Mr, X speaks ________Japanese ________ Chinese.

Mosquitoes pose a threat to human health. Controlling mosquitoes using chemicals may have undesired consequences. In Florida, authorities have used genetically modified mosquitoes to control the overall mosquito population. It remains to be seen if this novel approach has unforeseen consequences.

Which one of the following is the correct logical inference based on the information in the above passage?

In a class of five students  and , only one student is known to have copied in the exam. The disciplinary committee has investigated the situation and recorded the statements from the students as given below.

Statement of P: R has copied in the exam.

Statement of Q: S has copied in the exam.

Statement of R: P did not copy in the exam.

Statement of S: Only one of us is telling the truth.

Statement of T:  is telling the truth.

The investigating team had authentic information that  never lies.

Based on the information given above, the person who has copied in the exam is

Consider the following square with the four corners and the center marked as P, Q, R, S and  respectively.

Let  and  represent the following operations:  : rotation of the square by 180 degree with respect to the S-Q axis.

Y: rotation of the square by 180 degree with respect to the -R axis.

 : rotation of the square by 90 degree clockwise with respect to the axis perpendicular, going into the screen and passing through the point .

Consider the following three distinct sequences of operation (which are applied in the left to right order).

(1) XYZZ        (2)

(3) ZZZZ

Which one of the following statements is correct as per the information provided above?

A sum of money is to be distributed among P, Q, R and  in the proportion , respectively.

If R gets Rs. 1000 more than , what is the share of  (in Rs.)?

A trapezium has vertices marked as  and  (in that order anticlockwise). The side  is parallel to side SR.

Further, it is given that, ,  and .

What is the shortest distance between  and  (in  )?

The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole.

What is the maximum number of squares without a "hole in the interior" that can be formed within the  grid using the unit squares as building blocks?

An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery where the boundary walls are opaque. The location the security guard posted is identified such that all the inner space (shaded region in the plan) of the gallery is within the line of sight of the security guard. If the security guard does not move around the posted location and has a  view, which one of the following correctly represents the set of ALL possible locations among the locations  and , where the security guard can be posted to watch over the entire inner space of the gallery.

Consider the following inequalities.        

(i)

(ii)

Which one of the following expressions below satisfies the above two inequalities?

Four points , and  represent the vertices of a quadrilateral.

What is the area enclosed by the quadrilateral?