3 yr ago, total age of 5 members of the family = 17 x 5 = 85 yr
Present age of all the members of the family = 85 + 3 x 5 = 100 yr
Let the age of the child = N yr
Present avrage age of family = (100 + N) / 6
[At present total number of members = 5 + 1 = 6]
17 = 100N / 6
? 102 = 100 + N
? N = 2 yr
log √8 | is equal to: |
log 8 |
1 |
√8 |
1 |
4 |
1 |
2 |
1 |
8 |
1 |
2 |
log √8 | = | log (8)1/2 | = | ½log 8 | = | 1 | . |
log 8 | log 8 | log 8 | 2 |
The value of | ❨ | 1 | + | 1 | + | 1 | ❩ | is: |
log3 60 | log4 60 | log5 60 |
Given expression | = log60 3 + log60 4 + log60 5 |
= log60 (3 x 4 x 5) | |
= log60 60 | |
= 1. |
.009 | = .01 |
? |
Let | .009 | = .01; Then x = | .009 | = | .9 | = .9 |
x | .01 | 1 |
Evaluate : | (2.39)2 - (1.61)2 |
2.39 - 1.61 |
Given Expression = | a2 - b2 | = | (a + b)(a - b) | = (a + b) = (2.39 + 1.61) = 4. |
a - b | (a - b) |
⟹ 3√5 + √25 x 5 = 17.88
⟹ 3√5 + 5√5 = 17.88
⟹ 8√5 = 17.88
⟹ √5 = 2.235
∴ √80 + 6√5 = √16 x 5 + 6√5
= 4√5 + 6√5
= 10√5 = (10 x 2.235) = 22.35
The value of | 0.1 x 0.1 x 0.1 + 0.02 x 0.02 x 0.02 | is: |
0.2 x 0.2 x 0.2 + 0.04 x 0.04 x 0.04 |
Given expression = | (0.1)3 + (0.02)3 | = | 1 | = 0.125 |
23 [(0.1)3 + (0.02)3] | 8 |
❨ | √3 - | 1 | ❩ | 2 | simplifies to: |
√3 |
3 |
4 |
4 |
√3 |
4 |
3 |
4 |
3 |
❨ | √3 - | 1 | ❩ | 2 | = (√3)2 + | ❨ | 1 | ❩ | 2 | - 2 x √3 x | 1 |
√3 | √3 | √3 |
= 3 + | 1 | - 2 |
3 |
= 1 + | 1 |
3 |
= | 4 |
3 |
Which of the following fractions is greater than | 3 | and less than | 5 | ? |
4 | 6 |
1 |
2 |
2 |
3 |
4 |
5 |
9 |
10 |
4 |
5 |
3 | = 0.75, | 5 | = 0.833, | 1 | = 0.5, | 2 | = 0.66, | 4 | = 0.8, | 9 | = 0.9. |
4 | 6 | 2 | 3 | 5 | 10 |
Clearly, 0.8 lies between 0.75 and 0.833.
∴ | 4 | lies between | 3 | and | 5 | . |
5 | 4 | 6 |
What should come in place of both x in the equation | x | = | √162 | . |
√128 | x |
Let | x | = | √162 |
√128 | x |
Then x2 = √128 x 162
= √64 x 2 x 18 x 9
= √82 x 62 x 32
= 8 x 6 x 3
= 144.
∴ x = √144 = 12.
Given, (x/4) + (y/3) = 10/24
? (3x + 4y)/12 = 10/24
? 3x + 4y = 5 ...(i)
and (x/2) + y = 1
x + 2y = 2 ...(ii)
On multiplying Eq. (ii) by 2 and subtracting from Eq. (i).
3x + 4y = 5
2x + 4y = 4
- - -
--------------------------
x = 1
On putting the value of x in Eq. (ii), we get
x + 2y = 2
? 1 + 2y = 2
? y = 1/2
? x + y = 1 + 1/2 = 3/2
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