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MHTCET 20 Apr 2026 Shift 1 Paper

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Question : 119 of 150

Marks: +1, -0

The domain of the function

f(x)={ }^{(10-x)} C_{(x-6)}

is...

[6,10]
\{6, 7, 8, 9, 10\}
[6,8]
\{6, 7, 8\}

Solution:

Concept:

For

{ }^{n} C_{r}

to be defined,

n

and

r

must be non-negative integers and

r \leq n

.

Explanation:

Here,

n = 10-x

and

r = x-6

.

Both

n

and

r

must be non-negative:

10-x \geq 0 \Rightarrow x \leq 10

x-6 \geq 0 \Rightarrow x \geq 6

Also,

r \leq n

gives:

x-6 \leq 10-x

\Rightarrow 2x \leq 16 \Rightarrow x \leq 8

Combining:

6 \leq x \leq 8

Since

x

must be an integer,

x \in \{6,7,8\}

.

Answer:

Option D:

\{6,7,8\}

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