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Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

Which of the following statement(s) is/are 'CORRECT'?

Options

  1. ARolle's theorem is applicable to the function f(x)=1- [5] x^6 in the interval [-1,1]
  2. BThe value of _ x 0 ₀^x x e^ t^2 d t 1+x-e^x is equal to -2
  3. CIf a and b are any two unit vectors, then least value of 1 | a + b |^2 + 1 | a - b |^2 is equal to 2 .
  4. DThe angle between pair of tangents drawn to the curve 7 x^2-12 y^2=84 from M(1,2) is 4

Correct answer

B. The value of _ x 0 ₀^x x e^ t^2 d t 1+x-e^x is equal to -2

Step-by-step solution

(A) f(x)=1-x^ 6 / 5 f^ (x)=- 6 5 x^ 1 5 exist x (-1,1) and f (1)=0= f (-1) Rolle's theorem is applicable (B) _ x 0 ₀^x x e^ t^2 d t 1+x-e^x = _ x 0 x ( ₀^x e^ t^2 d t ) 1+x-e^x = _ x 0 x (e^ x^2 )+ ₀^x e^ t^2 d t 1-e^x ( 0 0 )= _ x 0 = x (e^ x^2 2 x )+e^ x^2 +e^ x^2 -e^x = 0+1+1 -1 =-2 (C) | a + b |=1+1+2 =2(1+ )=4 ^2 / 2 aligned & and | a - b |^2=1+1-2 =2(1- )=4 ^2 / 2 & 1 | a + b |^2 + 1 | a - b |^2 & = 1 4 ( ^2 2 + cosec ^2 2 ) & = & = 1 4 (1+ ^2 2 +1+ ^2 2 ) A.M. G.M & ^2 2 ^2 2 2 1 aligned (D) M(1,2) lies on t

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