CAT Question Bank (Quant)  Gaurav Sharma  Set 2

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q80) A circle is inscribed in a rhombus of diagonals measuring 12 cm and 24 cm. Find the area of the inscribed circle

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q81) f(x) = x + 1/x
[f(x)]^3 = f(x^3) + kf(1/x)
then find value of k
a) 1
b) 3
c) 3
d) 1

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q82) Consider a quadratic equation x^2– 35x + k = 0. How many values of k exist such that both the roots of the equation are prime numbers?
a) Zero
b) One
c) Five
d) Seven

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q83) If x + 1/x = root 3
Then the value of x^120 + x^72 + x^42 + x^24 + x^6 +1 = ?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q84) An ant is at one of the corners of a square prism with base 5 m × 5 m and height 10 m. What is the minimum distance (in metres) that the ant has to crawl to reach the farthest corner on the prism?
(a) sqrt150
(b) sqrt125
(c) sqrt200
(d) sqrt250

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q85) The difference between the compound interest (with annual compounding) and the simple interest earned in two years on a certain sum at the rate of 18% p.a. is Rs. 972. What will the same sum amount to (in Rs.) after three years at the rate of 18% p.a. when the interest is compounded annually?
(a) 49290.96
(b) 49116.00
(c) 49280.50
(d) 49382.96

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q86) The degree of each term of a polynomial P(x) is odd. When P(x) is divided by (x – 3), the remainder is 6. What is the remainder when P(x) is divided by (x^2 – 9)?
(a) 2x
(b) –36
(c) 0
(d) Cannot be determined

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q87) Number of real solutions of 1 + e^x  1 = e^x (e^x  2)

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q88) How may 3 digit numbers have the property that their digits taken from left to right form an AP or a GP ?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q89) The manufacturing cost per item of an article is Rs. 50 when 100 items are produced. It decreases by Rs.10 when 50 more items are produced. By what value would it decrease from the original if 100 items more than the original number were produced?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q90) If a, b are the roots of x^2 + x + 1 = 0 and c, d are the roots of x^2 + 3x + 1 = 0, then what is the value of (a – c)(b + d)(a + d)(b – c)?
(a) 8
(b) 10
(c) 4
(d) 3

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q91) If f(x, y) = minimum (x, y), for 4 ≥ x ≥ 1, find the maximum possible value of f((x + x^2), (1 + x^3)).

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q92) A train met with an accident 150 kms from station A. It completed the remaining journey at 5/6 of previous speed and reached 15 mins late at station B. Had the accident taken place 30 km further, it would have been only 7 mins late. Find the speed of the train and distance between A and B.

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q93) On a circle there are 10 points each of which is connected with each other with a straight line. How many triangles will be formed which lies completely inside the circle?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q94) In Cricket, a batsman can score 0, 1, 2, 3, 4 or 6 runs of a ball. What is the number of distinct sequences in which exactly 30 runs can be scored in an over of six balls? Assume that all the runs are scored by batsmen only and there are no extra balls/runs.
(a) 36
(b) 71
(c) 77
(d) 86

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q95) In how many ways can 83 be expressed as the sum of two natural numbers that are coprime to each other?

gaurav_sharma last edited by gaurav_sharma
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q96) Find all prime numbers p for which 5p + 1 is a perfect square

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q97) If in a certain number system the difference of 5333 and 555 is 4445 then find the sum of the numbers 5333 and 555

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q98) When 242 is divided by a certain divisor the remainder obtained is 8. When 698 is divided by the same divisor the remainder obtained is 9. When the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4. What is the value of the divisor?
a) 11
b) 17
c) 13
d) 23
e) None of these

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q99) A twodigit natural number is ‘q’ times the sum of its digits. The number formed by interchanging the digits is how many times the sum of its digits?
a) 9  q
b) q + 1
c) q  1
d) 11  q