Question : A tailor buys lining clothes from a wholesale merchant and cheats him by using a measurement tape that is 5 cm longer than the normal tape. The tailor offers the customers at cost price while stitching different garments and uses measurement tape which is 5 cm shorter than the normal tape. The gain percent is:

Option 1: $15$%

Option 2: $10 \frac{10}{25}$%

Option 3: $10$%

Option 4: $10 \frac{10}{19}$%

Question : PQ is a chord of length 8 cm of a circle with centre O and radius 5 cm. The tangents at P and Q intersect at a point T. The length of TP is:

Option 1: $\frac{20}{3}\ \text{cm}$

Option 2: $\frac{21}{4}\ \text{cm}$

Option 3: $\frac{10}{3}\ \text{cm}$

Option 4: $\frac{15}{4}\ \text{cm}$

Question : The sides of a triangle are 9 cm, 6 cm, and 5 cm. What is the value of the circumradius of this triangle?

Option 1: $\frac{9 \sqrt{2}}{2} \mathrm{~cm}$

Option 2: $\frac{9 \sqrt{3}}{5} \mathrm{~cm}$

Option 3: $\frac{9 \sqrt{3}}{4} \mathrm{~cm}$

Option 4: $\frac{27 \sqrt{2}}{8} \mathrm{~cm}$

Question : BL and CM are medians of $\triangle$ABC right-angled at A and BC = 5 cm. If BL=$\frac{3\sqrt5}{2}$ cm, then the length of CM is

Option 1: $2\sqrt5$ cm

Option 2: $5\sqrt2$ cm

Option 3: $10\sqrt2$ cm

Option 4: $4\sqrt5$ cm

Question : $\triangle $KLM is a right-angled triangle. $\angle$M = 90$^{\circ}$, KM = 12 cm and LM = 5 cm. What is the value of $\sec$ L?

Option 1: $\frac{13}{12}$

Option 2: $\frac{5}{12}$

Option 3: $\frac{12}{5}$

Option 4: $\frac{13}{5}$

Question : Let ABC be a triangle right-angled at B. If $\tan A = \frac{12}{5}$, then find the values of $\operatorname{cosec A}$ and $\sec A$, respectively.

Option 1: $\frac{13}{10}, \frac{5}{13}$

Option 2: $\frac{13}{12},\frac{13}{5}$

Option 3: $\frac{10}{13}, \frac{5}{13}$

Option 4: $\frac{12}{13}, \frac{5}{13}$