SSC CPO 9th Dec 2019 Shift-2

If $$x^{4}+ x^{2} y^{2}+y^{4}=21$$, and $$x^{2}+xy+y^{2} = 3,$$ then what is the value of 4xy?

If x is subtracted from each of the numbers 20, 37, 54 and 105, then the numbers so obtained in this order are in proportion. What is the mean proportional between (7x - 5) and (x + 1)?

If 60% of (x — y) =45% (x + y) and y = k% ofx, then 21% of k is equal to

By selling an article for ₹1,134, Anu suffers as much loss as she would have gained by selling it at 10% profit. If she sells it for ₹1,354.50, then her profit percentage is

A can do $$\frac{2}{5}$$ of a work in 6 days and B can do $$\frac{2}{3}$$ of the same work in 12 days. A and B worked together for 6 days. C alone completed the remaining work in 8 days. A and C, working together, will complete the same work in:

If $$x^2 -\sqrt{7}x +1 =0$$, then $$(x^3 + x^{-3}) = ?$$

A, B and C can do piece ofwork in 30 days, 45 days and 90 days, respectively. A starts the work and heis assisted by B and C togetheron every third day. In how many dayswill the work be completed?

The value of $$\frac{1}{\sqrt{7-4\sqrt{3}}}$$ is closest to

A, B and started a business with their capitals in the ratio 4 : 2 : 9. At the end of every quarter, A halves his capital, whereas B doubles his capital and C leaves his capital unchanged. If at the end of a year, A’s profit was ₹24,000, then what is the total profit (in ₹) is

A circle touches the side BC of a $$\triangle$$ABC at P and also touches AB and AC produced at Q and R, respectively. If the perimeter of $$\triangle$$ABC = 26.4 cm, then the length of AQ is: