KEAM Paper 2 Mock Test - 9 - JEE MCQ

Period of cot 3x is π/3 and period of cos (4x + 3) is π/2 
⇒ L.C.M. is π, hence the answer.

Since, sin 190° = - sin 10°, sin 200° = - sin 20°, 
sin 210° = - sin 30°, sin 360° = sin 180° = 0 etc.
Hence all the terms in the expression cancels out, therefore answer is 0.

Probability of getting atleast seven points 
= Probability of getting 7 points or 8 points 
= Prob. of getting 7 points + Prob. of getting 8 points. 
Seven points in four matches can be obtained in the following four different ways :
2, 2, 2, 1; 
2, 2, 1, 2; 
2, 1, 2, 2; 
1, 2, 2, 2
The probability of each of these ways = (0.50)^{3 x} (0.05) (by multiplication theorem for independent events) 
= 0.00625
Hence, probability of getting 7 points = ^{4 x} (0.00625) (by add. Theorem) 
= 0.0250.
Eight points in four matches can be obtained only in one way i.e. 2, 2, 2, 2.
Hence, Prob. of getting 8 points = (0.50)⁴ = 0.0625
Thus, the required prob. = 0.250 + 0.0625 = 0.0875.