1
JEE Main 2023 (Online) 30th January Evening Shift
Numerical
+4
-1 A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is p. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colour is $q$. If $p: q=m: n$, where $m$ and $n$ are coprime, then $m+n$ is equal to :
2
JEE Main 2023 (Online) 25th January Evening Shift
Numerical
+4
-1 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 __________.

3
JEE Main 2023 (Online) 24th January Evening Shift
Numerical
+4
-1 Three urns A, B and C contain 4 red, 6 black; 5 red, 5 black; and $$\lambda$$ red, 4 black balls respectively. One of the urns is selected at random and a ball is drawn. If the ball drawn is red and the probability that it is drawn from urn C is 0.4 then the square of the length of the side of the largest equilateral triangle, inscribed in the parabola $$y^2=\lambda x$$ with one vertex at the vertex of the parabola, is :

4
JEE Main 2022 (Online) 29th July Evening Shift
Numerical
+4
-1
Out of Syllabus The sum and product of the mean and variance of a binomial distribution are 82.5 and 1350 respectively. Then the number of trials in the binomial distribution is ____________.

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