Question
There are 15 numbers such that average of first 12
numbers is 35 while the average of last five numbers is 52. Find the 12th number, if the ratio between 11th and 12th number is 5:3, respectively.Solution
Sum of first 12 numbers = (12 x 35) = 420 Sum of last 5 numbers = (52 x 5) = 260 Sum of 11th and 12th number = (420 - 260) = 160 So, 12th number = 160 x (3/8) = 60
The minimum value of 45 sin2 θ + 28 cos2 θ is

Evaluate the following:
sin 60° × cos 30° + sin 30° × cos 60°
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If tan² 45°- cos² 60° x sin 45° cos 45° cot 30°, then find the value of 'x'.
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