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JEE Advanced
Exam
JEE Advanced
Subject
Mathematics
Chapter
Trigonometry

JEE Advanced · Mathematics · Trigonometry

The values of ' t ' which satisfies (t-[| x|])!=3!5!7! is/are...

The values of ' t ' which satisfies (t−[∣sin⁡x∣])!=3!5!7!(\mathrm{t}-[|\sin \mathrm{x}|])!=3!5!7! is/are (where [.] denotes greatest integer function) -

Options

  1. A99
  2. B1010
  3. C1111
  4. D1212

Correct answer

C. 1111

Step-by-step solution

(t−[∣sin⁡x∣])!=3!5!7! If x=nπ+π2,(n∈I) then (t−1)!=3!5!7!⇒(t−1)!=10!⇒t−1=10⇒t=11 If x≠nπ+π2,(n∈I) then (t−0)!=10!⇒t=10\begin{aligned} & (t-[|\sin x|])!=3!5!7! \\ & \text { If } x=n \pi+\frac{\pi}{2},(n \in I) \\ & \text { then }(t-1)!=3!5!7! \\ & \Rightarrow \quad(t-1)!=10! \\ & \Rightarrow \quad t-1=10 \Rightarrow t=11 \\ & \text { If } \quad x \neq n \pi+\frac{\pi}{2},(n \in I) \\ & \text { then }(t-0)!=10!\Rightarrow t=10\end{aligned}
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