For the following questions answer them individually
If $$x + y + z = 1, xy + yz + zx = xyz = -4$$, then what is the value of $$(x^3 + y^3 + z^3)?$$
Ina trapezium PQRS, PQ is parallel to RS and diagonals PR and QS intersect at O. If PQ= 4 cm. SR = 10 cm, then what is area($$\triangle POQ$$) : area($$\triangle SOR$$) ?
A shopkeeper buys an article at 30% discount on its marked price and sells it at 5% discount onits marked price. If he earns a profit of ₹65, then whatis the marked price (in ₹) of the article?
If $$\tan \theta = \sqrt{5}$$, then the value of $$\frac{\cosec^2 \theta + \sec^2 \theta}{\cosec^2 \theta - \sec^2 \theta}$$ is:
A sum of ₹6342 is divided amongst A, B, C and in theratio 3 : 4: 8 : 6. What is the difference between the shares of B and D?
If $$x^2 - 5\sqrt{2}x + 1 = 0$$, then what is the value of $$\frac{\left(x^3 + \frac{1}{x}\right)}{x^2 + 1} ?$$
Simplify the following expression :
$$6 \div 4 of 3 - 4 \div 6 \times (13 - 10) - 2 \times 15 \div 6 \times 6$$
A sum of ₹3125 amounts to 3515.20 in 3 years at x %p.a., interest being compounded yearly. What will be the simple interest (in ₹) on the same sum and for the same time at (x + 2) %p.a.?
A can complete a work in 60 days. B is 25% more efficient than A. They work together for 15 days. C alone completes the remaining work in 14 days. B and C together will complete $$\frac{5}{8}th$$ part of the original work in:
