Join C - F ∆CFD ~ ∆EOD CD/FD = ED/OD 2r/8 = 5/r 2r² = 40 r² = 20 . Area of the circle : πr² = 20π

Possible remainders when a perfect cube is divided by 7 are 1 , 6 or 0. RHS is of the form 7k + 3 but LHS is never of the form 7k + 3 Hence no integr...

All perfect squares are of the form 8a , 8a + 4 or 8a + 1 . 4k +1 = 4 ( 2m +1) + 1 = 8m + 5 4k + 2 = 4 ( 2m + 1) + 2 = 8m + 6 4k + 3 = 4 ( 2m + 1) + 3...

Let the cost price of 1 pen be Rs 1. CP of 11 pens = MP of 9 pens = Rs. 11CP of 9 pens = Rs 9. if profit is p% then , 9 x ( 100 + p)/100 = 11 x ( 100...

PFA the solution:

PFA the solution:

PFA the solution

Denominator ( a - b)^3 is a multiple of 3 so ( a-b) must be a multiple of 3 Option (C).

Aniket, 16/3 is not possible as 20/(16/3) = 3.xyz means his average speed is more than thrice while coming back which is not possible

|____d_____|______________2d___________|d/2v + 2d/v = 20 5d/2v = 20 d/v = 8. |____d_____|______________2d___________|d/v + 2d/2v = T T = 2d/v = 2 x ...

Alternative Approach : speed of a train => x and the boy's speed => y.Now when the train goes in the same direction as the boy relative speed i...

first term : 1 Sum of first 3 terms : 2 Sum of first 5 terms : 3 Sum of first 7 terms : 4 ......................................Sum of first n terms :...

120 - y is a perfect sqy can take 10 different values ( All perfect squares less than 120) so, 10 different values for x

(abcde.....)/37 = bcde.... abcde.... = 37 × bcde.... a × 10ⁿ + bcde..... = 37bcde a × 10ⁿ = 36bcde..... Smallest value of a which makes LHS a ...

From 112 to 118 => sum of the product of the digits will be (1 x 1 x 2 )+ (1 x 1 x 4) , (1 x 1 x 6) , ......, (1x 1 x 8) From 122 to 118 =>sum o...