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help me in solving these questions

1)Triangle ABC is an acute angled triangle. A transversal intersects the side BC produced at D and AC and AB at points E and F respectively Then (BD / DC) * (CE/EA) * (AF/FB) = ? a.1/3 b.1/2 c.2/5 d.1 e.Not Attempted 2)There are four machines that makes gears for a factory . The fastest machine can make one gear in two hours . The slowest machine makes one gear in 3 hours . which of the following cannot be the value of the average time taken by each to make a gear ? a. 2.2 hours b. 2.3 hours c. 2.6 hours d. 2.68 hours 3)The smallest positive integer which can be expressed as a sum of two different cubes in two different ways is: a.1000 b.729 c.1729 d.1728 4)if a+b+c=0 , where a ? b ? c then [(a2)/(2a2+bc)] +[(b2)/(2b2+ac)] + [(c2)/(2c2+ab)] is equal to a. 4 b. 5 c. 6 d. 7 5)The maximum possible value of y = min(1/2 - 3x2/4 , 5x2/4) for the range 0 < x < 1 is a. 1/3 b. 1/2 c. 5/27 d. 5/16 thanks in advance.

Hey Sekhar could you please

Hey Sekhar could you please tell the TEST or QBM number so that I can check the question directly from there Else write the questions properly because when you just copy paste the formatting changes and now one can differentiate between 2 and ² And mentioning the number ll helps others who ll be also looking for the solution of that question If you are posting it from other source like TIME/CL then also mention that

I cld nt understand the

I cld nt understand the first question and 4/5 are not in proper format. Answer to Q2. Let the other two m/c takes 2 hrs(thats the minimum time) then avg time taken = 2 + 2 + 2 + 3 /4 =2.25 So in any case it cant be less than 2.25 Answer a. 2.2 Answer to Q3. 1729 = 9 ³ + 10³ and 1729 = 12 ³ + 1 ³ It’s easy if you know the cubes of first 15 numbers

test is FLT-M006

questions are from FLT-M006.

Taxicab Numbers Curious

Taxicab Numbers Curious properties sometimes lurk within seemingly undistinguished numbers. Consider the story concerning Indian mathematician Srinivasa Ramanujan (1887–1920). His friend G.H. Hardy (1877–1947) once remarked that the taxi by which he had arrived had a "dull" number—1729, or 7 x 13 x 19. Ramanujan was quick to point out that 1729 is actually a "very interesting" number. It's the smallest whole number expressible as a sum of two cubes in two ways: Both 13 + 123 and 93 + 103 equal 1729. The first published reference to this property of the integer 1729 is in the writings of 17th-century French mathematician Bernard Frénicle de Bessy (1605–1670). GOOD TO KNOW SOME TRIVIA !!!

Nice work manSeems you got