This is a CSIR-NET June 2017 Part A question of Life Sciences and Physical Sciences

Which of the following is the odd one out?

1. Isosceles triangle 2. Square 3. Regular hexagon 4. Rectangle

by Christy Varghese

This is a CSIR-NET June 2016 Part A question of Mathematical Sciences, Chemical Sciences, Earth Sciences.

Question discussed: A mine supplies 10000 tons of copper ore, containing an average of 1.5 wt% copper, to a smelter every day. The smelter extracts 80% of the copper from the ore on the same day. What is the production of copper in tons/day?

(1) 80 (2) 12 (3) 120 (4) 150

Discussed by – Christy Varghese

This is a CSIR-NET December 2016 Part A question of Mathematical Sciences, Chemical Sciences, Earth Sciences.

Question discussed: A milkman adds 10 litres of water to 90 litres of milk. After selling 1/5th of the total quantity, he adds water equal to the quantity he has sold. The proportion of water to milk he sells now would be

(1) 72: 28 (2) 28: 72 (3) 20: 80 (4) 30: 70

Discussed by – Christy Varghese

This is a CSIR-NET December 2016 Part A question of Mathematical Sciences, Chemical Sciences, Earth Sciences.

Question discussed: The mid-point of the arc of a semicircle is connected by two straight lines to the ends of the diameter as shown. What is the ratio of the shaded area to the area of the triangle?

(1) π/2 -1 (2) (π-1)/2 (3) π – 1/2 (4) 2π – 1/4

Discussed by – Christy Varghese

This is a CSIR-NET June 2016 Part A question of Life Sciences, Physical Sciences.

Question discussed: Two iron spheres of radii 12 cm and 1 cm are melted and fused. Two new spheres are made without any loss of iron. Their possible radii could be:

(1) 9 and 4 cm (2) 9 and 10 cm (3) 8 and 5 cm (4) 2 and 11 cm

History: 1729 is the Ramanujan number after a famous anecdote of the British mathematician G. H. Hardy regarding a visit to the hospital to see Srinivasa Ramanujan. In Hardy’s words: “I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. “No,” he replied, “it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.” The two different ways are: 1729 = 1cube + 12cube = 9cube + 10cube

P.S. If you know about the Ramanujan Number, the step of finding the values of x and y using trial and error can be skipped as these are the only two different ways the number 1729 can be expressed as the sum of two cubes.

Discussed by – Christy Varghese

This is a CSIR-NET December 2016 Part A question of Life Sciences, Physical Sciences.

Question discussed: Comparing numerical values, which of the following is different from the rest?

(1) The ratio of the circumference of a circle to its diameter.

(2) The sum of the three angles of a plane triangle expressed in radians.

(3) 22/7

(4) The net volume of a hemisphere of unit radius, and a cone of unit radius and unit height.

Discussed by – Christy Varghese