For the following questions answer them individually
If $$a^{2} - 4a+ 1 = 0$$ , then the value of $$a^{2} +a+\frac{1}{a}+\frac{1}{a^{2}}$$ is:
If $$\left(X-\frac{1}{x}\right)=\frac{7}{3}$$, what is the value of $$\left(X^{3}-\frac{1}{x^{3}}\right)=?$$
If the average marks of three batches of 30, 50 and 70 students is 55, 70 and 70 respectively, then the average marks of all the students is:
Compute the compound interest on ₹ 8,400 for one and half years at 12% rate of interest per annum, compounded half yearly.
Triangles ABC and PQR are similar to each other. If m$$\left(\overline {BC}\right) = 5$$ cm, m$$\left(\overline {QR}\right) = 12.5$$ cm, and m$$\left(\overline {PQ}\right)= 6.25$$ cm, find m$$\left(\overline {AB}\right)$$.
The speed of a train is 108 km/h. The distance covered by the train in 11 seconds will be:
The base of a 12 m-high wooden solid cone has a circumference of 44 m. Find its volume.
(use $$\pi=\frac{22}{7}$$)
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