1
JEE Main 2023 (Online) 11th April Evening Shift
Numerical
+4
-1

Let the probability of getting head for a biased coin be $$\frac{1}{4}$$. It is tossed repeatedly until a head appears. Let $$\mathrm{N}$$ be the number of tosses required. If the probability that the equation $$64 \mathrm{x}^{2}+5 \mathrm{Nx}+1=0$$ has no real root is $$\frac{\mathrm{p}}{\mathrm{q}}$$, where $$\mathrm{p}$$ and $$\mathrm{q}$$ are coprime, then $$q-p$$ is equal to ________.

2
JEE Main 2023 (Online) 31st January Evening Shift
Numerical
+4
-1
Let A be the event that the absolute difference between two randomly choosen real numbers in the sample space $[0,60]$ is less than or equal to a . If $\mathrm{P}(\mathrm{A})=\frac{11}{36}$, then $\mathrm{a}$ is equal to _______.
3
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 :
4
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 __________.