[B].
[C].
[D].
Answer: Option C
Explanation:
| log (264) | = 64 x log 2 |
| = (64 x 0.30103) | |
| = 19.26592 |
Its characteristic is 19.
Hence, then number of digits in 264 is 20.
[B].
[C].
[D].
Answer: Option B
Explanation:
Unit digit in 795 = Unit digit in [(74)23 x 73]
= Unit digit in [(Unit digit in(2401))23 x (343)]
= Unit digit in (123 x 343)
= Unit digit in (343)
= 3
Unit digit in 358 = Unit digit in [(34)14 x 32]
= Unit digit in [Unit digit in (81)14 x 32]
= Unit digit in [(1)14 x 32]
= Unit digit in (1 x 9)
= Unit digit in (9)
= 9
Unit digit in (795 – 358) = Unit digit in (343 – 9) = Unit digit in (334) = 4.
So, Option B is the answer.
| 1 |
| 3 |
[B].
| 1 |
| 4 |
[C].
| 1 |
| 5 |
[D].
| 1 |
| 7 |
Answer: Option C
Explanation:
Suppose the vessel initially contains 8 litres of liquid.
Let x litres of this liquid be replaced with water.
| Quantity of water in new mixture = | 3 – | 3x | + x | litres | ||
| 8 |
| Quantity of syrup in new mixture = | 5 – | 5x | litres | ||
| 8 |
| 3 – | 3x | + x | = | 5 – | 5x | |||||
| 8 | 8 |
5x + 24 = 40 – 5x
10x = 16
| x = | 8 | . |
| 5 |
| So, part of the mixture replaced = | 8 | x | 1 | = | 1 | . | ||
| 5 | 8 | 5 |
[B].
[C].
[D].
Answer: Option C
Explanation:
log 2x = 10 x = 210.
logxy = 100
y = x100
y = (210)100 [put value of x]
y = 21000.
[B].
[C].
[D].
Answer: Option C
Explanation:
Required sum = (2 + 4 + 6 + … + 30)
This is an A.P. in which a = 2, d = (4 – 2) = 2 and l = 30.
Let the number of terms be n. Then,
tn = 30 a + (n – 1)d = 30
2 + (n – 1) x 2 = 30
n – 1 = 14
n = 15
| Sn = | n | (a + l) | = | 15 | x (2 + 30) = 240. |
| 2 | 2 |
[B].
[C].
[D].
Answer: Option D
Explanation:
Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.
x = 7.
[B].
[C].
[D].
Answer: Option D
Explanation:
S.I. = Rs. (15500 – 12500) = Rs. 3000.
| Rate = | 100 x 3000 | % | = 6% | |
| 12500 x 4 |
Video Explanation: https://youtu.be/SIcQu1HOmOk