Important Questions of Application of Derivatives Mathematics | Zigya

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11.

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

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12.

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

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13.

The radius of a circle, having minimum area, which touches the curve y = 4 – x2 and the lines, y = |x| is

  • 4 space left parenthesis square root of 2 space plus 1 right parenthesis
  • 2 left parenthesis square root of 2 space plus 1 right parenthesis
  • 2 left parenthesis square root of 2 space minus 1 right parenthesis
  • 2 left parenthesis square root of 2 space minus 1 right parenthesis
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14.

Let y be an implicit function of x defined by x2x – 2xxcoty – 1 = 0. Then y′ (1) equals 

  • -1

  • 1

  • log 2

  • log 2

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15.

Given P(x) = x4+ ax3 + cx + d such that x = 0 is the only real root of P′ (x) = 0. If P(–1) < P(1),then in the interval [–1, 1].

  • P(–1) is the minimum and P(1) is the maximum of P

  • P(–1) is not minimum but P(1) is the maximum of P

  • P(–1) is the minimum but P(1) is not the maximum of P

  • P(–1) is the minimum but P(1) is not the maximum of P

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16.

Suppose the cube x3– px + q has three distinct real roots where p > 0 and q > 0. Then which one of the following holds?

  • The cubic has minima at square root of straight p over 3 end root and maxima at –square root of straight p over 3 end root

  • The cubic has minima at –square root of straight p over 3 end root and maxima atsquare root of straight p over 3 end root

  • The cubic has minima at both square root of straight p over 3 end root and- square root of straight p over 3 end root

  • The cubic has minima at both square root of straight p over 3 end root and- square root of straight p over 3 end root

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17.

The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is 

  • (x – 2)y′2 = 25 – (y – 2)2 

  • (y – 2)y′2 = 25 – (y – 2)2

  • (y – 2)2y′2= 25 – (y – 2)

  • (y – 2)2y′2= 25 – (y – 2)

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18.

The function f(x) = tan-1 (sinx + cosx) is an increasing function in

  • (π/4, π /2)

  • (–π/2, π /4)

  • (0, π /2)

  • (0, π /2)

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19.

If straight x space equals space straight e to the power of straight y plus straight e to the power of straight y plus.... to space infinity end exponent space comma space straight x space greater than thin space 0 comma space then space dy over dx space is

  • x /x+1

  • x-1/x

  • 1/x

  • 1/x

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20.

The normal to the curve x = a(1 + cosθ), y = asinθ at ‘θ’ always passes through the fixed point

  • (a, 0)

  • (0, a)No

  • (0,0)

  • (0,0)

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