Delhi SI CPO Nov 25 Shift-1

PA and PB are two tangents from a point P outside the circle with centre O. If A and are points on the circle such that $$\angle APB = 142^\circ$$, then $$\angle OAB$$ is equal to:

Two pipes A and can fill a tank in 12 hours and 18 hours, respectively. Both pipes are opened simultaneously. In how much time will the empty tank be filled completely?

The perimeter of a square is half the perimeter of a rectangle. The perimeter of the square is 40 m. If its breadth is two- thirds of its length, then what is the area (in $$m^2$$) of the rectangle?

Three successive discounts of 12%, 13% and 11% are equivalent to an approximate single discount of:

If $$(5 \sqrt 5 x^3 - 3 \sqrt 3 y^3) \div (\sqrt 5 x - \sqrt 3 y) = (Ax^2 + By^2 + Cxy),$$ then what is the value of $$(3A - B - \sqrt 15 C)$$ ?

A and B can do job in 10 days and 5 days, respectively. They worked together for two days, after which B was replaced by C and the work was finished in the next three days. How long will C alone take to finish 40% of the job?

The price of diesel is increased by 26%. A person wants to increase his expenditure by 15% only. By what percentage, correct to one decimal place, should he decrease his consumption?

The given pie chart represents the popularity of ice-cream flavours in the year 2005.

In 2005, if 40% of the ‘other’ category is mix fruit flavour and 1570 people surveyed preferred mix fruit flavour, then how many people were surveyed?

In $$\triangle ABC, BD \perp AC$$ at D. E is a point on BC such that $$\angle BEA = x^\circ$$. If $$\angle EAC = 62^\circ$$ and $$\angle EBD = 60^\circ$$,then the value of $$x$$ is:

A person was standing on a road near a mall. He was 1215 m away from the mall and able to see the top of the mall from the road in such a way that the top of a tree, which is in between him and the mall, was exactly in line of sight with the top of the mall. The tree height is 20 m and it is 60 m away from him. How tall (in m) is the mall?