1
JEE Main 2021 (Online) 26th August Morning Shift
Numerical
+4
-1
If y = y(x) is an implicit function of x such that loge(x + y) = 4xy, then $${{{d^2}y} \over {d{x^2}}}$$ at x = 0 is equal to ___________.
2
JEE Main 2021 (Online) 17th March Morning Shift
Numerical
+4
-1
If $$f(x) = \sin \left( {{{\cos }^{ - 1}}\left( {{{1 - {2^{2x}}} \over {1 + {2^{2x}}}}} \right)} \right)$$ and its first derivative with respect to x is $$- {b \over a}{\log _e}2$$ when x = 1, where a and b are integers, then the minimum value of | a2 $$-$$ b2 | is ____________ .
3
JEE Main 2020 (Online) 2nd September Evening Slot
Numerical
+4
-0
If y = $$\sum\limits_{k = 1}^6 {k{{\cos }^{ - 1}}\left\{ {{3 \over 5}\cos kx - {4 \over 5}\sin kx} \right\}}$$,

then $${{dy} \over {dx}}$$ at x = 0 is _______.
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