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- Question
- If P = { 1, 2, 3 } and Q = { 4 , 5 } then what is the value of P × Q?
Options- A. { (4 , 5) , (1 , 5) , (2 , 4) , (2 , 5) , (3 , 4) , (3 , 5) }
- B. { (1 , 4) , (4 , 5) , (2 , 4) , (2 , 5) , (3 , 4) , (3 , 5) }
- C. { (1 , 4) , (1 , 5) , (2 , 4) , (3 , 5) , (3 , 4) , (3 , 5) }
- D. { (1 , 4) , (1 , 5) , (2 , 4) , (2 , 5) , (2 , 4) , (3 , 5) }
- Correct Answer
-
ExplanationThe Cartesian product X × Y of sets X , Y is the set of all ordered pairs ( x , y ).
Two ordered pairs ( x1 , y1 ), ( x2 , y2 ) .
Given that P = { 1, 2, 3 } and Q = { 4 , 5 } then,
P x Q = { 1, 2, 3 } x { 4 , 5 }
? P x Q = { 1 } x { 4 , 5 } , { 2 } x { 4 , 5 } , { 3 } x { 4 , 5 }
? P x Q = { 1 , 4 } , { 1 , 5 } , { 2 , 4 } , { 2 , 5 } , { 3 , 4 }, { 3 , 5 }
? P x Q = { (1 , 4 ) , ( 1 , 5 ) , ( 2 , 4 ) , ( 2 , 5 ) , ( 3 , 4 ), ( 3 , 5) } - 1. Find what is that first years in which a sum of money will become more than double in amount if put out at compound interest at the rate of 10% per annum?
Options- A. 6th years
- B. 7th years
- C. 8th years
- D. Data inadequate Discuss
- 2. What amount will be received on a sum of ? 1750 in 2 1/ 2 yr, if the interest is compounded at the rate of 8% pa?
Options- A. ? 2125
- B. ? 2122.85
- C. ? 2100
- D. ? 2200 Discuss
- 3. During the first year, the population of a village is increased by 5% and the second year, it is diminished by 5%. At the end of the second year, its population was 47880. What was the population at the beginning of the first year?
Options- A. 45500
- B. 48000
- C. 43500
- D. 53000 Discuss
- 4. The simple interest on a certain sum of money for 3 yr at 8 % pa is half the compound interest on ? 8000 for 2 yr at 10 % pa. Find the sum on which simple interest is calculated
Options- A. ? 3500
- B. ? 3800
- C. ? 4000
- D. ? 3600 Discuss
- 5. A sum of ? 8448 is to be divided between A and B who are respectively 18 and 19 yr old, in such a way that if their shares be invested at 6.25 % per annum at compound interest, they will receive equal amounts on attaining the age of 21 yr. The present share of A is
Options- A. ? 4225
- B. ? 4352
- C. ? 4096
- D. ? 4000 Discuss
- 6. If A and B have n elements in common, how many elements do A × B and B × A have in common?
Options- A. n
- B. n3
- C. n2
- D. None of these Discuss
- 7. If U = {a, b, c, d, e, f}, A = {a, b, c}, B = {c, d, e, f}, C = {c, d, e}, find (A ? B) ? (A ? C).
Options- A. {c}
- B. {a}
- C. {b}
- D. {d} Discuss
- 8. If U = {a, b, c, d, e, f}, A = {a, b, c}, find (U ? A)?.
Options- A. U
- B. A
- C. ?
- D. None of these Discuss
- 9. Let A = {1, 3, 5} and B = {x: x is an odd natural number < 6}. Which of the following is false?
Options- A. A ? B
- B. B ? A
- C. A = B
- D. None of these Discuss
- 10. Let A = {?, {?}, 1, {1, ?}, 7}. Which of the following is false?
Options- A. ? ? A
- B. {?} ? A
- C. {1} ? A
- D. {7, ?,} ? A Discuss
Sets and Functions problems
Search Results
Correct Answer: 8th years
Explanation:
Here, P(1 + 10/100)t > 2P
? (11/10)t > 2
When t = 8 ? (11/10)8 = 2.14358
t =7 ? (11/10)7 = 1.9487
By trial, [11 x 11 x 11 x 11 x 11 x 11 x 11 x 11] / [10 x 10 x 10 x 10 x 10 x 10 x 10 x 10] >2
Hence, the first years in which sum of money will become more than double in amount is 8th year
Correct Answer: ? 2122.85
Explanation:
Given, P = ? 1750, R = 8%,
n = 2 and a/b = 1/2
According to the formula,
Amount = P(1 + R/100)n x [1 + {(a/b) x R}/100]
=1750 (1 + 8/100 )2 [1 + {(1/2) x 8} /100]
=1750 (27/25)2 x 26/25
= 1750 x (27/25) x (27/25) x (26/25)
=? 2122.848
= ? 2122.85
Correct Answer: 48000
Explanation:
Let the population at the beginning of the first year be N .
Then, according to the question,
N x [1+ 5/100] x [1 - 5/100] = 47880
? N x (105/100) x (95/100) = 47880
? N = 47880 x (100/105) x (100/95) = 48000
Correct Answer: ? 3500
Explanation:
CI = 8000 x (1 + 10/100)2 - 8000
= 8000 x (11/10) x (11/10) - 8000
= ? 9680 - 8000
= ? 1680
? Sum = (840 x 100)/(3 x 8) = ? 3500
[ ? SI is half of CI ]
? SI = 1680/2 = ? 840
Correct Answer: ? 4096
Explanation:
Let shares of A and B be ? N and ? (8448 - N), respectively,
Amount got by A after 3 yr = Amount got by B after 2 yr
N(1 + 6.25/100)3 = (8448 - N) x (1 + 6.25/100)2
? 1 + 6.25/100 = (8448 - N)/N
? 1 + 1/16 = (8448 - N)/N
? 17/16 = (8448 - N)/N
? 17N = 135168 - 16N
? N = 4096
Correct Answer: n2
Explanation:
NA
Correct Answer: {c}
Explanation:
A ? B = {a, b, c} ? {c, d, e, f}
A ? B = { c }
A ? C = { a, b, c } ? { c, d, e }
A ? C = { c }
? (A ? B) ? (A ? C) = { c }.
Correct Answer: ?
Explanation:
U ? A = {a, b, c, d, e, f} ? {a, b, c} = {a, b, c, d, e, f} = U
(U ? A)? = ?.
Correct Answer: None of these
Explanation:
NA
Correct Answer: {1} ? A
Explanation:
NA
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