A shopkeeper buys shirts from a producer and sells them at 20% profit. A customer has to pay ₹3,186.00 including 18% taxes, per shirt. At what price did the shopkeeper buy each shirt from the producer?

If, for non-zero real variables $x$, $y$, and real parameter $a > 1$,

$x : y = (a + 1) : (a - 1)$,

then, the ratio $(x^2 - y^2) : (x^2 + y^2)$ is

In the given text, the blanks are numbered (i)–(iv). Select the best match for all the blanks.

Following a row ____(i) ______ the shopkeeper ____(ii) ______ the price of a frying pan, the cook stood ____(iii) ______ a row to withdraw cash _____(iv) ______ the ATM booth.

In the following figure,

• CD = 5 cm, BE = 10 cm, AE = 12 cm,
• ∠DAB = ∠DCB, and ∠DAE = ∠DBC = 90°

Points AFCD create a rhombus.

The length of BF (in cm) is