Match List-I with List-II
List-I (Expressions):
(A) Find x
(B) Evaluate: , n = 6, r = 2
(C) If , find .
(D)
List-II (Values):
(I) 1
(II) 100
(III) 64
(IV) 30
Choose the correct answer from the optio

Question

Match List-I with List-II
List-I (Expressions):
(A)  Find x
(B) Evaluate: , n = 6, r = 2
(C) If , find .
(D) 
List-II (Values):
(I) 1
(II) 100
(III) 64
(IV) 30
Choose the correct answer from the options given below:

FirstInTest · Accepted Answer

Correct answer: C. (A) $1/6! + 1/7! = x/8!$
Multiply by $8!$: $8!/6! + 8!/7! = x$
$8 	imes 7 + 8 = x$
$56 + 8 = x \Rightarrow x = 64$. So, (A) matches with (III).
(B) Evaluate: $\frac{n!}{(n-r)!}$ for n = 6, r = 2. This is $^nP_r$.
$^6P_2 = 6 	imes 5 = 30$. So, (B) matches with (IV).
(C) If $^nC_9 = ^nC_8$, then $n = 9 + 8 = 17$. We need to find $^nC_{17}$, which is $^17C_{17} = 1$. So, (C) matches with (I).
(D) $^6P_3 - ^5P_2$
$^6P_3 = 6 	imes 5 	imes 4 = 120$
$^5P_2 = 5 	imes 4 = 20$
$120 - 20 = 100$. So, (D) matches with (II).
Final Matching: (A) - (III), (B) - (IV), (C) - (I), (D) - (II). This corresponds to option 3.

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