1
WB JEE 2012
+1
-0.33
Two decks of playing cards are well shuffled and 26 cards are randomly distributed to a player. Then, the probability that the player gets all distinct cards is
A
$${}^{52}{C_{26}}$$ / $${}^{104}{C_{26}}$$
B
2 $$\times$$ $${}^{52}{C_{26}}$$ / $${}^{104}{C_{26}}$$
C
213 $$\times$$ $${}^{52}{C_{26}}$$ / $${}^{104}{C_{26}}$$
D
226 $$\times$$ $${}^{52}{C_{26}}$$ / $${}^{104}{C_{26}}$$
2
WB JEE 2024
+1
-0.25

Two smallest squares are chosen one by one on a chess board. The probability that they have a side in common is

A
$$\frac{1}{9}$$
B
$$\frac{2}{7}$$
C
$$\frac{1}{18}$$
D
$$\frac{5}{18}$$
3
WB JEE 2024
+1
-0.25

Two integers $$\mathrm{r}$$ and $$\mathrm{s}$$ are drawn one at a time without replacement from the set $$\{1,2, \ldots, \mathrm{n}\}$$. Then $$\mathrm{P}(\mathrm{r} \leq \mathrm{k} / \mathrm{s} \leq \mathrm{k})=$$

(k is an integer < n)

A
$$\frac{\mathrm{k}}{\mathrm{n}}$$
B
$$\frac{\mathrm{k}}{\mathrm{n}-1}$$
C
$$\frac{\mathrm{k}-1}{\mathrm{n}}$$
D
$$\frac{k-1}{n-1}$$
4
WB JEE 2024
+1
-0.25

A biased coin with probability $$\mathrm{p}(0<\mathrm{p}<1)$$ of getting head is tossed until a head appears for the first time. If the probability that the number of tosses required is even is $$\frac{2}{5}$$, then $$\mathrm{p}=$$

A
$$\frac{1}{4}$$
B
$$\frac{1}{3}$$
C
$$\frac{2}{3}$$
D
$$\frac{3}{4}$$
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