1
JEE Main 2021 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Let $$f:R - \left\{ {{\alpha \over 6}} \right\} \to R$$ be defined by $$f(x) = {{5x + 3} \over {6x - \alpha }}$$. Then the value of $$\alpha$$ for which (fof)(x) = x, for all $$x \in R - \left\{ {{\alpha \over 6}} \right\}$$, is :
A
No such $$\alpha$$ exists
B
5
C
8
D
6
2
JEE Main 2021 (Online) 20th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Let [ x ] denote the greatest integer $$\le$$ x, where x $$\in$$ R. If the domain of the real valued function $$f(x) = \sqrt {{{\left| {[x]} \right| - 2} \over {\left| {[x]} \right| - 3}}}$$ is ($$-$$ $$\infty$$, a) $$]\cup$$ [b, c) $$\cup$$ [4, $$\infty$$), a < b < c, then the value of a + b + c is :
A
8
B
1
C
$$-$$2
D
$$-$$3
3
JEE Main 2021 (Online) 18th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Let f : R $$-$$ {3} $$\to$$ R $$-$$ {1} be defined by f(x) = $${{x - 2} \over {x - 3}}$$.

Let g : R $$\to$$ R be given as g(x) = 2x $$-$$ 3. Then, the sum of all the values of x for which f$$-$$1(x) + g$$-$$1(x) = $${{13} \over 2}$$ is equal to :
A
3
B
5
C
2
D
7
4
JEE Main 2021 (Online) 18th March Morning Shift
MCQ (Single Correct Answer)
+4
-1
The real valued function
$$f(x) = {{\cos e{c^{ - 1}}x} \over {\sqrt {x - [x]} }}$$, where [x] denotes the greatest integer less than or equal to x, is defined for all x belonging to :
A
all real except integers
B
all non-integers except the interval [ $$-$$1, 1 ]
C
all integers except 0, $$-$$1, 1
D
all real except the interval [ $$-$$1, 1 ]
JEE Main Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination
JEE MainJEE AdvancedWB JEE
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Medical
NEET
© ExamGOAL 2023