Answer: A Check the digits A =1,2,3,4,......9 Note that for a perfect square number with ten's place odd, unit's place of the number must be 6. 66*66 = 4356 Then D=4.
Q. No. 20:
A certain number when divided by 222 leaves a remainder 35, another number when divided by 407 leaves a remainder 47. What is the remainder when the sum of these two numbers is divided by 37?
Answer: C Number of zeroes will be decided by the power of 2 and 5 in the product. Since, the power of 5 is less than the power of 2 hence number of zero will be equal to power of 5. Power of 5 = 55*1010*1515.......*100100 =>(5+10+15+20+ (25*2)+ 30+40+.....) =>(5+10+15+....100) + (25+50+75+100) => 20/2 [2*5 + 19*5] + 250 => 1050+250 = 1300
Q. No. 22:
Two prime numbers A, B(A<B) are called twin primes i they differ by 2 (e.g 11,13,or 41,43....)If A and B are twin primes with B>23, then which of the following numbers would always divide A+B?
Answer: A Any prime number greater than 3 will be in the form of 6x+1 or 6x-1. Thus both prime number are twins let first be 6x-1 and 2nd be 6x+1 Sum = 12x Thus it is always divisible by 12.
Q. No. 23:
IBM-Daksh observes that it gets a call at an interval of very 10 minutes from Seattle, at every 12 minutes from Arizonia, at the interval of 20 minutes from New York and after every 25 minutes it gets the call from Newark. If in the early morning at 5:00 a.m. it has received the calls simultaneously from all the four destinations, then at which time it will receive the calls at a time from all places on the same day?
Answer: A IBM – Daksh gets simultaneous calls from all the placers after an interval of time given bythe LCM of 10, 12, 20 and 25 which is 300. So, the next simultaneous calls are receivedafter 300 minutes or after 5 hours or at 10:00a.m.Hence (A) is correct.
Q. No. 24:
The number obtained by interchanging the two digits of a two digit number is less than the original number by 27. If the difference between the two digits of the number is 3, what is the original number ?
Answer: D Let the number be xy. The number = 10x+y On interchanging the digits of the number = 10y+x => 10x+y - 10y-x = 27 => x-y = 3 Now, y is not equal to zero and the set of digits satisfying the condition are :- (9,6), (8,5), (7,4), (6,3), (5,2), (4,1) We can't reach on the distinct answer.