Consider the equation in real numbers ∣ x − 3∣ + ∣ x + 9∣ = a , a ∈ R . Match the statements/expressions in Column I with those in Column II. Column I (A) As a ranges over R , the maximum possible num

Question

Consider the equation in real numbers ∣ x − 3∣ + ∣ x + 9∣ = a , a ∈ R . Match the statements/expressions in Column I with those in Column II. Column I (A) As a ranges over R , the maximum possible number of integral solutions is (B) For a > lo g 27 ​ 81 , , the number of solutions cannot be (C) For a = 13 , the number of solutions is (D) For at least one solution, a cannot take the value(s) Column II (P) 2 (Q) 0 (R) 13 (S) 1

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The line y = k , k < 12 doesn't meet the above curve k = 2 meets the curve at infinite points belonging to [ − 9 , − 3 ] k > 12 meets the curve at two points For k = 12 , the line y = k meets the curve y = ∣ x − 3∣ + ∣ x + 9∣ at 13 integral points. Note that lo g 27 81 = 4/3 A) The maximum possible number of integral solutions is 13 which happens when a = 12 B) For 4/3 < a<12 the number of solutions = 0 ] a=12, the number of solutions is infinite a>12, the number of solutions is two.

Mathematics - Application of Derivative Question with Solution | TestHub

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