In \(\bigtriangleup\) XYZ, XKZ = 90O, XK = 15cm, XZ = 25cm and YK = 8cm. Find the area of \(\bigtriangleup\)XYZ

A. 190 sq.cm

B. 20 sq.cm

C. 210 sq.cm

D. 160sq.cm

E. 320sq.cm

In the figure, MNQP is a cyclic quadrilateral. MN and Pq are produced to meet at X and NQ and MP are produced to meet at Y. If MNQ = 86^o and NQP = 122^o find (x^o, y^o)

A. 28^o, 36^o

B. 36^o, 28^o

C. 43^o, 61^o

D. 61^o, 43^o

E. 36^o, 43^o

In the figure POQ is the diameter of the circle PQR. If PSR = 145o, find xo

A. 25^o

B. 35^o

C. 45^o

D. 125^o

E. 55^o

In the figure, GHIJKLMN is a cube of side a. Find the length of HN.

A. \(\sqrt{3a}\)

B. 3a

C. 3a²

D. a\(\sqrt{2}\)

E. a\(\sqrt{3}\)

In the figure, PQ is the tangent from P to the circle QRS with SR as its diameter. If QRS = \(\theta\)^oand RQP = \(\phi\)^o, which of the following relationships between \(\theta\)^o and \(\phi\)^o is correct

A. \(\theta\)^o + \(\phi\)^o = 90²

B. \(\phi\)^o = 90² - 2\(\theta\)^o

C. \(\theta\)^o = \(\phi\)^o

D. \(\phi\)^o = 2\(\theta\)^o

E. \(\theta\)^o + 2\(\phi\)^o

In the figure, the area of the shaded segment is

A. 3\(\pi\)

B. 9\(\frac{\sqrt{3}}{4}\)

C. 3 \(\pi - 3 \frac{\sqrt{3}}{4}\)

D. \(\frac{(\sqrt{3 - \pi)}}{4}\)

E. \(\pi + \frac{9 \sqrt{3}}{4}\)

In the figure, find angle x

A. 100^o

B. 120^o

C. 60^o

D. 110^o

E. 140^o