# CAT Question Bank (Quant) - Gaurav Sharma - Set 2

• Q7) A 25 ft long ladder is placed against the wall with its base 7 ft the wall. The base of the ladder is drawn out so that the top comes down by half the distance that the base is drawn out. This distance is in the range:
a. (2, 7)
b. (5, 8)
c. (9, 10)
d. (3, 7 )
e. None of the above

• Q8) What is the sum of the first 46 prime numbers?
a) 3266
b) 3087
c) 4226
d) 3936
e) 4227

• Q9) If P Q R are three points on a circle, What is the maximum area of the triangle formed by them where radius of circle is 'a' units?

• 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.

• Q11) The highest power of 2 in 10! + 11! + 12! + 13! + ...+ 1000! is
(a) 8
(b) 9
(c) 10
(d) 11

• 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?

• Q13) How many 10-digit positive integers with distinct digits are multiples of 11111?
a) 1234
b) 2345
c) 3456
d) 4567
e) None of these

• Q14) For how many natural numbers less than 10^5 the sum of their digits equal to 10?

• 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

• Q16)

• Q17)

• 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

• 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

• Q20) Find the remainder when 1 × 2 + 2 × 3 + 3 × 4 + … + 98 × 99 + 99 ×100 is divided by 101.

• Q21) What are the last two digits of (86789)^41?

• 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

• Q23) Last 2 digits of the number (299)^33

• 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

• Q25) Last digit of the LCM of(3^2003-1) and (3^2003+1) :
a. 8
b. 2
c. 4
d. 6

• Q26) What is the remainder when x + x^9 + x^25 + x^49 + x^81 is divided by (x^3 - x)?

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