1
JEE Main 2023 (Online) 25th January Evening Shift
Numerical
+4
-1
Change Language

25% of the population are smokers. A smoker has 27 times more chances to develop lung cancer than a non smoker. A person is diagnosed with lung cancer and the probability that this person is a smoker is $$\frac{k}{10}%$$. Then the value of k is __________.

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2
JEE Main 2023 (Online) 25th January Evening Shift
Numerical
+4
-1
Change Language

A triangle is formed by X-axis, Y-axis and the line $$3x+4y=60$$. Then the number of points P(a, b) which lie strictly inside the triangle, where a is an integer and b is a multiple of a, is ____________.

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3
JEE Main 2023 (Online) 25th January Evening Shift
Numerical
+4
-1
Change Language

The remainder when (2023)$$^{2023}$$ is divided by 35 is __________.

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4
JEE Main 2023 (Online) 25th January Evening Shift
Numerical
+4
-1
Change Language

If $$\int\limits_{{1 \over 3}}^3 {|{{\log }_e}x|dx = {m \over n}{{\log }_e}\left( {{{{n^2}} \over e}} \right)} $$, where m and n are coprime natural numbers, then $${m^2} + {n^2} - 5$$ is equal to _____________.

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