Answer: C) 98 mts Explanation: Let the distance between home and school is 'x'.Let actual time to reach be 't'.Thus, x/4 = t + 4 ---- (1)and x/6 = t - 30 -----(2)Solving equation (1) and (2)=> x = 98 mts.

Answer: A) 1:7 Explanation: Let the speed of the trains be x and y respectively length of train1 = 47xlength of train2 = 31yRelative speed= x + yTime taken to cross each other = 33 s=> 47x+31yx+y= 33=> (47x + 31 y) = 33(x + y)=> 14x = 2y=> x/y = 2/14 = 1/7  = 1:7

Answer: B) 1/2 Explanation: Multiples of 3 below 20 are 3, 6, 9, 12, 15, 18 Multiples of 5 below 20 are 5, 10, 15, 20 Required number of possibilities = 10Total number of possibilities = 20Required probability = 10/20 = 1/2.

Answer: D) 3/4 Explanation: Let S be the sample space.Here n(S)= 23 = 8Let E be the event of getting atmost two heads. Then,n(E) = {(H,T,T), (T,H,T), (T,T,H), (H,H,T), (T,H,H), (H,T,H)}Required probability = n(E)/n(S) = 6/8 = 3/4.

Answer: B) 2 Explanation: Given a2 + b2 = c2   Now  1logc+ab  + 1logc-ab    = logbc+a + logbc-a   = logbc2-a2 = 2logbb = 2

Answer: B) (1+2m)/2 Explanation: log4928 = 12log77×4   = 12+122log72= 12+log72= 12 + m= 1+2m2.

Answer: D) 2 Explanation: Since 653xy is divisible by 5 as well as 2, so y = 0.Now, 653x0 must be divisible by 8.So, 3x0 must be divisible by 8. This happens when x = 2x + y = (2 + 0) = 2.

Answer: C) 12 Explanation: we can do this by trial and error method. Putting x = 2,we get 2²(2² - 1) = 12.checking with other integers, the above equation always gives a value which is a multiple of 12,So, x²(x² - 1) is always divisible by 12.