Question 34 — JEE Main 23 Jan 2026 (S I)

Solution

$(\mathrm{P}, \mathrm{P}, \mathrm{P})(\mathrm{QQ})(\mathrm{RR}) \mathrm{S}, \mathrm{T}, \mathrm{U}, \mathrm{V}$
(i) 3 same, 1 diff. $(\mathrm{P}, \mathrm{P}, \mathrm{P}, \mathrm{R}) \rightarrow 1 \times{ }^{6} \mathrm{C}_{1} \times\left(\frac{4!}{3!}\right)=6 \times 4=24$
(ii) 2 same, 2 diff. ( $\mathrm{Q}, \mathrm{Q}, \mathrm{P}, \mathrm{T}) \rightarrow{ }^{3} \mathrm{C}_{1} \times{ }^{6} \mathrm{C}_{2} \times\left(\frac{4!}{2!}\right)=3 \times 15 \times 12=450+90=540$
(iii) 2 same, 2 same $(\mathrm{P}, \mathrm{P}, \mathrm{R}, \mathrm{R}) \rightarrow{ }^{3} \mathrm{C}_{2} \times\left(\frac{4!}{2!2!}\right)=\frac{3 \times 24}{4}=18$
(iv) 4 different $(\mathrm{P}, \mathrm{R}, \mathrm{U}, \mathrm{V}) \rightarrow{ }^{7} \mathrm{C}_{4}(4!)=\frac{7.6 .5}{6} \times 24=42(20)=840$

Total such words $=24+540+18+840=1422$ Answer(1422)