Quant Boosters  Hemant Yadav  Set 3

Q5) Find the remainder when x^4  x^3 + x^2  x + 1 divides x^24  x^13  x^7 + x^6 + 1.

Q6) If a and b are coprime to each other, then what will be the largest possible greatest common divisor of a + 201b and 201a + b.

Q7) Find the number of terms in the expansion of (1 + x^6 + x^13)^100

Q8) How many different values n can take if exponent of n in 100! is 24?
[OA : 22]

Q9) Find the number of ordered triplets (a, b, c) of positive integers such that lcm(a, b) = 72, lcm(b, c) = 600 and lcm(c, a) = 900.
[OA : 15]

Q10) Find all triplets (x, y, z) such that x, y, z, x  y, y  z and x  z all are prime positive integers
OA : [ Only (2,5,7)]

Q11) A date is written in the format MMDDYYYY. For example today it's 03262016. What will be the next date when all the eight digits used are distinct?
[OA : 06/17/2345]

Q12) What is the smallest possible number of students in a classif the percent of girls is less than 50 but at least 47?
[OA : 17]

Q13) If a, b, c are in A.P, then the value of a^3 + c^3 + 6abc is
a) 8b
b) 8b^3
c) 6b^3
d) none of these[OA : b]

Q14) If a and b are twodigit prime numbers such that a^2  b^2 = 2a + 14b + 48. Find the largest possible value of a + b.
[ OA : 89 + 97 = 186]

Q15) Find the greatest positive integer n so that 3^n divides 70! + 71! + 72!

Q16) A rectangular billiards table is 3 meters by 4 meters. A ballis on the long edge at distance (1/3)√5 from a corner. Amit hit it in such a way that it strikes each of the other walls once and returns to its starting point. How many meters did the ball travel?
(Ball can be considered to have radius 0.)

Q17) A rectangular box having dimensions a X b X c, where a, b, c are integers and 1 ≤ a ≤ b ≤ c.If volume and surface area of this box are equal then how many such rectangular boxes are possible.

Q18) What would be the highest power of 2 in 15^4096  1
a. 16
b. 15
c. 17
d. 14

Q19) A and B are running on a circular track. A runs in anticlockwise and completes a lap every 90 seconds while B runs in clockwise direction and completes a lap every 80 seconds. Both start from the start line at the same time. At some random time between 10 minutes and 11 minutes after they begin to run, a photographer standing inside the track takes a picture that shows onefourth of the track, centered on the starting line. What is the probability that both A and B are in the picture?
[OA : 3/16]

Q20) A number N when divided by 20, remainder is k. How many different possible remainders can we get if N is divided by 200?
[OA : 10]

Q21) Solve for integers x and y such that x^2  3y = 1008, where 0 ≤ x, y ≤ 100.
[OA : 2 solutions. (33,27), (36,96)]

Q22) For a natural number 'p', f(p) represents the number of natural numbers 'q' for which the equation x² + qx + p = 0 has integral roots. What is the smallest value of 'p' for which f(p) = 6?

Q23) What is the unit digit of 2^78  3^80 ?
[OA : 7]

Q24) 3 candles which can burn for 30, 40 and 50 minutes respectively are lit at different times. All three are burning simultaneously for 10 minutes and for 20 minutes exactly one of them is burning. The number of minutes in which exactly two of them are burning
(a) 35
(b) 45
(c) 70
(d) 90
(e) none of these