UPSC 2017 CDS II Math Paper

Remember: The point of intersection of the perpendicular bisectors of the sides of a triangle is the circumcentre of the triangle. In an obtuse triangle, the circumcentre lies outside the triangle, whereas for an acute triangle, the circumcentre lies inside the triangle.
Thus, the point of intersection of the perpendicular bisectors of the sides of a triangle may lie outside the triangle.
Hence, statement 1 is correct.
Remember: The point of intersection of the perpendiculars drawn from the vertices to the opposite sides of a triangle is the orthocentre of the triangle. In an obtuse triangle, the orthocentre lies outside the triangle whereas for an acute triangle, the orthocentre lies inside the triangle. The orthocentre of a right triangle is the vertex of the right angle.
Thus, the point of intersection of the perpendiculars drawn from the vertices to the opposite sides of a triangle may lie on two sides.
Hence, statement 2 is correct.
Solution for the next 5 items
Total number of students = 1200
Number of students studying Mathematics=

20

100

×1200=240
Number of boys studying Mathematics = 150
Number of girls studying Mathematics =240−150=90
Number of students studying PhysicsNumber of boys studying Physics=

60

100

×300=180
Number of girls studying Physics =300−180=120
Number of students studying Statistics = 320
Number of girls studying Statistics = 250
Number of boys studying Statistics=320−250=70
Number of students studying ChemistryNumber of girls studying Chemistry =

3

5

×340=204
Number of boys studying Chemistry=340−204=136