Answer: B) 19/90 Explanation: ASSISTANT→AAINSSSTT STATISTICS→ACIISSSTTT Here N and C are not common and same letters can be A, I, S, T. Therefore  Probability of choosing A =  2C19C1×1C110C1 = 1/45   Probability of choosing I = 19C1×2C110C1 = 1/45 Probability of choosing S = 3C19C1×3C110C1 = 1/10 Probability of choosing T = 2C19C1×3C110C1 = 1/15 Hence, Required probability =   145+145+110+115= 1990

Answer: B) 13 Explanation:  Let   Let x=333 = 333    Then, logx = 33 log3     = 27 x 0.47712 = 12.88224    Since the characteristic in the resultant value of log x is 12   ∴The number of digits in x is (12 + 1) = 13    Hence the required number of digits in 333is 13.

Answer: B) 3/2 Explanation:  = log 33 + log 23+ log 103log10×3×22        =log33 12+log 23+log 10312log(10×3×22)                 =12log 33+3 log 2+12 log103log10+log3+log22                 =32log 3 + 2 log 2 + log 10log 3 + 2 log 2 + log 10 = 32

Answer: B) 0 Explanation: = log tan10+log tan890 + log tan20+ log tan880+⋯⋯+log tan450     = log [tan10 × tan890] + log [tan20 × tan880 ] +⋯⋯+log1     ∵ tan(90-θ)=cotθ and tan 450=1     = log 1 + log 1 +.....+log 1    = 0.

Answer: C) p > q Explanation: kl>k+1l+1 for (k,l) > 0 and  k > l        Let     k = x+1    and   l = x       Therefore, x+1x>(x+1)+1(x)+1        (x + 1) > x       Therefore, log(x+1)log(x)>log(x+2)log(x+1)       ⇒logxx+1 >logx+1x+2

Let the speed of Kaushik be Sk and speed of Piyush be Sp and let the time taken by Piyush be t second then,  SkSp = 800t+20600t = 23since given ratio   t = 20 s   Speed of Piyush = Sp = 600/20 = 30 m/s   and    Speed of Kaushik = 800/40 = 20 m/s

Answer: B) 7.5 min Explanation: B runs around the track in 10 min.  i.e ,    Speed of B = 10 min per round  Therefore,  A beats B by 1 round   Time taken  by A to complete 4 rounds    = Time taken by B to complete 3 rounds    = 30 min    Therefore, A's speed = 30/4 min per round = 7.5 min per round  Hence, if the race is only of one round A's time over the course = 7 min 30 sec

Answer: B) 8 Explanation:     AmitBharatNo.of Days4540Efficiency2.22Percent(=145)2.5 Percent(=140)   Amit did the work in 56 days = 56×145×2=2845    Therefore, Rest work 17/45 was done by Amit and Bharath = 174517360 = 8 days       ( since Amit and Bharath  do the work in one day = 145+140=17360)