For integers a, b and c, what would be the minimum and maximum values respectively of a + b + c if log |a| + log |b| + log |c| = 0?
-3 and 3
The logarithm rule gives \(\log|abc|=0\Rightarrow|abc|=1\). Nonzero integer absolute values must each be 1. Each variable is therefore ±1, giving minimum sum −3 and maximum 3.
Important Questions from Numerical Computation
If \({\left( {z + \frac{1}{z}} \right)^2} = 98\), compute \(\left( {{z^2} + 1/\;{z^2}\;} \right)\)
- In the context of measures of surfaces, which one of the following is $not$ correct?
Ratio of the angles of a triangle are 1 : 2 : 6. What is the smallest angle?
Two design consultants, P and Q, started working from 8 AM for a client. The client budgeted a total of USD 3000 for the consultants. P stopped working when the hour hand moved by 210 degrees on the clock. Q stopped working when the hour hand moved by 240 degrees. P took two tea breaks of 15 minutes each during her shift, but took no lunch break. Q took only one lunch break for 20 minutes, but no tea breaks. The market rate for consultants is USD 200 per hour and breaks are not paid. After paying the consultants, the client shall have USD_remaining in the budget.
Leila aspires to buy a car worth Rs. 10,00,000 after 5 years. What is the minimum amount in Rupees that she should deposit now in a bank which offers 10% annual rate of interest, if the interest was compounded annually?
