The price of a refrigetor, P is 5 times that of a cooler Q. If then price of P increases by `40%.` then what is the change in the total price of the refrigerator and cooler put together ?
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A die is thrown 7 times. What is the chance that an odd number turns up (i) exactly 4 times (ii) at least 4 times
Probability of success is 3/6=1/2. `thereforep=1/2andq=1/2` (i) For exactly 4 successes, the required probability is `""^(7)C_(4)((1)/(2))^(4)((1)/(2))^(3)=35/128` (ii) For at least 4 successes, the required probability is `""^(7)C_(4)((1)/(4))^(4)((1)/(2))^(3)+""^(7)C_(5)((1)/(2))^(5)((1)/(2))^(2)` `+""^(7)C_(6)((1)/(2))^(6)((1)/(2))^(1)+""^(7)C_(7)((1)/(2))^(7)` `=35/128+21/128+7/128+1/128=64/128=1/2`
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A fair coin is tossed `n` times. if the probability that head occurs 6 times is equal to the probability that head occurs 8 times, then find the value
Correct Answer - `n=14` According to question `""^(n)C_(6)((1)/(2))^(6)((1)/(2))^(n-6)=""^(n)C_(8)((1)/(2))^(8)((1)/(2))^(n-8)` `or ""^(n)C_(6)((1)/(2))^(n)=""^(n)C_(8)((1)/(2))^(n)` `or""^(n)C_(6)=""^(n)C_(8)=""^(n)C_(n-8)` `implies6=n-8orn=14`
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A die is thrown a fixed number of times. If probability of getting even number 3 times is same as the probability of getting even number 4 times, then
Correct Answer - D According to the givn condition, `""^(n)C_(3)((1)/(2))^(n)=""^(n)C_(4)((1)/(2))^(n),` where n is the number of times die is thrown. `therefore""^(n)C_(3)=""^(n)C_(4)impliesn=7` Thus, the required probability is `=""^(7)C_(1)((1)/(2))^(7)=(7)/(2^(7))=(7)/(128)`
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A coin is tossed `2n` times. The chance that the number of times one gets head is not equal to the number of times one gets tails is `((2n !))/((n !)^
Correct Answer - C The required probability is 1- probability of getting equal number of heads and tails `=1-""^(2n)C_(n)((1)/(2))^(n)((1)/(2))^(2n-n)` `=1-((2n)!)/((n!)^(2))xx(1)/(4^(n))`
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What is the percentage change in distance if the force of attraction between two point charges increases to 4 times keeping magnitude of charges const
Correct Answer - [Decreased to 50% of initial value]
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Three coins are tossed 100 times, and three heads one head occurred 14 times and head did not occur 23 times. Find the probability of getting more tha
Correct Answer - `(63)/(100)`
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Simla is cooler than Delhi because ………………….
C) Simla is in higher altitude
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A coin is tossed 500 times and we get heads : 285 times and tails : 215 times When a coin is tossed at random , what is probability of getting (i) a h
Correct Answer - (i) 0.57 (ii) 0.43
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Two coins are tossed 400 times and we get two heads : 112 times, one head , 160 times , 0 head , 128 times . When two coins are tossed at random , wha
Correct Answer - (i) 0.28 (ii) 0.4 (iii) 0.32
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Consider a particle of mass \( m \) having linear momentum \( P \) at position \( r \) relative to the origin \( O \). Which of the following equations correctly relates \( r , P , L \) ? a) \( \left[\left(\frac{d L}{d t}\right)+r x\left(\frac{d P}{d t}\right)\right]=0 \) b) \( \left[\left(\frac{d L}{d t}\right)-r x\left(\frac{d P}{d t}\right)\right]=0 \) c) \( \left[\left(\frac{d L}{d t}\right) \times\left(\frac{d r}{d t}\right) \times P\right]=0 \) d) \( \left[\left(\frac{d L}{d t}\right)-\left(\frac{d r}{d t}\right) \times P\right]=0 \)
Correct answer is (b) We know that \(\tau\) = r × F ∵ \(\tau\) \(= \frac{dL}{dt},\) \(F = \frac{dP}{dt}\) \(\left(\frac{dL}{dt}\right) = r \times \left(\frac{dP}{dt}\right)\) \(\left(\frac{dL}{dt}\right) - r \times \left(\frac{dP}{dt}\right) = 0\)
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