CAT Question Bank (Quant)  Gaurav Sharma  Set 1

Q87) If the letters of the word REGULATIONS be arranged at random then find the probability that there will be exactly four letters between R and E

Q88) A, B, C and D are participating in a tabletennis tournament which ends with only one winner. Their respective probabilities of winning are 1/8, 1/4, 1/6, and 2/9. What is the probability that C wins the tournament given that A doesn’t?

Q89) P, Q, R and S are planning to write the MET (Management Entrance Test). Their respective probabilities of passing are 1/7, 1/6, 4/21, and 2/9. What is the probability that at least one among P and S passes the test?

Q90) A, B, C and D are participating in a tabletennis tournament which ends with only one winner. Their respective probabilities of winning are 1/8, 1/4, 1/6, and 2/9. What is the probability that none of the A, B, C or D wins the tournament?

Q91) At the beginning of a party, each person present shook hands with all other people present and there were in all 28 handshakes. In the midst of the party, 2 persons left due to an emergency. Now, the number of males and females present in the party was equal. At the end, each female shook hands only with every female present and each male shook hands only with every male present. What is the total number of handshakes that took place at the party?

@gaurav_sharma 9:1


Q92)

Q93) The midpoints of the adjacent sides of a triangle are joined. The midpoints of the adjacent sides of the resultant triangles are also joined. The ratio of the area of the central small triangle to the original triangle is:
a) 1 : 4
b) 1 : 8
c) 1 : 12
d) 1 : 16
e) 1 : 24

Q94) In a convex octagon,two diagonals are drawn at random.The probability that the diagonals intersect inside the octagon is ?

Q95) What is the number of distinct terms in the expansion of (a + b + c)^20?
(1) 231
(2) 253
(3) 242
(4) 210
(5) 228

Q96) BE and AD are the medians of an equilateral triangle ΔABC and intersecting at O. Find the area of quadrilateral DOEC. A(ΔABC) = 156 sq. cm.
a) 26 sq. cm
b) 39 sq. cm
c) 52 sq. cm
d) 65 sq. cm
e) 78 sq. cm

Q97) Adjacent sides of a parallelogram are 21 cm and 27 cm. One of its diagonals is 24 cm in length. Find its other diagonal.
a) 25 cm
b) 42 cm
c) 32 cm
d) 22 cm
e) 45 cm

Q98) At first, a room is empty. Each minute, either one person enters or two people leave. After exactly 3^1999 minutes, could the room contain
a) 3^1000 +1
b) 3^1000 + 2
c) 3^1000
d) CBD

Q99) In one exam, students were asked to find out the sum of all numbers less than 400 that are divisible by 8 but leave a remainder 1 when divided by 7. However, by mistake, Atul calculated the sum of all the numbers less than 400 that are divisible by 7 but leave a remainder 1 when divided by 8. By how much was Atul's answer different from the answer to the problem originally asked?

Q100) There is a 3 digit no. ABC. The no. Is a perfect square and the no. of factors of ABC is also a perfect square.
 If A + B + C is also a perfect square then what is the no of factors of the six digit number ABCABC.
 what is the no of factors of the 6 digit no ABCABC if the cube of the product of the digits of the no ABC is not divisible by 5?

@gaurav_sharma option b

@gaurav_sharma is it 0???