JEE Questions for Maths Applications Of Derivatives Quiz 12 - MCQExams.com


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  • –1
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  • 0.5
  • 1

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  • a = b and c ≠ b
  • a = c and a ≠ b
  • a ≠ b and c ≠ d
  • a = b = c

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  • None of the above

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  • 1
  • 2)
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  • Does not exist
  • None of these

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  • Maths-Applications of Derivatives-10353.png
  • Constant

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  • n
  • n –1
  • n!
  • (n –1)!

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  • 0
  • 1
  • –1

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The volume of a spherical balloon is increasing at the rate of 40 cubic centimetre per minute. The rate of change of the surface of the balloon at the instant when its radius is 8 centimetre, is

  • Maths-Applications of Derivatives-10366.png
  • 5 sq. cm/min
  • 10 sq.cm/min
  • 20 sq. cm/min
The radius of the cylinder of maximum volume, which can be inscribed in a sphere of radius R is

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The distance travelled s (in metre) by a particle in t seconds is given by, s = t3 + 2t2 + t. The speed of the particle after 1 second will be
  • 8 cm/sec
  • 6 cm/sec`
  • 2 cm/sec
  • None of these
If y = 4x – 5 is tangent to the curve y2 = px3 + q at (2, 3), then
  • p = 2, q = –7
  • p = – 2, q = 7
  • p = –2, q = –7
  • p = 2, q = 7

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The value of a so that the sum of the squares of the roots of the equation x2 – (a – 2)x – a + 1 = 0 assume the least value, is
  • 2
  • 1
  • 3
  • 0
N characters of information are held on magnetic tape, is batches, of x characters each; the batch processing time is α + β x2 seconds; α and β are constants. The optimal value of x for fast processing is

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  • 0
  • 2)
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  • 3
  • 1
  • 2

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In [0, 1] Lagrange’s mean value theorem is NOT applicable to

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OA and OB are two roads enclosing an angle of 120o X and Y start from ‘O’ at the same time. X travels along OA with a speed 4 km/hour and Y travels along OB with a speed 3 km/hour. The rate at which the shortest distance between X and Y is increasing after 1 hour is
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  • 2)
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  • 3 and 4

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  • 2)
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  • 2 and 3

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  • 0
  • 1
  • 2
  • 3
  • 3 and 4

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  • h is increasing whenever f is increasing
  • h is increasing whenever f is decreasing
  • h is decreasing whenever f is decreasing
  • Nothing can be said in general
  • 1 and 3
Which of the following curves cut the parabola y2 = 4ax at right angles
  • x2 + y2 = a2
  • y = e–x/2a
  • y = ax
  • x2 = 4ay
  • 2 and 4

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  • ALL

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  • 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 false
  • Statement 1 is false, statement 2 is true

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It is a continuous function f defined on the real line R, assume positive and negative values in R then the equation f(x) = 0 has root in R. For example, if it is known that a continuous function f on R is positive at some point and its minimum value is negative then the equation f(x) = 0 has a root in R. Consider f(x) = kex – x for all real x where k is a real constant.
The line y = x meets y = kex for k ≤ 0 at
  • No point
  • One point
  • Two points
  • More than two points
It is a continuous function f defined on the real line R, assume positive and negative values in R then the equation f(x) = 0 has root in R. For example, if it is known that a continuous function f on R is positive at some point and its minimum value is negative then the equation f(x) = 0 has a root in R. Consider f(x) = kex – x for all real x where k is a real constant.
The positive value of k for which kex – x = 0 has only one root is

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  • 1
  • e

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It is a continuous function f defined on the real line R, assume positive and negative values in R then the equation f(x) = 0 has root in R. For example, if it is known that a continuous function f on R is positive at some point and its minimum value is negative then the equation f(x) = 0 has a root in R. Consider f(x) = kex – x for all real x where k is a real constant.
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  • Maths-Applications of Derivatives-10489.png
  • 2)
    Maths-Applications of Derivatives-10490.png

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  • Maths-Applications of Derivatives-10492.png

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  • g is increasing on (1, ∞)
  • g is decreasing on (1, ∞)
  • g is increasing on (1,and decreasing on (2, ∞)
  • g is decreasing on (1,and increasing on (2, ∞)

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  • Both P and Q are true
  • P is true and Q is false
  • P is false and Q is true
  • Both P and Q are false
This section contains some integer type questions. The answers to each of the questions is a single – digit integer, ranging from 0 to 9
The minimum value of the sum of real numbers a–5, a–4, 3a–3,1,a8 and a10, where a > 0 is
  • 5
  • 6
  • 8
  • 7
This section contains some integer type questions. The answers to each of the questions is a single – digit integer, ranging from 0 to 9
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  • 2
  • 3
  • 1
  • 8
This section contains some integer type questions. The answers to each of the questions is a single – digit integer, ranging from 0 to 9
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  • 2
  • 3
  • 4
  • 1
This section contains some integer type questions. The answers to each of the questions is a single – digit integer, ranging from 0 to 9
Let p(x) be real polynomial of least degree which has a local maximum at x = 1 and a local minimum at x = 3. If p(= 6 and p(= 2, then p’(is
  • 9
  • 5
  • 13
  • 4

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  • 2)
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  • None of these

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