All Free Mathematics MCQs with Answers

• A. 180
• B. 360
• C. 540
• D. 1260

Explanation: The three numbers have prime factors 2^2 x 3^3 x 5^5, 2^3 x 3^2 x 5^2 x 7, and 2^4 x 3^4 x 5 x 11 x 7^2.

• A. 13/16
• B. 15/16
• C. 17/26
• D. 25/26

Explanation: Factorising gives 1095 = 3 x 5 x 73 and 1168 = 16 x 73, so their common factor is 73.

• A. 99
• B. 101
• C. 176
• D. 182

Explanation: For n = p^a x q^b, the number of divisors is (a + 1)(b + 1). Thus 99 = 3^2 x 11 has 6 divisors, 101 has 2, 176 = 2^4 x 11 has 10, and 182…

• A. 2 * 2 * 3 * 3 * 7
• B. 2 * 2 * 2 * 3 * 7
• C. 3 * 3 * 3 * 3 * 7
• D. 2 * 3 * 3 * 3 * 7

Explanation: Divide 252 successively by its prime factors: 252 = 2 x 126 = 2 x 2 x 63 = 2 x 2 x 3 x 3 x 7.

• A. 35
• B. 37
• C. 42
• D. 30

Explanation: The largest equal can size is the H.C.F. of 80, 144 and 368: H.C.F.(80,144,368) = 16 litres.

• A. 16
• B. 17
• C. 18
• D. 19

Explanation: A divisor that leaves remainder 3 must divide 19 - 3 = 16, 83 - 3 = 80 and 67 - 3 = 64.

• A. 5
• B. 6
• C. 7
• D. 8

Explanation: The greatest number that divides all three numbers exactly is their H.C.F.

• A. 1020
• B. 1026
• C. 1030
• D. 1022Everyday Science Quiz

Explanation: The number must be 2 more than a common multiple of 3, 4 and 5. Their L.C.M.

• A. 4/11
• B. 1
• C. 2/33
• D. 19/66

Explanation: There are 12 socks, so the total number of pairs is C(12,2) = 66. Same-colour pairs are C(4,2) + C(3,2) + C(5,2) = 6 + 3 + 10 = 19, giving…

• A. 13/51
• B. 1/17
• C. 1/26
• D. 13/17

Explanation: The chance that the first card is a club is 13/52, and without replacement the chance that the second is a club is 12/51.

• A. 1/13
• B. 2/13
• C. 1/26
• D. 1/52

Explanation: There are two favourable cards, the queen of clubs and the king of hearts, out of 52 cards. Therefore the probability is 2/52 = 1/26.

• A. 1/26
• B. 3/52
• C. 15/26
• D. 11/26

Explanation: With replacement, the two draws are independent. The probability of a red first card is 26/52 = 1/2, and the probability of a king second…

• A. 1/6
• B. 5/8
• C. 3/8
• D. 5/6Pakistan Studies Quiz

Explanation: Use the complement: the probability of selecting no graduate is C(6,3) ÷ C(10,3) = 20 ÷ 120 = 1/6, because 6 of the 10 people are…

• A. 18/35
• B. 12/35
• C. 17/35
• D. 19/35

Explanation: They agree when both speak truth or both speak falsely. The probability is (3/5 x 4/7) + (2/5 x 3/7) = 12/35 + 6/35 = 18/35.

• A. 5/21
• B. 5/14
• C. 9/14
• D. 16/21

Explanation: There are C(10,5) = 252 ways to choose five people. For at least two couples, choose two couples in C(5,2) = 10 ways and one of the…

• A. 0.4869
• B. 0.5904
• C. 0.6234
• D. 0.5834

Explanation: It is easier to use the complement: the probability that none of the 4 tickets wins is 0.8 x 0.8 x 0.8 x 0.8 = 0.4096.

• A. 1/10
• B. 9/10
• C. 1/5
• D. 3/10

Explanation: Treat the specified pair as one block. The block and the other 8 books can be arranged in 9!

• A. 0
• B. 1/7
• C. 2/7
• D. 5/7

Explanation: A leap year has 366 days = 52 weeks plus 2 extra days, so exactly two consecutive weekdays occur 53 times.

• A. 10/17
• B. 10/19
• C. 46/105
• D. Cannot be determined

Explanation: The actual set of 15 consecutive numbers is not given, and the number of primes and odd numbers can change with the starting number.

• A. 4/9
• B. 5/9
• C. 7/9
• D. 8/9

Explanation: There are 5 x 4 = 20 favorable pairs with one white and one red ball, out of C(9,2) = 36 total pairs. Thus the probability is 20/36 = 5/9.