General Mathematics

Question: If`log_5 (x^2 + x) - log_5 (x + 1) = 2,` then the value of x is :
A
`5`

B
`32`

C
`25`

D
`10`

Note: `log_5 (x^2 + x) - log_5 (x + 1)` `= 2 ⇒ log_5 ((x^2 + x)/(x + 1))` `= 2` `:.log_5 [ (x (x + 1)/(x + 1)]` `= 2 or log_5 x` `= 2 or x = 5^2` `= 25.`
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Question: If log x + log y = log (x + y), then :
A
`x = y`

B
`xy = 1`

C
`y = (x - 1)/x`

D
`y = x/(x - 1)`

Note: `log x + log y` `= log (x + y) ⇒ log (x + y)` `= log (xy)` `:. x + y = xy` `or y(x - 1)` `= x or y = x/(x - 1)`
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Question: If` log_10 125 + log_10 8 = x,` then x is equal to :
A
`3`

B
`- 3`

C
`1/3`

D
`.064`

Note: `log_10 125 + log_10 8` `= x ⇒ log_10 (125 xx 8) = x.` `:. x = log_10 (1000)` `= log_10 (10^3)` `= 3 log_10 10` `= (3 xx 1) = 3`
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Question: The value of `[1/(log(p/q) x) + 1/(log(q/r) x) + 1/(log(r/p) x)]` is :
A
`3`

B
`2`

C
`1`

D
`0`

Note: Not available
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Question: The present worth of Rs.`2310` due `2 1/2` years hence, the rate of interest being `15%` per annum, is :
A
`Rs. 1750`

B
`Rs. 1680`

C
`Rs. 1840`

D
`Rs.1443.75`

Note: `p.w. = Rs.((100 xx 2310)/(100 + (15 xx 5/2))` `= Rs. 1680.`
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Question: If the true discount on a sum due `2` years hence at `14%`per annum be Rs. 168, the sum due is :
A
`Rs. 768`

B
`Rs. 968`

C
`Rs. 1960`

D
`Rs. 2400`

Note: p.w. = (100 xx T. D.)/(R xx T)` `= (100 xx 168)/(14 xx 2)` `= 600` :. sum = (p. W. + T. D) `= Rs. (600 + 168)` `= Rs. 768.`
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Question: The true discount on Rs. `2562` due `4` months hence is Rs. `122`. The rate per cent is :
A
`12%`

B
`13 1.3%`

C
`15%`

D
`14%`

Note: p.w = Rs. (2562 - 122)` `= Rs. 2440. `:. S.l. on Rs. 2440` For `4` month is Rs. `122`. `:. Rate = ((100 xx 122)/(2440 xx 1/3))%` `= 15%`
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Question: The true discount on Rs.`1760` due after a certain time at `12%` per annum is Rs.`160`.The time after which it is due is :
A
`6 months`

B
`8 months`

C
`9 months`

D
`10 months`

Note: `p.w. = `(1760 - 160)` `= Rs. 1600` `:. S.l. on Rs. 1600 at`12%` is Rs. 160`. `:. Time = ((100 xx 160)/(1600 xx 12))` `= 5/6 years` `= (5/6 xx 12) months ` `= 10 months
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Question: The true discount on a bill due `9` months hence at `16%` per annum is Rs. `189`. The amount of the bill is :
A
`Rs. 1386`

B
`Rs. 1764`

C
Rs. 1575`

D
`Rs. 2268`

Note: Let p.w. be Rs. x. Then, S.l on Rs. x at `16%` for `9` months `= Rs. 189.` `:. x xx 16 xx 9/12 xx 1/100` `= 189 or x 1575.` `:. P.W. = Rs. 1575.` `:. sum due = P.W. + T.D.` `= Rs. (1575 + 189)` `= Rs. 1764.`
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Question: The interest on Rs.`750` for `2` years is the same as the true discount on Rs.`960` due `2` years hence. If the rate of interest is the same in both cases, it is :
A
`12%`

B
`14%`

C
`15%`

D
`16 2/3%`

Note: S.l. on Rs.`750 T.D. on Rs. 960.` This means p.w. of Rs.`960. due `2` years hence is `Rs. 750.` `:. T.D. = Rs. (960 - 750)` `= Rs. 210.` Thus, S.l on Rs.`750` for `2` years is Rs.`210` :. Rate` = ((100 xx 210)/(750 xx 2))%` `= 14%`
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Question: If`log_5 (x^2 + x) - log_5 (x + 1) = 2,` then the value of x is :

Question: If log x + log y = log (x + y), then :

Question: If` log_10 125 + log_10 8 = x,` then x is equal to :

Question: The value of `[1/(log(p/q) x) + 1/(log(q/r) x) + 1/(log(r/p) x)]` is :

Question: The present worth of Rs.`2310` due `2 1/2` years hence, the rate of interest being `15%` per annum, is :

Question: If the true discount on a sum due `2` years hence at `14%`per annum be Rs. 168, the sum due is :

Question: The true discount on Rs. `2562` due `4` months hence is Rs. `122`. The rate per cent is :

Question: The true discount on Rs.`1760` due after a certain time at `12%` per annum is Rs.`160`.The time after which it is due is :

Question: The true discount on a bill due `9` months hence at `16%` per annum is Rs. `189`. The amount of the bill is :

Question: The interest on Rs.`750` for `2` years is the same as the true discount on Rs.`960` due `2` years hence. If the rate of interest is the same in both cases, it is :