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- Question
A student was asked to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of x ?
Options- A. 6
- B. 7
- C. 8
- D. 9
- Correct Answer
- 7
ExplanationClearly, we have (3 + 11 + 7 + 9 + 15 + 13 + 8 + 19 + 17 + 21 + 14 + x) / 12 = 12.
or 137 + x = 144 or x = 144 - 137 = 7.
- 1.
If x = 2 + ?3, y = 2 - ?3, then the value of x 2 + y 2 is x3 + y3
Options- A. 7 38
- B. 7 40
- C. 7 19
- D. 7 26 Discuss
- 2. Which of the following pairs of sets are comparable?
Options- A. A = {1, 3, 5}, and B = {3, 2, 5, 6}
- B. A = {x: x ? N and x ? 10} and B = {1, 2, 3,?, 10, 11}
- C. A = {1, 2, 3, {4, 5}}, and B = {1, 2, 3, 4, 5}.
- D. None of these Discuss
- 3. In an examination, 30% of the total students failed in Hindi, 45% failed in English and 20% failed in both the subjects. Find the percentage of those who passed in both the subjects.
Options- A. 35.7%
- B. 35%
- C. 40%
- D. 45% Discuss
- 4. There are 80 families in a small extension area. 20 per cent of these families own a car each. 50 per cent of the remaining families own a motor cycle each. How many families in that extension do not own any vehicle?
Options- A. 30
- B. 32
- C. 23
- D. 36 Discuss
- 5. 10 yr before, the ratio of ages of A and B was 13 : 17. After 17 yr from now, the ratio of their ages will be 10 : 11. The present age of B is
Options- A. 23 yr
- B. 40 yr
- C. 27 yr
- D. 44 yr Discuss
- 6. Which of the following sets is infinite?
Options- A. {x: x is a prime number, x is even}
- B. Set of all river in India
- C. Set of all concentric circles
- D. None of above Discuss
- 7. Mangulal a shopkeeper, marks the prices of his goods at 20% higher than the original price. After that he allows a discount of 5%. What profit or loss did he get?
Options- A. 14% (profit)
- B. 14% (loss)
- C. 16% (loss)
- D. 16% (profit) Discuss
- 8. In a class, 50 students play cricket, 20 students play football and 10 play both cricket and football. How many play at least one of these two games?
Options- A. 60
- B. 45
- C. 55
- D. 65 Discuss
- 9. Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
Options- A. 180
- B. 175.50
- C. 170
- D. 169.50 Discuss
- 10. If A and B are two sets such that A has 40 elements, A ? B has 60 elements and A ? B has 10 elements, how many elements does B have?
Options- A. 40
- B. 30
- C. 45
- D. 50 Discuss
More questions
Correct Answer: 7 26
Explanation:
Correct Answer: A = {x: x ? N and x ? 10} and B = {1, 2, 3,?, 10, 11}
Explanation:
(a) 1? A but 1? B and 6 ? B but 6 ? A.
? A and B are not comparable.
(b) A = {x: x ? N and x ? 10} = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
Clearly, A ? B ? A and B are comparable.
(c) {4, 5} ? A but {4, 5} ? B and 4 ? B but 4 ? A.
? A and B are not comparable.
Correct Answer: 45%
Explanation:
Let the number of students be 100. Number of students who failed in Hindi is 30%.
n(H) = 30
Number of students who failed in English is 45%.
? n(E) = 45
Number of students who failed in both the subjects is 20%. n(H ? E) = 20
Applying the rule,
n(H ? E) = n(H) + n(E) - n(H ? E)
= 30 + 45 - 20 = 55
Percentage of students who failed in Hindi or English or both the subjects = 55%
Number of students who passed in both the subjects = 100 - 55 = 45%
Correct Answer: 32
Explanation:
Given in the question,
20% of 80 = 20 * 80 / 100 = 16
Remaining 50%
= (80 ? 16) × 50 / 100 = 32
No. of families not owning any vehicle
= 80 ? (32 + 16) = 80 ? 48 = 32
Correct Answer: 27 yr
Explanation:
Let the ages of A and B 10 yr before were 13k yr and 17k yr, respectively.
Then, present age of A = 13k + 10
and present age of B = 17k + 10
According to the question,
? (13k + 10 + 17) / (17k + 10 + 17) = 10/11
? (13k + 27) / (17k + 27) = 10/11
? 143k + 297 = 170k + 270
? 27k = 27
? k = 1
Hence, present age of B = 17 x 1 + 10 = 27 yr
Correct Answer: Set of all concentric circles
Explanation:
NA
Correct Answer: 14% (profit)
Explanation:
Given that, a = 20% and b = 5%
According to the formula
Required percentage = [20 - 5 - {20 x (5/100)}% = 14%
Correct Answer: 60
Explanation:
Given: n(C) = 50, n(F) = 20, n(C ? F) = 10.
Number of students playing at least one of these two games = n (C ? F) = n (C) + n (F) ? n (C ? F)
= 50 + 20 ? 10 = 60.
Correct Answer: 175.50
Explanation:
Here first two varieties of tea are mixed in equal ratio.
So their average price = (126 + 135) /2 = Rs. 130.50
Let price of the third variety per kg be Rs. A; then now mixture is formed by two varieties one at Rs. 130.50 per kg and other at Rs. A per kg in the same ratio 2 : 2 i.e, 1 : 1
By the rule of alligation,
(A - 153) / (22.50) = 1
? A ? 153 = 22.50
? A = Rs. 175.50
Correct Answer: 30
Explanation:
Given in the question ,
n(A) = 40, n(A ? B) = 60 and n(A ? B) = 10.
As we know the formula,
n(A ? B) = n(A) + n(B) ? n(A ? B)
Putting these values in the formula, we get
60 = 40 + n(B) ? 10
? n(B) = 30.
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