Most Important Selected Qs for JEE AdvancedMathematicsDeterminants

Let f(x)= | array ccc 2 x & ^2 x & 0 1 & 2 x & ^2 x 0 & 1 & 2 x array | , then

Options

Af(x) is independent of x
Bf^ ( / 2)=0
C_ - / 2 ^ / 2 f(x) d x=0
DTangent to the curve y=f(x) at x=0 is y=0

Correct answer

D. Tangent to the curve y=f(x) at x=0 is y=0

Step-by-step solution

f(x)= | array ccc 2 x & ^2 x & 0 1 & 2 x & ^2 x 0 & 1 & 2 x array |=2 x (4 ^2 x- ^2 x )- ^2 x(2 x)=6 ^3 x-2 ^3 x aligned & f(x)=4 ^3 x & f^ (x)=12 ^2 x x aligned (B) f^ ( / 2)=12 ^2( / 2) ( / 2)=0 (C) f(-x)=-f(x) odd function _ - 2 ^ 2 f(x) d x=0 (D) at x=0, y=0 ( d y d x )_ (0,0) =0 tangent at (0,0) aligned & y-0= ( d y d x )_ (0,0) (x-0) & y=0 aligned

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