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- Question
Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
Options- A. 3/4
- B. 3/8
- C. 5/16
- D. 2/7
- Correct Answer
- 3/4
ExplanationIn a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.
Then, E= {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3,4),(3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
n(E) = 27.
P(E) = n(E)/n(S) = 27/36 = 3/4.
- 1. A certain sum becomes ? 600 in a certain time at the rate of 6% simple interest. The same sum amounts to ? 200 at the rate of 1% simple interest in the same duration. Find the sum and time.
Options- A. ? 120 and 662/3 yr
- B. ? 150 and 662/3 yr
- C. ? 130 and 662/3 yr
- D. ? 160 and 662/3 yr Discuss
- 2. A can do a work in 15 days. A and B together do the same work in 10 days. If they are paid ? 1500 for the work, how should the money be divided between A and B?
Options- A. 1000, 500
- B. 500, 1000
- C. 750, 750
- D. None of these Discuss
- 3. The tank-full of petrol in Arun's motor-cycle lasts for 10 days. If he starts using 25% more everyday, how many days will the tank-full of petrol last?
Options- A. 5
- B. 6
- C. 7
- D. 8 Discuss
- 4. Value of ? in expression
78.9 ÷ (343)1.7 x (49)4.8 = 7? is
Options- A. 13.4
- B. 12.8
- C. 11.4
- D. 9.6 Discuss
- 5. Construct a quadratic equation whose roots have the sum = 6 and product = ?16.
Options- A. x2 - 6x - 16 = 0
- B. x2 + 6x - 16 = 0
- C. x2 - ?3x - 16 = 0
- D. None of these Discuss
- 6. ? 6 + ?6 + ?6 +........ is equal to
Options- A. 2
- B. 5
- C. 4
- D. 3 Discuss
- 7. If X and Y are two sets such that X ? Y has 18 elements, X has 8 elements, and Y has 15 elements, how many elements does X ? Y have?
Options- A. 5
- B. 7
- C. 9
- D. 11 Discuss
- 8. In a group of 50 people, 35 speak Hindi, 25 speak both Hindi and English and all the people speak Hindi or English or both. The number of people who speak English only is:
Options- A. 40
- B. 20
- C. 15
- D. 10 Discuss
- 9. If U = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11},
A = {2, 4, 7},
B = {3, 5, 7, 9, 11} and
C = {7, 8, 9, 10, 11}.
compute: (A ? U) ? (B ? C)
Options- A. {7}
- B. {9}
- C. {6}
- D. {5} Discuss
- 10. Solve the below equation.
173.5 x 177.3 ÷ 174.2 = 17?
Options- A. 8.4
- B. 8
- C. 6.6
- D. 6.4 Discuss
More questions
Correct Answer: ? 120 and 662/3 yr
Explanation:
According to the question.
([P + (P x 6 x T)/100] - [P + (P x 1 x T)/100] = 600 - 200
? 5PT/100 = 400
? PT = 8000
Again, for 6% rate,
SI = PTR/100 = (8000 x 6)/100 = ? 480
? Sum = 600 - 480 = ? 120
As we have, PT = 8000
? T = 8000/120 = 200/3 = 662/3 yr
Correct Answer: 1000, 500
Explanation:
Correct Answer: 8
Explanation:
Let us assume that Arun uses N units of petrol everyday. so the amount of of petrol in the tank when it is full will be 10N. If he starts using 25% more petrol everyday. then the units of petrol he now use everyday will be
N(1 + 25/100) = 1.25N
So, the number of days his petrol will now last will be equal to (amount of petrol in tank) / (number of units used everyday)
= (10N) / (1.25N) = 10 / 1.25
= 8 days
Correct Answer: 13.4
Explanation:
78.9 ÷ (343)1.7 x (49)4.8 = 7?
Apply the law of Fractional Exponents and Laws of Exponents
(am)(an) = am+n
am÷an=am?n
am/an=am?n
(am)n = amn
78.9 ÷ (343)1.7 x (49)4.8 = 7?
? 78.9 ÷ (73)1.7 x (72)4.8 = 7?
? 78.9 ÷ 75.1 x 79.6 = 7?
? 78.9 - 5.1 + 9.6 = 7?
? 718.5 - 5.1 = 7?
? ? = 13.4
Correct Answer: x2 - 6x - 16 = 0
Explanation:
Given that :- sum of the roots = 6
And Product of two roots = -16
The required quadratic equation is x2 ? (sum of the roots) x + (product of the roots) = 0
? x2 - 6x - 16 = 0
Correct Answer: 3
Explanation:
As per the given above question , we have
Let, x = 6 + ?6 + ?6 + ?6 +........
On squaring both sides, we have
x2 = 6 + ?6 + ?6 + ?6 +........
? x2 = 6 + x
? x2 - x - 6 = 0
? x2 - 3x + 2x - 6 = 0
? x( x - 3 ) + 2( x - 3 ) = 0
? ( x - 3 ) ( x + 2 ) = 0
? x = 3 and x ? ?2 because numbers are positive.
Thus , correct answer will be 3 .
Correct Answer: 5
Explanation:
Given in the question ,
n(X ?Y) = 18, n(X) = 8, n(Y) = 15.
Using the formula
n(X ? Y) = n(X) + n(Y) ? n(X ? Y), we get n(X ? Y) = 8 + 15 ? 18 = 5.
Correct Answer: 10
Explanation:
Draw a figure and calculate.
Number of people speak English only
= 50 ? (10 + 25)
= 15
Correct Answer: {7}
Explanation:
A ? U = {2, 4, 7} ? {2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
A ? U = {2, 4, 7};
B ? C = {3, 5, 7, 9, 11} ? {7, 8, 9, 10, 11}.
B ? C = {3, 5, 7, 8, 9, 10, 11}.
Then (A ? U) ? (B ? C) = {2, 4, 7,} ? {3, 5, 7, 8, 9, 10, 11}
(A ? U) ? (B ? C) = {7}.
Correct Answer: 6.6
Explanation:
173.5 x 177.3 ÷ 174.2 = 17?
Apply the Laws of Exponents ::
(am) x (an) = am+n
Fractional Exponents ::
am÷ a n=am?n
? 173.5 + 7.3 - 4.2 = 17?
? 176.6 = 17?
? ? = 6.6
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