Aptitude miscellaneous
- The minute hand of a big wallclock is 35cm long. Taking π = 22/7, length of the arc, its extremity moves in 18 seconds is :
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As per the given in question ,
Traced arc length by minute hand in 60 × 60 seconds = 2πr
radius = 35 cm∴ Length of arc made in 18 seconds = 2πr × 18 60 × 60
Correct Option: B
As per the given in question ,
Traced arc length by minute hand in 60 × 60 seconds = 2πr
radius = 35 cm∴ Length of arc made in 18 seconds = 2πr × 18 60 × 60 Length of arc made in 18 seconds = 2 × 22 × 35 × 18 = 1.1 cm. 7 60 × 60
- A die with faces numbered from 1 to 6 is thrown twice. The probability, that the numbers shown up differ by 2, is
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As per the given in question ,
Total possible outcomes n( S ) = 6 × 6 = 36
Favourable number of cases n( E ) = (1, 3), (3, 1), (2, 4), (4,2), (3,5), (5,3), (4,6), (6,4) = 8∴ Required probability = n( E ) n( S )
Correct Option: B
As per the given in question ,
Total possible outcomes n( S ) = 6 × 6 = 36
Favourable number of cases n( E ) = (1, 3), (3, 1), (2, 4), (4,2), (3,5), (5,3), (4,6), (6,4) = 8∴ Required probability = n( E ) n( S ) Required probability = 8 = 2 36 9
- If log (0.57) = 1.756 then the value of log 57 + log (0.57)³ + log √0.57 is :
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Given in question , log 57 + log (0.57)³ + log √0.57
{ ∴ log ( ab ) = log a + log b and log ( a )n = nloga }log 57 + log (0.57)³ + log ( 0.57 )1 /2 = log [(0.57) × 100]+ 3 log 0.57 + 1 log 0.57 2 = log 100 + log (0.57) + 3 log (0.57) + 1 log (0.57) 2 = 2 + 9 log(0.57) [∵ log 100 = log 10² = 2log 10 = 2] 2
Correct Option: A
Given in question , log 57 + log (0.57)³ + log √0.57
{ ∴ log ( ab ) = log a + log b and log ( a )n = nloga }log 57 + log (0.57)³ + log ( 0.57 )1 /2 = log [(0.57) × 100]+ 3 log 0.57 + 1 log 0.57 2 = log 100 + log (0.57) + 3 log (0.57) + 1 log (0.57) 2 = 2 + 9 log(0.57) [∵ log 100 = log 10² = 2log 10 = 2] 2 = 2 + 9 × (1.756) 2 = 2 + 9 × 0.756 - 9 2 2
= 2 + 3.402 - 4.5 = 0.902
- If log102 = 0.3010 and log107 = 0.8451, then the value of log102.8 is :
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Given that , log102.8 = log10( 4 × 0.7 )
∴ log a = log a - log b b = log10 
2 × 2 × 7 
10
Correct Option: A
Given that , log102.8 = log10( 4 × 0.7 )
∴ log a = log a - log b b = log10 2 × 2 × 7 10
= log102 + log102 + log107 – log1010
= 0.3010 + 0.3010 + 0.8451 – 1 { ∴ log1010 = 1 }
Hence , Log102.8 = 1.4471 – 1 = 0.4471
- I walk a certain distance and ride back taking a total time of 37 minutes. I could walk both ways in 55 minutes. How long would it take me to ride both ways ?
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On the basis of given details in question ,
Walking + Riding ≡ 37 mintues ...(i)
2 × Walking ≡ 55 minutes ...(ii)
By equation (i) × 2 – equation (ii), we getCorrect Option: B
On the basis of given details in question ,
Walking + Riding ≡ 37 mintues ...(i)
2 × Walking ≡ 55 minutes ...(ii)
By equation (i) × 2 – equation (ii), we get
2 × Riding = 2 × 37 – 55 = 74 – 55 = 19 minutes
