1
JEE Main 2026 (Online) 28th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The sum of all the elements in the range of $f(x) = \text{Sgn}(\sin x) + \text{Sgn}(\cos x) + \text{Sgn}(\tan x) + \text{Sgn}(\cot x)$, $x \neq \frac{n\pi}{2}, n \in \mathbb{Z}$, where

$\text{Sgn}(t) = \begin{cases} 1, & \text{if } t > 0 \\ -1, & \text{if } t < 0 \end{cases}$

is :

A

4

B

0

C

2

D

-2

2
JEE Main 2026 (Online) 28th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If $g(x)=3 x^2+2 x-3, f(0)=-3$ and $4 g(f(x))=3 x^2-32 x+72$, then $f(g(2))$ is equal to:
A

$\frac{7}{2}$

B

$-\frac{25}{6}$

C

$\frac{25}{6}$

D

$-\frac{7}{2}$

3
JEE Main 2026 (Online) 24th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $f$ be a function such that $3 f(x)+2 f\left(\frac{m}{19 x}\right)=5 x, x \neq 0$, where $m=\sum\limits_{i=1}^9(i)^2$. Then $f(5)-f(2)$ is equal to

A

36

B

9

C

-9

D

18

4
JEE Main 2026 (Online) 22nd January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $f(x)=[x]^2-[x+3]-3, x \in \mathbf{R}$, where [.] is the greatest integer funtion. Then

A

$f(x)=0$ for finitely many values of $x$

B

$f(x)<0$ only for $x \in[-1,3)$

C

$\int\limits_0^2 f(x) \mathrm{d} x=-6$

D

$f(x)>0$ only for $x \in[4, \infty)$

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