Question on production of copper – Solution (CSIR-NET December 2016 Part A)

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

Question on proportion of milk and water – Solution (CSIR-NET December 2016 Part A)

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

Question on Semicircle – Solution (CSIR-NET December 2016 Part A)

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

Question on two iron spheres – Solution (CSIR-NET December 2016 Part A)

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

Question on pi – Solution (CSIR-NET December 2016 Part A)

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