WB JEE 2012 | Permutations and Combinations Question 11 | Mathematics

WB JEE 2012

MCQ (Single Correct Answer)

-0.33

A vehicle registration number consists of 2 letters of English alphabet followed by 4 digits, where the first digit is not zero. Then, the total number of vehicles with distinct registration numbers is

26² $$\times$$ 10⁴

$${}^{26}{P_2}$$ $$\times$$ $${}^{10}{P_4}$$

$${}^{26}{P_2}$$ $$\times$$ 9 $${}^{10}{P_3}$$

26² $$\times$$ 9 $$\times$$ 10³

WB JEE 2024

MCQ (Single Correct Answer)

-0.25

The numbers $$1,2,3, \ldots \ldots, \mathrm{m}$$ are arranged in random order. The number of ways this can be done, so that the numbers $$1,2, \ldots \ldots ., \mathrm{r}(\mathrm{r}<\mathrm{m})$$ appears as neighbours is

$$(m-r)$$ !

$$(\mathrm{m}-\mathrm{r}+1)$$ !

$$(\mathrm{m}-\mathrm{r})!\mathrm{r}$$ !

$$(\mathrm{m}-\mathrm{r}+1)!\mathrm{r}$$ !

WB JEE 2024

MCQ (Single Correct Answer)

-0.5

Five balls of different colours are to be placed in three boxes of different sizes. The number of ways in which we can place the balls in the boxes so that no box remains empty is

160

140

180

150

WB JEE 2024

MCQ (Single Correct Answer)

-0.5

$$ \text { If } 1000!=3^n \times m \text { where } m \text { is an integer not divisible by } 3 \text {, then } n= $$

498

298

398

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