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1
JEE Main 2022 (Online) 29th July Morning Shift
Numerical
+4
-1
Change Language

$$\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}$$ should be an inner orbital complex. Ignoring the pairing energy, the value of crystal field stabilization energy for this complex is $$(-)$$ ____________ $$\Delta_{0}$$. (Nearest integer)

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2
JEE Main 2022 (Online) 29th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let R be a relation from the set $$\{1,2,3, \ldots, 60\}$$ to itself such that $$R=\{(a, b): b=p q$$, where $$p, q \geqslant 3$$ are prime numbers}. Then, the number of elements in R is :

A
600
B
660
C
540
D
720
3
JEE Main 2022 (Online) 29th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$z=2+3 i$$, then $$z^{5}+(\bar{z})^{5}$$ is equal to :

A
244
B
224
C
245
D
265
4
JEE Main 2022 (Online) 29th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let A and B be two $$3 \times 3$$ non-zero real matrices such that AB is a zero matrix. Then

A
the system of linear equations $$A X=0$$ has a unique solution
B
the system of linear equations $$A X=0$$ has infinitely many solutions
C
B is an invertible matrix
D
$$\operatorname{adj}(\mathrm{A})$$ is an invertible matrix

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