List of top Mathematics Questions on permutations and combinations asked in WBJEE

If \( {}^9P_3 + 5 \cdot {}^9P_4 = {}^{10}P_r \), then the value of \( 'r' \) is:
The value of the expression \( {}^{47} C_4 + \sum_{j=1}^{5} {}^{52-j} C_3 \) is:
Out of $7$ consonants and $4$ vowels, words are formed each having $3$ consonants and $2$ vowels. The number of such words that can be formed is
If $\frac{1}{^{5}C_{r}}+\frac{1}{^{6}C_{r}} =\frac{1}{^{4}C_{r}}$, then the value of $r$ equals to
$^{15}C_{3} +\,^{15}C_{5} + .. ...+\,^{15}C_{15} $ will be equal to
The number of ways four boys can be seated around a round-table in four chairs of different colours is
If $\,^{16}C_{r} =\, ^{16}C_{r+1}$, then the value of $\, ^{r}P_{r-3}$ is
The forces with magnitudes 5,3 and 1 unit are acting on a particle in the direction of the vectors 6i^+2j^+3k^;3i^−2j^+6k^ and 2i−3j^−6k^, respectively. They remain constant while the particle is displaced from the point A(2,−1,−3) to B(5,−1,1). The work done is