For the following questions answer them individually
Solve the following equation.
$$\left(7^{3} - 7^{2} + 6 \right) \times \left(6^{3} - 2^{3} - 3^{2} + 1 \right) \div \left(21^{2} + 20^{2} - 41 \right) $$= ___________.
What is the greatest positive integer that divides 554, 714 and 213 leaving the remainder 43, 57 and 67, respectively?
If $$\cos \theta + \sin \theta = \sqrt{2} \cos \theta$$, find the value of $$\left(\cos \theta - \sin \theta\right)$$.
60 men can complete a work in 40 days. They start work together but after every 10 day, 5 men leave the work. In how many days will the work be completed?
If the number 8764x5 is divisible by 9, then find the least possible value of $$x$$ where $$x$$ is a two-digit number.
If a,b,c are all non-zero and a+b+c = 0 find the value of $$\frac{a^{2}}{bc}+\frac{b^{2}}{ca}+\frac{c^{2}}{ab}$$
Ajay buys 18 oranges for ₹90 and sells 15 oranges for ₹105. Find the percentage of his gain.
The monthly incomes of Ravi and Shiv are in the ratio 1 : 2 and their monthly expenditures are in the ratio 1 : 3. If each saves ₹4,000 per month, then find the monthly income of Shiv.
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