In a class of 72 students, 32 students cleared only Maths exam and 16 cleared only Physics exam. If four students could not clear both the subjects' exams, then how many students cleared both the subjects' exams? Ops: A. 20 B. 18 C. 10 D. 15 Q 28. How many numbers between 40,000 and 50,000 can be formed with the digits 0, 1, 2, 3, 4, 5, 6 when the repetition of digits is not allowed? Ops: A. 360 B. 480 C. 880 D. 720 Q 29. The average of marks obtained by 76 candidates in a certain examination is 32. If the average score of passed candidates is 40 and that of the failed candidates is 2, what is the number of candidates who failed the examination? Ops: A. 7 B. 12 C. 9 D. 16 Q 30. Mary selects a number out of first 32 even numbers at random. What is the probability that this number will be a multiple of 4? Ops: A. 1/3 B. 2/3 C. 3/5 D. 1/2
Question
In a class of 72 students, 32 students cleared only Maths exam and 16 cleared only Physics exam. If four students could not clear both the subjects' exams, then how many students cleared both the subjects' exams? Ops: A. 20 B. 18 C. 10 D. 15
Q 28. How many numbers between 40,000 and 50,000 can be formed with the digits 0, 1, 2, 3, 4, 5, 6 when the repetition of digits is not allowed? Ops: A. 360 B. 480 C. 880 D. 720
Q 29. The average of marks obtained by 76 candidates in a certain examination is 32. If the average score of passed candidates is 40 and that of the failed candidates is 2, what is the number of candidates who failed the examination? Ops: A. 7 B. 12 C. 9 D. 16
Q 30. Mary selects a number out of first 32 even numbers at random. What is the probability that this number will be a multiple of 4? Ops: A. 1/3 B. 2/3 C. 3/5 D. 1/2
Solution
Sure, here are the answers to your questions:
Q27: The total number of students is 72. Subtract the number of students who cleared only Maths (32), only Physics (16), and those who didn't clear both (4). So, 72 - 32 - 16 - 4 = 20 students cleared both the subjects' exams. So, the answer is A. 20.
Q28: The number must start with 4 (1 way). The remaining 4 digits can be any of the remaining 6 digits (0, 1, 2, 3, 5, 6). So, the number of ways = 1 * 6 * 5 * 4 * 3 = 360. So, the answer is A. 360.
Q29: The total marks obtained by all candidates is 76 * 32 = 2432. Let's say the number of candidates who failed is x. So, the total marks of passed candidates is 2432 - 2x. This should be equal to 40 * (76 - x). Solving this equation gives x = 16. So, the answer is D. 16.
Q30: The first 32 even numbers are 2, 4, ..., 64. Out of these, the numbers which are multiple of 4 are 4, 8, ..., 64. There are 16 such numbers. So, the probability is 16/32 = 1/2. So, the answer is D. 1/2.
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