1
JEE Main 2025 (Online) 28th January Morning Shift
Numerical
+4
-1
Change Language

Quantitative analysis of an organic compound (X) shows following % composition.

C : $14.5 \%$

Cl : 64.46%

H: 1.8 %

(Empirical formula mass of the compound $(\mathrm{X})$ is _________ $\times 10^{-1}$

(Given molar mass in $\mathrm{g} \mathrm{~mol}^{-1}$ of $\mathrm{C}: 12, \mathrm{H}: 1, \mathrm{O}: 16, \mathrm{Cl}: 35.5$)

Your input ____
2
JEE Main 2025 (Online) 28th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $\mathrm{A}(x, y, z)$ be a point in $x y$-plane, which is equidistant from three points $(0,3,2),(2,0,3)$ and $(0,0,1)$.

Let $\mathrm{B}=(1,4,-1)$ and $\mathrm{C}=(2,0,-2)$. Then among the statements

(S1) : $\triangle \mathrm{ABC}$ is an isosceles right angled triangle, and

(S2) : the area of $\triangle \mathrm{ABC}$ is $\frac{9 \sqrt{2}}{2}$,

A
both are false
B
only (S2) is true
C
only (S1) is true
D
both are true
3
JEE Main 2025 (Online) 28th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $f(x)=\frac{2^x}{2^x+\sqrt{2}}, \mathrm{x} \in \mathbb{R}$, then $\sum_\limits{\mathrm{k}=1}^{81} f\left(\frac{\mathrm{k}}{82}\right)$ is equal to

A
$82$
B
$81 \sqrt{2}$
C
$41$
D
$\frac{81}{2}$
4
JEE Main 2025 (Online) 28th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The sum, of the squares of all the roots of the equation $x^2+|2 x-3|-4=0$, is

A
$6(2-\sqrt{2})$
B
$3(3-\sqrt{2})$
C
$3(2-\sqrt{2})$
D
$6(3-\sqrt{2})$
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