1
JEE Main 2023 (Online) 10th April Evening Shift
Numerical
+4
-1
Change Language

The specific conductance of $$0.0025 ~\mathrm{M}$$ acetic acid is $$5 \times 10^{-5} \mathrm{~S} \mathrm{~cm}^{-1}$$ at a certain temperature. The dissociation constant of acetic acid is __________ $$\times ~10^{-7}$$ (Nearest integer)

Consider limiting molar conductivity of $$\mathrm{CH}_{3} \mathrm{COOH}$$ as $$400 \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}$$

Your input ____
2
JEE Main 2023 (Online) 10th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$S = \left\{ {z = x + iy:{{2z - 3i} \over {4z + 2i}}\,\mathrm{is\,a\,real\,number}} \right\}$$. Then which of the following is NOT correct?

A
$$y + {x^2} + {y^2} \ne - {1 \over 4}$$
B
$$(x,y) = \left( {0, - {1 \over 2}} \right)$$
C
$$x = 0$$
D
$$y \in \left( { - \infty , - {1 \over 2}} \right) \cup \left( { - {1 \over 2},\infty } \right)$$
3
JEE Main 2023 (Online) 10th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways, in which they can be transported, is :

A
560
B
1680
C
3360
D
1120
4
JEE Main 2023 (Online) 10th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the number $$(22)^{2022}+(2022)^{22}$$ leave the remainder $$\alpha$$ when divided by 3 and $$\beta$$ when divided by 7. Then $$\left(\alpha^{2}+\beta^{2}\right)$$ is equal to :

A
13
B
10
C
20
D
5
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