CBSE Class 12 Sample Paper for 2024 Boards

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

## (d) A is false but R is true.

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Checking Assertion ASSERTION (A): đ(đĽ) has a minimum at đĽ=1. Finding minimum of đ(đ) Differentiating w.r.t. x đâ(đĽ) =(đĽâ1)^3 (đĽâ3)^2 Putting fâ(đ) = 0 (đĽâ1)^3 (đĽâ3)^2 = 0 Thus, either ă"(x â 1)" ă^2 = 0 and (đĽâ3)^2 = 0 â´ x = 1, 3 Checking maxima or minima at x = 1 â´ x = 1 is a point of minima Hence, Assertion is true Checking Reason REASON (R): When đ/đđĽ(đ(đĽ))<0,âđĽâ(đââ, a ) and đ/đđĽ(đ(đĽ))>0,âđĽâ(đ,đ+â); where ^â˛ đ ' is an infinitesimally small positive quantity, then đ(đĽ) has a minimum at đ=đ, provided đ(đ) is continuous at đ=đ. Here, reasoning is describing the 1st derivative test fâ(x) < 0 for x â(đââ, a) i.e. fâ(x) < 0 on left of x = a fâ(x) > 0 for x â(đ,đ+â) i.e. fâ(x) > 0 on right of x = a Since when sign fâ(x) changes from negative to positive, it is Minima Hence, Reason is true Is Reason a Correct explanation for Assertion? Since we used the concept mentioned in Reasoning to check Assertion Therefore, Reasoning is a correct explanation for Assertion So, Assertion is true Reasoning is true And, Reasoning is a correct explanation for Assertion So, the correct answer is (a)