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Question

List I has four entries and List II has four entries. Each entry of List I has a unique match in List II.

List IList II(A)Let f be a real-valued differentiable (P)18function on R such that f(1)=6and f(2)=2. Thenlimh0f(3cosh+4sinh2)f(1)f(3eh5sech+4)f(2) is equal to(B)If (0.5)log3log1/5(x245)>1, then the least (Q)4positive integral value of x is(C)The value of limx1sin2(x3+x2+x3)1cos(x24x+3) is(R)5(D)Number of points of non-differentiability of(S)2f(x)=min(|sinx|,|cosx|,14)in (0,π) is

Which of the following is the only CORRECT combination?

A
(C)(Q)
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B
(D)(Q)
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C
(C)(P)
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D
(D)(S)
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Solution

The correct option is C (C)(P)
(C)
limx1sin2(x3+x2+x3)1cos(x24x+3)
=limx1sin2(x3+x2+x3)(x3+x2+x3)2(x3+x2+x3)21cos(x24x+3)
=limx11(x24x+3)21cos(x24x+3)(x3+x2+x3)2(x24x+3)2
=limx112(x3+x2+x3x24x+3)2
=2l2, where l=limx13x2+2x+12x4=62=3
Limit =2(3)2=18

(D)


Hence, graph of min(|sinx|,|cosx|,14) can be plotted as


Clearly, from the graph, total number of non-differentiable points of f(x) in the interval (0,π) is 5.

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