 2022 (27 June Evening Shift)
Let f be a differentiable function in $\left( {0,{\pi \over 2}} \right)$. If $\int\limits_{\cos x}^1 {{t^2}\,f(t)dt = …
Topic: JEE Main 2022 (27 June Evening Shift)
If m and n respectively are the number of local maximum and local minimum points of the function $f(x) = \int\limits_0^…
Topic: JEE Main 2022 (27 June Evening Shift)
