Experienced in teaching IITJEE Mains and Advanced-Mathematics.
Intro to a simple problem with objectives to be attained. Then I proceed with underlying motives, strategies or tricks (you may call). Ending with your doubts clarified and few selected problems.
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The graph shrinks vertically 5 times i.e. every f(x) shall decrease to 5 times the previous value. For continuous graphs, it is quite observable if graphs are drawn in a plane with same reference axes appearing as if the graph has been pressed from both top and bottom.
15% of MP = Rs 160 MP= Rs 160*100/15 =Rs 1066.67 SP= MP – Discount =Rs (1066.67-160) =Rs 906.67
(385*30/100/17) - ((sqrt x)*11/100) = 350 (385*30/100/17) - 350 = ((sqrt x)*11/100) 6.79 - 350 = ((sqrt x)*11/100) -343.21 = ((sqrt x)*11/100) -343.21*100/11 = sqrt x sqrt x = -3120.101 x doesn't have any real roots, only complex ones x = 55.858i, -55.858i
fraction of work done in a day by 25 men = 1/14 fraction of work done in 5 days by 25 men = (1/14)*5 After 5 days, fraction of work left to be done by 20 men = 1 - (1/14)*5 = 9/14 fraction of work done by 20 men in a day = 20/(14*25) fraction of work done by 20 men in x days = (20/(14*25)) * x where x = number of days taken by 20 men to complete the rest of the work which is equal to 9/14 implying.... (20/(14*25)) * x = 9/14 x = 11.25 days total days = x + 5 = 16.25
the third one : 7x^2 + 8x + 1 = 7(x^2 + 8x/7 + 1/7) ...........................(1) as we know the quadratic polynomial's general equation is a(x-b)(x-c) = a(x^2 -(b+c)x + bc) so comparing it with the (1), we get bc = 1/7
Sir helped a lot to grasp the core concepts and avoid the redundant data to cram, the mode the coaching Institutes prefer to crack the exam. deeply indebted to sir.
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