P ---------------------------Q Time taken by Deepak to travel 20km : 2hours Time taken by Sandeep to travel 20km : 1 hour Time taken by Pawan to trave...

A |_____d_______|B let the time taken by B be t min , Time taken by A =. t - 8 min d/ [d/t + d/(t-8)] = 3 t(t-8)/(t-8+t) = 3 t^2 - 8t = 6t - 24 t = 12...

Inradius of a right angled triangle : [ sum of legs - hypotenuse ]/2

PFA the solution :

take 10! common N = 10! ( 1 + 11 x 12 + 11 x 12 x 13 x 14 +.........) = 10! x ( an odd number ) hence the highest power of 2 in N = highest power of...

33. In order to divisible by 99, 123N321 should be a multiple of 9 and 11 . 1 + 2 + 3 + N + 3 + 2 + 1 = 12 + N should be a multiple of 9 Only poss...

12 Alternative Approach: put x = 0 in the expression x² - 2ax + a² + a - 3 it reduces to a² + a - 3 = 0 a = -1/2 + (√13)/2 and -1/2 + √13/2 Here...

Solution to the Q. 12.

Solution to the Q. 10 a and b are roots So , a + b = a² + b² and ab = a²b² => ab(ab - 1) i) a = 0 => b = 0 or 1 ii) b = 0 => a = 0 or 1 i...

(Any odd number )^ (4k ) ends with 1 or 5 *( odd multiples of 5 )^(Any natural number ) ends with 5. (Any even number )^4k ends with 6 or 0 *(Even m...