2. Find the least number which when divided by 35,leaves remainder 25,when divided by45,leaves remainder 35 and when divided by 55,leaves remainder 45?
Sol: 3455
Hint: l.c.m of(35,45,55) minus 10
l.c.m is 3465.Hence the answer is 3455.
3. What is the remainder left after dividing 1!+2!+3!+...+100! By 7?
Sol: 5
Hint: 7! Onwards all terms are divisible by 7 as 7 is one of the factor. So there is no remainder left for those terms. i.e. remainder left after dividing 7!+8!+9!+..+100! Is 0.The only part to be consider is=1!+..+6!=873;
The remainder left after dividing 873 by 7 is 5.Hence the remainder is 5.
4. Two identical pack of cards A and B are shuffled thoroughly.
One card is picked from A and shuffled with B. The top card from pack A is turned up. If this is the Queen of hearts, what are the chances that the top card in B will be the King of hearts?
Sol: 52/2703
Hint: There are two cases to be considered.
Case1: King of hearts is drawn from pack A and shuffled with pack B.
Probability of drawing king of hearts from pack A=1/51(as queen of hearts is not to be drawn. Probability of having King of hearts on the top of the pack B=2/53
So, total probability of case 1=(1/51)*(2/53)=2/(51*53)
Case 2: King of hearts is not drawn from pack A
Probability of not drawing king of hearts from pack A=50/51(as queen of hearts is not to be
drawn).Probability of having king of hearts on the top of the pack B=1/53
So total probability, the required probability is=2/(51*53)+50/(51*53)
1. Find the next no. in the series 1, 2 ,4 ,13 ,31 ,62 ,124 ,__
Sol: 253
Hint: This is series of 1,2,4,8,16,32,64,128 with the base 5.
2. Expand RISC
Sol: Reduced Instruction Set Computing.
3. At what time after 4.00p.m. is the minutes hand of a clock
exactly aligned with the hour hand?
Sol: 4:21:49.5
Hint: Assume that x minutes after 4.00pm minute hand exactly aligns with and hour hand.
For every minute, minute hand travels 6 degrees.
Hence, for x minutes it will travel 6*x degrees. For every minute, hour hand travels ½ degrees. Hence for x minutes it will travel x/2 degrees. At 4.00pm the angle between minute hand and hour hand is 120 degrees. Also, after x minutes, minute hand and hour hand are exactly aligned. So the angle with respect to 12 i.e. Vertical plane will be same. Therefore,
Hint: stack overflow. main function calls itself again and again. Each time the function is called its return address is stored in the call stack. Since there is no condition to terminate the function call, the call stack overflows at runtime. So it terminates the program and results in an error.
5. A class of 100 students.24 of them are girls and 32 are not. Which base is used here?
Sol: 6
Hint: Let the base be x. Therefore (x*x + x*0+0)=(2*x+4)+(3*x+2)