If $$a^{b}b^{a} (c^{d} + d^{c}) = c^{d}d^{c} (a^{b} + b^{a}),$$ where $$a, b, c, d eq 0,$$ which of

If a b b a ( c d + d c ) = c d d c ( a b + b a ) , a^{b}b^{a} (c^{d} + d^{c}) = c^{d}d^{c} (a^{b} + b^{a}), a b b a ( c d + d c ) = c d d c ( a b + b ...

Banking SBI PO Prelims Medium Simplification/ Approximation MCQ

a^{b}b^{a} (c^{d} + d^{c}) = c^{d}d^{c} (a^{b} + b^{a}),

where

a, b, c, deq 0,

which of the following statements is/are correct?

$\frac{1}{b^{a}} + \frac{1}{a^{b}} = \frac{1}{c^{d}} + \frac{1}{d^{c}}$
If
$a^{b} - d^{c} = 0,$ then $c^{d}$ must be equal to $b^{a},$ for all real values of $a, b, c, d.$
Given
$c=0,$ then $a^{b} + b^{a} = 1,$ assuming $d$ is a non-zero number.

Only 1

Only 2

Only 1 & 3

Only 3

None of the above

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