Let f(n) = ( 1) × ( 2) ×..... (n), n ∈ ℕ , then the number of elements in the set A = \ f(1), f(2),.......... , f(6)\ & that are positive are

Correct answer: B. 4 1, 2, 3 are positive and 4, 5, 6 are negative Hence f (1), f (2), f (3), f(5) are positive while in f (4) there are exactly one negative and three positive terms. Similarly, f ( 6 ) & is negative&

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Trigonometric Ratios & Identities

NTA Abhyas 2020 · Mathematics · Trigonometric Ratios & Identities

Let f(n) = ( 1) × ( 2) ×..... (n), n ∈ ℕ , then the number of...

Let

f\left(n\right) = \left(\sin 1\right) \times \left(\sin 2\right) \times..... \sin \left(n\right), \forall n \in \mathbb{N}

, then the number of elements in the set

A = \left\{f\left(1\right), f\left(2\right),.......... , f\left(6\right)\right\}

& that are positive are

Options

A $3$
B $4$
C $5$
D $2$

Correct answer

B. $4$

Step-by-step solution

\sin 1, \sin 2, \sin 3

are positive and

\sin 4, \sin 5, \sin 6

are negative
Hence

f \left(1\right), f \left(2\right), f \left(3\right), f\left(5\right)

are positive while in

f \left(4\right)

there are exactly one negative and three positive terms. Similarly,

f ( 6 )

& is negative&

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