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Q. 1. A variable takes value x with frequency n+x –1Cx, x = 0, 1, 2, …n. The mode of the variable is.................. (1982 - 2 Marks)

Ans. n

Sol. Frequency for variable x is n + x  –1Cx where x = 0, 1, 2, .......n.
Mode is the variable for which freq. is max.
Now, nCr is max for r = n/2, if n is even

Fill in the Blanks: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advancedif n is odd.

If n + x – 1  is even then for max value of n + x –1Cx,

Fill in the Blanks: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced=n –1 , ∴ freq 2n–2Cn–1

If n + x – 1 is odd then for max value of n+x-1Cx

Fill in the Blanks: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced x=n , ∴ freq 2n–1Cn

But we know 2n–1Cn =Fill in the Blanks: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced

i.e., 2n–1Cn >2n–2Cn–1

∴ Mode should be n.

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