Let f, g : R $\to$ R be functions defined by
$f(x) = \left\{ {\matrix{ {[x]} & , & {x < 0} \cr {|1 - x|} & , & {x \ge 0} \cr } } \right.$ and $g(x) = \left\{ {\matrix{ {{e^x} - x} & , & {x < 0} \cr {{{(x - 1)}^2} - 1} & , & {x \ge 0} \cr } } \right.$ where [x] denote the greatest integer less than or equal to x. Then, the function fog is discontinuous at exactly :
Previous 10 Questions — JEE Main 2022 (28 June Evening Shift)
Nearest first
1
2
3
4
5
If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1 : 7 an…
Topic: JEE Main 2022 (28 June Evening Shift)
The term independent of x in the expansion of $(1 - {x^2} + 3{x^3}){\left( {{5 \over 2}{x^3} - {1 \over {5{x^2}}}} \rig…
Topic: JEE Main 2022 (28 June Evening Shift)
The number of ways to distribute 30 identical candies among four children C1, C2, C3 and C4 so that C2 receives at leas…
Topic: JEE Main 2022 (28 June Evening Shift)
Let f(x) be a quadratic polynomial such that f($-$2) + f(3) = 0. If one of the roots of f(x) = 0 is $-$1, then the sum …
Topic: JEE Main 2022 (28 June Evening Shift)
Let R1 = {(a, b) $\in$ N $\times$ N : |a $-$ b| $\le$ 13} andR2 = {(a, b) $\in$ N $\times$ N : |a $-$ b| $\ne$ 13}. The…
Topic: JEE Main 2022 (28 June Evening Shift)
Next 10 Questions — JEE Main 2022 (28 June Evening Shift)
Ascending by ID
1
2
3
4
5
6
7
8
9
10
Let f : R $\to$ R be a differentiable function such that $f\left( {{\pi \over 4}} \right) = \sqrt 2 ,\,f\left( {{\pi …
Topic: JEE Main 2022 (28 June Evening Shift)
Let f : R $\to$ R be a continuous function satisfying f(x) + f(x + k) = n, for all x $\in$ R where k > 0 and n is a po…
Topic: JEE Main 2022 (28 June Evening Shift)
The area of the bounded region enclosed by the curve $y = 3 - \left| {x - {1 \over 2}} \right| - |x + 1|$ and the x-axi…
Topic: JEE Main 2022 (28 June Evening Shift)
Let x = x(y) be the solution of the differential equation $2y\,{e^{x/{y^2}}}dx + \left( {{y^2} - 4x{e^{x/{y^2}}}} \righ…
Topic: JEE Main 2022 (28 June Evening Shift)
Let the slope of the tangent to a curve y = f(x) at (x, y) be given by 2 $\tan x(\cos x - y)$. If the curve passes thro…
Topic: JEE Main 2022 (28 June Evening Shift)
Let a triangle be bounded by the lines L1 : 2x + 5y = 10; L2 : $-$4x + 3y = 12 and the line L3, which passes through th…
Topic: JEE Main 2022 (28 June Evening Shift)
Let a > 0, b > 0. Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola ${{{x^2}…
Topic: JEE Main 2022 (28 June Evening Shift)
Let $\overrightarrow a = \alpha \widehat i + 2\widehat j - \widehat k$ and $\overrightarrow b = - 2\widehat i + \alp…
Topic: JEE Main 2022 (28 June Evening Shift)
If vertex of a parabola is (2, $-$1) and the equation of its directrix is 4x $-$ 3y = 21, then the length of its latus …
Topic: JEE Main 2022 (28 June Evening Shift)
The probability that a randomly chosen one-one function from the set {a, b, c, d} to the set {1, 2, 3, 4, 5} satisfies …
Topic: JEE Main 2022 (28 June Evening Shift)
