Quantitative Aptitude - Arithmetic Ability Questions

In ΔPQR, S and T are points on side PQ and PR respectively. ST is parallel to QR. If S divides PQ in the ratio 4:1 and length of QR is 15 cm,what is the length of ST?

The lengths of diagonals of a rhombus are 24cm and 10cm the perimeter of the rhombus (in cm ) is :

What is the value of tan 6° tan 36° tan 84° tan 54° tan 45°?

What is the value of 2sec2A?

For triangle PQR, find equation of altitude PS if co­-ordinates of P, Q and R are (6,2), (0,3) and (­-4,5) respectively?

Find the value of  x3 - y3, if x - y = 4 and xy = 12.

The value of sinθ+sin∅cosθ+cos∅ + cosθ-cos∅sinθ-sin∅ is

If a + b = 1, then a4 + b4 - a3 - b3 - 2a2b2 + ab is equal to