1
JEE Main 2022 (Online) 28th June Evening Shift
Numerical
+4
-1
Change Language

If the system of linear equations
$$2x - 3y = \gamma + 5$$,
$$\alpha x + 5y = \beta + 1$$, where $$\alpha$$, $$\beta$$, $$\gamma$$ $$\in$$ R has infinitely many solutions then the value
of | 9$$\alpha$$ + 3$$\beta$$ + 5$$\gamma$$ | is equal to ____________.

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2
JEE Main 2022 (Online) 28th June Evening Shift
Numerical
+4
-1
Change Language

Let $$A = \left( {\matrix{ {1 + i} & 1 \cr { - i} & 0 \cr } } \right)$$ where $$i = \sqrt { - 1} $$. Then, the number of elements in the set { n $$\in$$ {1, 2, ......, 100} : An = A } is ____________.

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3
JEE Main 2022 (Online) 28th June Evening Shift
Numerical
+4
-1
Change Language

Sum of squares of modulus of all the complex numbers z satisfying $$\overline z = i{z^2} + {z^2} - z$$ is equal to ___________.

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4
JEE Main 2022 (Online) 28th June Evening Shift
Numerical
+4
-1
Change Language

Let S = {1, 2, 3, 4}. Then the number of elements in the set { f : S $$\times$$ S $$\to$$ S : f is onto and f (a, b) = f (b, a) $$\ge$$ a $$\forall$$ (a, b) $$\in$$ S $$\times$$ S } is ______________.

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