Question
Find the number of ways to arrange each letter of the
word 'COMMITTEE' such that all the vowels always come together.Solution
Take all the vowels (OIEE) as one entity.
Number of letters now = 5 + 1 = 6!
Number of ways to arrange all the letters = 6! ÷ (2! × 2!) = 720 ÷ 4 = 180
Number of ways to arrange vowels = 4! ÷ 2! = 24 ÷ 2 = 12
Required number of ways = 180 × 12 = 2,160
- If sec 2P = sin² 60⁰ + sec 60⁰ - cos² 30⁰, then determine the value of (√3tan P + cot² P)
Find the value of the given trigonometric expression:
(sin 25°cos 65° + cos²25°) × sin 30° + (cos 60°tan 45°) × sec 60°
...If cos² x + sin x = 5/4, then find the value of 'sin x'.
If sin A - cos A = 3/7, then find value of sinA + cos B, where A is an acute angle.
The Value of (sin38˚)/(cos52˚)+ (cos12˚)/(sin78˚)- 4cos²60˚ is
- Find the value of sin²40° + sin²50° + cos²60° + cos²30°.
Find the value of the given expression.
2 × (sec 60° – sin 30°)
If tan θ + cot θ = 5, find the value of tan²θ + cot²θ.
Evaluate the following:
sin 25° × cos 65° + sin 65° × cos 25°
If cos 2A = 1, then find cos A
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