JEE MAIN Logarithms And Indices Previous Year Questions (PYQs) – Page 2 of 2
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Showing 17 questions
The largest value of $ n $, for which $ 40^n $ divides $ 60! $, is:
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Solution
$ 40^n = 2^{3n} \times 5^n $
$ E_2(60!) = \left[ \frac{60}{2} \right] + \left[ \frac{60}{2^2} \right] + \left[ \frac{60}{2^3} \right] + \left[ \frac{60}{2^4} \right] + \left[ \frac{60}{2^5} \right] $
$ = 30 + 15 + 7 + 3 + 1 = 56 $
$ E_5(60!) = \left[ \frac{60}{5} \right] + \left[ \frac{60}{5^2} \right] $
$ = 12 + 2 = 14 $
$ \therefore n = \min \left( \frac{56}{3}, 14 \right) = 14 $
If $\log_e a,;\log_e b,;\log_e c$ are in an A.P. and
$\log_e a-\log_e(2b),;\log_e(2b)-\log_e(3c),;\log_e(3c)-\log_e a$ are also in an A.P., then $a:b:c$ is equal to:
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Solution
The sum of all real values of $x$ satisfying the equation
$2^{(x-1)(x^{2} + 5x - 50)} = 1$ is:
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Solution
The largest $n \in \mathbb{N}$ such that $3^n$ divides $50!$ is:
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Solution
The sum of the roots of the equation:- $x + 1 - 2{\log _2}(3 + {2^x}) + 2{\log _4}(10 - {2^{ - x}}) = 0$, is :
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Solution
If the fractional part of the number $\left\{\dfrac{2^{403}}{15}\right\}$ is $\dfrac{k}{15}$, then $k$ is equal to:
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Solution
The product of all solutions of the equation $e^{5(\log_e x)^2+3}=x^8,\ x>0$, is:
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Solution
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