CAT Question Bank (Quant)  Gaurav Sharma  Set 2

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q10) Find the no of positive divisor of N^2 such that the positive divisor are less than N and do not divide N completely. where N = 2^17 * 3^9 * 5^3.

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q11) The highest power of 2 in 10! + 11! + 12! + 13! + ...+ 1000! is
(a) 8
(b) 9
(c) 10
(d) 11

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q12) Two points are chosen randomly on the circumference of a circle. What is the probability that the distance between the 2 points is at least 'r', the radius of the circle?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q13) How many 10digit positive integers with distinct digits are multiples of 11111?
a) 1234
b) 2345
c) 3456
d) 4567
e) None of these

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q14) For how many natural numbers less than 10^5 the sum of their digits equal to 10?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q15) f is a real function such that f(x + y) = f(xy) for all real values of x and y. If f(– 5) = 5, then the value of f(– 25) + f(25) is
a. 5
b. 10
c. 0
d. 25

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q16)

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q17)

gaurav_sharma last edited by gaurav_sharma
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q18) The sum of 2 five digit numbers AMC10 and AMC12 is 123422. What is A + M + C ?
a) 10
b) 11
c) 12
d) 13
e) 14

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q19) A positive integer n has exactly 4 positive divisors that are perfect fifth powers, exactly 6 positive divisors that are perfect cubes, and exactly 12 positive divisors that are perfect squares. Find the least possible number of possible integers that are divisors of n

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q20) Find the remainder when 1 × 2 + 2 × 3 + 3 × 4 + … + 98 × 99 + 99 ×100 is divided by 101.

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q21) What are the last two digits of (86789)^41?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q22) All the divisors of 360, including 1 and the number itself, are summed up. The sum is 1170. What is the sum of the reciprocals of all the divisors of 360?
a. 3.25
b. 2.75
c. 2.5
d. 1.75

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q23) Last 2 digits of the number (299)^33

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q24) Find the remainder when 1^39 + 2^39 + 3^39 + 4^39 + ... + 12^39 is divided by 39.
a. 0
b. 1
c. 12
d. 38

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q25) Last digit of the LCM of(3^20031) and (3^2003+1) :
a. 8
b. 2
c. 4
d. 6

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q26) What is the remainder when x + x^9 + x^25 + x^49 + x^81 is divided by (x^3  x)?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q27) A number when divided by 8 leaves remainder 3 and quotient Q. The number when divided by 5 leaves remainder 2 and quotient Q + 8. What is the number?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q28)

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q29) In how many ways can 4 distinct balls be distributed into 3 identical boxes?
a) 14
b) 17
c) 11
d) 6