Multiple Choice QuestionsA wire of length 2 units is cut into two parts which are bent respectively to form a square of side=x units and a circle of radius=r units. If the sum of the areas of the square and the circle so formed is minimum, then:
2x=(Ï€+4)r
(4−π)x=πr
x=2r
x=2r
Let f (x) be a polynomial of degree four having extreme values at x =1 an x =2. If 
 then f(2) is equal toÂ
-8
-4
0
0
A spherical balloon is filled with 4500Ï€ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72Ï€ cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is
9/7
7/9
2/9
2/9
Let a, b ∈ R be such that the function f given by f(x) = ln |x| + bx
2+ ax, x ≠0 has extreme values at x = –1 and x = 2.
Statement 1: f has local maximum at x = –1 and at x = 2.
Statement 2:Â 
Statement 1 is false, statement 2 is true
Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (-3, 1) and has eccentricity 
 is
3x2 + 5y2 -32 = 0
5x2 + 3y2 - 48 = 0
3x2 + 5y2 - 15 = 0Â
3x2 + 5y2 - 15 = 0Â
The two circles x2 + y2 = ax and x2 + y2 = c2(c > 0) touch each other if
2|a| = c
|a| = c
a = 2c
a = 2c
If two tangents drawn from a point P to the parabola y2= 4x are at right angles, then the locus of P is
X = 1
2x +1 = 0
x = -1
x = -1
The radius of a circle, having minimum area, which touches the curve y = 4 – x2 and the lines, y = |x| is
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