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Ques1) From a fixed point P on the circumference of a circle of radius a , the perpendicualr PR is drawn to the tangent at Q (a variable point). Show that the max area of triangle PQR is [3 (3) 1/2 / 8 ] a 2 . Ques2) If f '' (x) + f ' (x) + f 2 (x) = x 2 be the differential equation of a curve and let P be the point of maxima , then show that the number of tangents which can be drwn from P to x 2 - y 2 is 2. Ques3) If a differentiable function f (x) has arelative minimum at x = 0, then the function y = f(x) = ax 2 +bx+c has a relative minimum at x=0, then which of the following is / are correct :- (a) b = 0 , all a (b) b=0, a> -(1/2) f ' (0) (c) a=0, b=0 (d) a=0 , b=0, c=2.

Ques1) From a fixed point P on the circumference of a circle of radius a , the perpendicualr PR is drawn to the tangent at Q (a variable point). Show that the max area of triangle PQR is [3 (3)1/2  / 8 ] a2.


Ques2) If f '' (x) + f ' (x)  + f 2(x) = x 2 be the differential equation of a curve and let P be the point of maxima , then show that the number of tangents which can be drwn from P to x 2 -  y 2  is 2.


Ques3) If a differentiable function f (x) has  arelative minimum at x = 0, then the function y = f(x) = ax2+bx+c has a relative minimum at x=0, then which of the following is / are correct :-


(a) b = 0 , all a            (b) b=0, a> -(1/2) f ' (0)    (c) a=0, b=0        (d) a=0 , b=0, c=2.

Grade:12

2 Answers

prashant kumar
16 Points
12 years ago
Askiitian.Expert Rajat
24 Points
12 years ago

Hi Tushar

Please post different questions in a different post, i.e., one question per post.

Regards

Rajat

 

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