1. If three distinct numbers are chosen randomly from the first 100 natural numbers, then the probability that all three of them are divisible by both 2 and 3 is
a. 4/33 b. 2/33 c. 4/25 d. 4/35 e. 4/1155
2.If a, b and c are three integers such that at least two of them are unequal, and ω (≠1) is a cube root of unity, then the least value of the expression |a + bω + cω²| is
a. 1
b. 0
c. √3/2
d. 1/2
3. If y = y(x) is a function of x satisfying the relation x cos y + y cos x = π, then y"(0) equals
a. 1
b. -1
c. -π
d. π
4. The area bounded by the parabolas y = (x+1)² and y = (x-1)² and the line y = 1/4 is
a. 1/6 sq. units
b. 4/3 sq. units
c. 1/3 sq. units
d. 4 sq units
5. A unbiased cubical die is rolled until one appears. The probability that an even number of trials is required is
a. 5/6
b. 6/11
c. 5/11
d. 1/6
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