1
JEE Main 2025 (Online) 23rd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $\mathrm{A}, \mathrm{B}, \operatorname{and}\left(\operatorname{adj}\left(\mathrm{A}^{-1}\right)+\operatorname{adj}\left(\mathrm{B}^{-1}\right)\right)$ are non-singular matrices of same order, then the inverse of $A\left(\operatorname{adj}\left(A^{-1}\right)+\operatorname{adj}\left(B^{-1}\right)\right)^{-1} B$, is equal to

A
$\frac{A B^{-1}}{|A|}+\frac{B A^{-1}}{|B|}$
B
$\operatorname{adj}\left(\mathrm{B}^{-1}\right)+\operatorname{adj}\left(\mathrm{A}^{-1}\right)$
C
$\mathrm{AB}^{-1}+\mathrm{A}^{-1} \mathrm{~B}$
D
$\frac{1}{|A B|}(\operatorname{adj}(B)+\operatorname{adj}(A))$
2
JEE Main 2025 (Online) 23rd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $\mathrm{R}=\{(1,2),(2,3),(3,3)\}$ be a relation defined on the set $\{1,2,3,4\}$. Then the minimum number of elements, needed to be added in R so that R becomes an equivalence relation, is:

A
9
B
8
C
7
D
10
3
JEE Main 2025 (Online) 23rd January Morning Shift
Numerical
+4
-1
Change Language

The sum of all rational terms in the expansion of $\left(1+2^{1 / 3}+3^{1 / 2}\right)^6$ is equal to _________.

Your input ____
4
JEE Main 2025 (Online) 23rd January Morning Shift
Numerical
+4
-1
Change Language

If the set of all values of $a$, for which the equation $5 x^3-15 x-a=0$ has three distinct real roots, is the interval $(\alpha, \beta)$, then $\beta-2 \alpha$ is equal to _________.

Your input ____
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