A surveyor has to measure the horizontal distance from her position to a distant reference point C. Using her position as the center, a 200 m horizontal line segment is drawn with the two endpoints A and B. Points A, B, and C are not collinear. Each of the angles ∠CAB and ∠CBA are measured as 87.8°. The distance (in m) of the reference point C from her position is nearest to

There are two identical dice with a single letter on each of the faces. The following six letters : Q, R, S, T, U and V, one on each of the faces. Any of the six outcomes are equally likely.

The two dice are thrown once independently at random.

What is the probability that the outcomes on the dice were composed only of any combination of the following possible outcomes : Q, U and V?

The price of an item is 10% cheaper in an online store S compared to the price at another online store M. Store S charges Rs.150 for delivery. There are no delivery charges for orders from the store M. A person bought the item from the store S and saved Rs.100. What is the price of the item at the online store S (in Rs.) if there are no other charges than what is described above?

The letters P, Q, R, S, T and U are to be placed one per vertex on a regular convex hexagon, but not necessarily in the same order.

Consider the following statements :

$$\bullet$$ The line segment joint R and S is longer than the line segment joining P and Q.

$$\bullet$$ The line segment joining R and S is perpendicular to the line segment joining P and Q.

$$\bullet$$ The line segment joining R and U is parallel to the line segment joining T and Q.

Based on the above statements, which one of the following options is CORRECT?