Answer: D) Option D Explanation: Let S be the sample space. Then,n(s) = number of ways of drawing 4 pearls out of 14 = C414 ways = 14×13×12×114×3×2×1= 1001 Let E be the event of drawing 4 pearls of the same colour.Then, E = event of drawing (4 pearls out of 5) or (4 pearls out of 4) or (4 pearls out of 5)   ⇒C15+ C44+ C15 = 5+1+5 =11  P(E) = n(E)n(S)=111001=191      Required probability = 1-191=9091

Answer: D) 1/14 Explanation: The 8 letters can be written in 8! ways.n(S) = 8!Let E be the event that the letters b,c,d,e always come together when the first 8 alphabets are written down.Now the letters a, (bcde), f, g and h can be arranged in 5! ways.The letters b,c,d and e can be arranged themselves in 4! ways.n(E) = 5! x 4!Now, the required P(E) = n(E)/n(S) = 5! x 4!/8! = 1/14Hence the answer is 1/14.

Answer: C) 66.6 mts Explanation: From above diagramAC represents the hill and DE represents the tower Given that AC = 100 m angleXAD = angleADB = 30° (∵ AX || BD ) angleXAE = angleAEC = 60° (∵ AX || CE) Let DE = h Then, BC = DE = h, AB = (100-h) (∵ AC=100 and BC = h), BD = CE tan 60°=AC/CE => √3 = 100/CE =>CE = 100/√3 ----- (1) tan 30° = AB/BD => 1/√3 = 100−h/BD => BD = 100−h(√3)∵ BD = CE and Substitute the value of CE from equation 1 100/√3 = 100−h(√3) => h = 66.66 mts The height of the tower = 66.66 mts.

Answer: C) 11/120 Explanation: Let the numbers be a and b.We know that product of two numbers = Product of their HCF and LCMThen, a + b = 55 and ab = 5 x 120 = 600.=> The required sum = (1/a) + (1/b) = (a+b)/ab=55/600 = 11/120

Answer: C) 5.76 kms Explanation: Speed in still water = 6 kmph Stream speed = 1.2 kmph Down stream  = 7.2 kmph Up Stream = 4.8 kmph x/7.2 + x/4.8 = 1 x = 2.88 Total Distance  = 2.88 x 2 = 5.76 kms

Answer: A) 50 yrs Explanation: Let the daughter age be 'x'Therefore, Son age = 5x, Mother age = 25x, Person age = 50x. Thus we get, x+5x+25x+50x = 8181x = 81x = 1 Daughter's age = 1, Son's = 5, Mother's = 25, Person's age = 50.

Answer: B) 9 yrs Explanation: Let the present ages of A and B be 'x' and 'y' respectively From the given data,  [(x-2) + (y-2)]/2 = 26 => x+y = 56 But given the age of A, 5 years hence is 40 yrs => present age of A = 40 - 5 = 35 yrs => x = 35 => y = 56 - 35 = 21 => Age of B = 21 yrs Given B is 5 years younger to C, => Age of C = 21 + 5 = 26 yrs => Required Difference between ages of A and C = 35 - 26 = 9 yrs.

Answer: B) 8 Explanation: Two digit numbers: The two digits can be 2 and 9: Two possibilities 29 and 92.Three-digit numbers: The three digits can be 1, 2 and 9 => 3! Or 6 possibilities.We cannot have three digits as (3, 3, 2) as the digits have to be distinct.We cannot have numbers with 4 digits or more without repeating the digits.So, there are totally 8 numbers.