1
WB JEE 2012
+1
-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
A
262 $$\times$$ 104
B
$${}^{26}{P_2}$$ $$\times$$ $${}^{10}{P_4}$$
C
$${}^{26}{P_2}$$ $$\times$$ 9 $${}^{10}{P_3}$$
D
262 $$\times$$ 9 $$\times$$ 103
2
WB JEE 2024
+1
-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

A
$$(m-r)$$ !
B
$$(\mathrm{m}-\mathrm{r}+1)$$ !
C
$$(\mathrm{m}-\mathrm{r})!\mathrm{r}$$ !
D
$$(\mathrm{m}-\mathrm{r}+1)!\mathrm{r}$$ !
3
WB JEE 2024
+2
-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

A
160
B
140
C
180
D
150
4
WB JEE 2024
+2
-0.5

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

A
498
B
298
C
398
D
98
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