Shortcut: 2times -> 6years 2^4 times -> 6*4=24 years So option B   [...]

When boy child gets born, they stop.so expected no. of boy as children=$1$till they don't get son, they keep having girls,expected no. of girls before a son gets born $E(G)=0.51(0) (if son gets born in 1st attempt) +0.49(1+E(G)) $So, $0.51E(G)=0.49$$E(G)=49/51$So by it they mean is before a boy comes, $49/51$ girls can be thereRatio of boys:girls= $1/49/51$$=51/49$ ANSWER=A [...]

Method 1: Let the length of the train be x. and time is given 12s S=D/T , so x=S*12   --- (i) In 2nd part, S=(x+170)/36   --- (ii) Equating both equation,  x/12=(x+170)/36 3x=x+170 x=85m S=85/12*(18/5) km/hr S=25.5 km/hr     Method 2(ShortTrick): If train cross its length in 12 seconds and 170 m bridge in (36-12) =24 seconds So, speed = (170/24) * (18/5)=25.5 km/hr   [...]

nth group starts with $(n-1)$$^{2}$ $+$ $1$ and ends with $n$$^{2}$ and every group consists $2n-1$ numbers $15th$ group starts with 196 and ends with $225$ $sum$ = $\frac{No of terms}{2}$ * $[first$ $term$+$last$ $term]$ = $\frac{29}{2} * [(196+1) + 225]$ = $6119$ [...]

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Another Approach: It is given 4th term=8 so consider an AP with 7 terms as following a-3d , a-2d , a-d , a , a+d , a+2d , a+3d Here 4th term = a = 8 Sum of the above series= 7*8=56 Answer= 56 [...]