Let f, g : R $\to$ R be two real valued functions defined as $f(x) = \left\{ {\matrix{ { - |x + 3|} & , & {x < 0} \cr {{e^x}} & , & {x \ge 0} \cr } } \right.$ and $g(x) = \left\{ {\matrix{ {{x^2} + {k_1}x} & , & {x < 0} \cr {4x + {k_2}} & , & {x \ge 0} \cr } } \right.$, where k1 and k2 are real constants. If (gof) is differentiable at x = 0, then (gof) ($-$ 4) + (gof) (4) is equal to :
Previous 10 Questions — JEE Main 2022 (26 June Morning Shift)
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$\mathop {\lim }\limits_{x \to {1 \over {\sqrt 2 }}} {{\sin ({{\cos }^{ - 1}}x) - x} \over {1 - \tan ({{\cos }^{ - 1}}x…
Topic: JEE Main 2022 (26 June Morning Shift)
The remainder when (2021)2023 is divided by 7 is :
Topic: JEE Main 2022 (26 June Morning Shift)
The ordered pair (a, b), for which the system of linear equations3x $-$ 2y + z = b5x $-$ 8y + 9z = 32x + y + az = $-$1h…
Topic: JEE Main 2022 (26 June Morning Shift)
Let $A = \left\{ {z \in C:\left| {{{z + 1} \over {z - 1}}} \right| < 1} \right\}$ and $B = \left\{ {z \in C:\arg \left(…
Topic: JEE Main 2022 (26 June Morning Shift)
Let $f(x) = {{x - 1} \over {x + 1}},\,x \in R - \{ 0, - 1,1\} $. If ${f^{n + 1}}(x) = f({f^n}(x))$ for all n $\in$ N, t…
Topic: JEE Main 2022 (26 June Morning Shift)
Next 10 Questions — JEE Main 2022 (26 June Morning Shift)
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The sum of the absolute minimum and the absolute maximum values of the function f(x) = |3x $-$ x2 + 2| $-$ x in the int…
Topic: JEE Main 2022 (26 June Morning Shift)
The area bounded by the curve y = |x2 $-$ 9| and the line y = 3 is :
Topic: JEE Main 2022 (26 June Morning Shift)
Let R be the point (3, 7) and let P and Q be two points on the line x + y = 5 such that PQR is an equilateral triangle.…
Topic: JEE Main 2022 (26 June Morning Shift)
If the two lines ${l_1}:{{x - 2} \over 3} = {{y + 1} \over {-2}},\,z = 2$ and ${l_2}:{{x - 1} \over 1} = {{2y + 3} \ove…
Topic: JEE Main 2022 (26 June Morning Shift)
The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about …
Topic: JEE Main 2022 (26 June Morning Shift)
Let $f(x) = 2{\cos ^{ - 1}}x + 4{\cot ^{ - 1}}x - 3{x^2} - 2x + 10$, $x \in [ - 1,1]$. If [a, b] is the range of the fu…
Topic: JEE Main 2022 (26 June Morning Shift)
