1
JEE Main 2023 (Online) 31st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
The absolute minimum value, of the function

$f(x)=\left|x^{2}-x+1\right|+\left[x^{2}-x+1\right]$,

where $[t]$ denotes the greatest integer function, in the interval $[-1,2]$, is :
A
$\frac{3}{4}$
B
$\frac{3}{2}$
C
$\frac{1}{4}$
D
$\frac{5}{4}$
2
JEE Main 2023 (Online) 31st January Morning Shift
MCQ (Single Correct Answer)
+4
-1
If the domain of the function $$f(x)=\frac{[x]}{1+x^{2}}$$, where $$[x]$$ is greatest integer $$\leq x$$, is $$[2,6)$$, then its range is
A
$$\left(\frac{5}{37}, \frac{2}{5}\right]-\left\{\frac{9}{29}, \frac{27}{109}, \frac{18}{89}, \frac{9}{53}\right\}$$
B
$$\left(\frac{5}{37}, \frac{2}{5}\right]$$
C
$$\left(\frac{5}{26}, \frac{2}{5}\right]$$
D
$$\left(\frac{5}{26}, \frac{2}{5}\right]-\left\{\frac{9}{29}, \frac{27}{109}, \frac{18}{89}, \frac{9}{53}\right\}$$
3
JEE Main 2023 (Online) 30th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
The range of the function $f(x)=\sqrt{3-x}+\sqrt{2+x}$ is :
A
$[2 \sqrt{2}, \sqrt{11}]$
B
$[\sqrt{5}, \sqrt{13}]$
C
$[\sqrt{2}, \sqrt{7}]$
D
$[\sqrt{5}, \sqrt{10}]$
4
JEE Main 2023 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1

Consider a function $$f:\mathbb{N}\to\mathbb{R}$$, satisfying $$f(1)+2f(2)+3f(3)+....+xf(x)=x(x+1)f(x);x\ge2$$ with $$f(1)=1$$. Then $$\frac{1}{f(2022)}+\frac{1}{f(2028)}$$ is equal to

A
8000
B
8400
C
8100
D
8200
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