Each of 10 letters A,H,I,M,O,T,U,V,W and X appears same when looked at in a mirror. They are called

English

Gujarati

Hindi

6.Permutation and Combination

normal

Each of the $10$ letters $A,H,I,M,O,T,U,V,W$ and $X$ appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many three letters computer passwords can be formed (no repetition allowed) with at least one symmetric letter ?

$720$

$12240$

$3360$

$14880$

Solution

$\left( \,\underset{Total\,\,\operatorname{se}lections}{\mathop{^{26}{{C}_{3}}}}\,-\,\underset{\begin{smallmatrix}
\operatorname{se}lection\,\,excluding \\
symmetric\,\,letters
\end{smallmatrix}}{\mathop{^{16}{{C}_{3}}}}\, \right)\times 3!=12240$

Standard 11

Mathematics

The number of ways in which any four letters can be selected from the word ‘$CORGOO$’ is

hard

There are $12$ volleyball players in all in a college, out of which a team of $9$ players is to be formed. If the captain always remains the same, then in how many ways can the team be formed

easy

Determine $n$ if

$^{2 n} C_{3}:^{n} C_{3}=11: 1$

medium

There are $9$ chairs in a room on which $6$ persons are to be seated, out of which one is guest with one specific chair. In how many ways they can sit

easy

If ${ }^{1} \mathrm{P}_{1}+2 \cdot{ }^{2} \mathrm{P}_{2}+3 \cdot{ }^{3} \mathrm{P}_{3}+\ldots+15 \cdot{ }^{15} \mathrm{P}_{15}={ }^{\mathrm{q}} \mathrm{P}_{\mathrm{r}}-\mathrm{s}, 0 \leq \mathrm{s} \leq 1$ then ${ }^{\mathrm{q}+\mathrm{s}} \mathrm{C}_{\mathrm{r}-\mathrm{s}}$ is equal to …. .

hard

(JEE MAIN-2021)