CUET UG 2025 — General Test Quantitative Reasoning

(A) $^{75}P_2 - ^{75}C_2$75P2​−75C2​

$$^{75}P_2 = \frac{75!}{73!}$$75P2​=73!75!​

$$= 75 × 74$$=75×74

$$= 5550$$=5550

$$^{75}C_2 = \frac{75 × 74}{2 × 1}$$75C2​=2×175×74​

$$= \frac{5550}{2}$$=25550​

$$= 2775$$=2775

$$^{75}P_2 - ^{75}C_2 = 5550 - 2775$$75P2​−75C2​=5550−2775

$$= 2775$$=2775

(A) matches with (III)

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(B) $^{5}P_5 - ^{10}C_3$5P5​−10C3​

$$^{5}P_5 = 5!$$5P5​=5!

$$= 5 × 4 × 3 × 2 × 1$$=5×4×3×2×1

$$= 120$$=120

$$^{10}C_3 = \frac{10 × 9 × 8}{3 × 2 × 1}$$10C3​=3×2×110×9×8​

$$= \frac{720}{6}$$=6720​

$$= 120$$=120

$$^{5}P_5 - ^{10}C_3 = 120 - 120$$5P5​−10C3​=120−120

$$= 0$$=0

(B) matches with (IV)

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(C) $^{16}C_{13} - ^{8}C_3$16C13​−8C3​

Using $^{16}C_{13} = ^{16}C_{16-13} = ^{16}C_3$16C13​=16C16−13​=16C3​:

$$^{16}C_3 = \frac{16 × 15 × 14}{3 × 2 × 1}$$16C3​=3×2×116×15×14​

$$= \frac{3360}{6}$$=63360​

$$= 560$$=560

$$^{8}C_3 = \frac{8 × 7 × 6}{3 × 2 × 1}$$8C3​=3×2×18×7×6​

$$= \frac{336}{6}$$=6336​

$$= 56$$=56

$$^{16}C_{13} - ^{8}C_3 = 560 - 56$$16C13​−8C3​=560−56

$$= 504$$=504

(C) matches with (I)

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(D) $^nP_4 = 360$nP4​=360

$$n(n-1)(n-2)(n-3) = 360$$n(n−1)(n−2)(n−3)=360

For $n = 6$n=6:

$$6 × 5 × 4 × 3 = 30 × 12$$6×5×4×3=30×12

$$= 360$$=360

Therefore $n = 6$n=6

(D) matches with (II)

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Final Matching:

(A) → (III) = 2775

(B) → (IV) = 0

(C) → (I) = 504

(D) → (II) = 6