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Applications of Derivatives Maths - Applications of Derivatives

Maharashtra Board - STD 12 - Maths (MSBSHSE - Semi English Medium). 201 questions in this chapter.

Question types

Applications of Derivatives question types

201 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

201
Questions
6
Question groups
5
Question types
Sample Questions

Applications of Derivatives questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ1 Mark
The approximate value of tan (44° 30′), given that 1° = 0.0175, is
  • A
    0.8952
  • B
    0.9528
  • C
    0.9285
  • ✓
    0.9825

Answer: D.

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Q 2MCQ1 Mark
If the tangent at $(1,1)$ on $y^2=x(2-x)^2$ meets the curve again at $P$, then $P$ is
  • A
    $(4, 4)$
  • B
    $(-1, 2)$
  • C
    $(3, 6)$
  • ✓
    $\left(\frac{9}{4}, \frac{3}{8}\right)$

Answer: D.

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Q 3MCQ1 Mark
The equation of the tangent to the curve $y =1-e^{\frac{x}{2}}$ at the point of intersection with $Y$-axisis
  • ✓
    x + 2y = 0
  • B
    2x + y = 0
  • C
    x – y = 2
  • D
    x + y = 2

Answer: A.

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Q 4MCQ1 Mark
The normal to the curve $x^2+2 x y-3 y^2=0$ at $(1,1)$
  • A
    meets the curve again in the second quadrant
  • B
    does not meet the curve again
  • C
    meets the curve again in the third quadrant
  • ✓
    meets the curve again in the fourth quadrant

Answer: D.

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Q 5MCQ1 Mark
If $x=-1$ and $x=2$ are the extreme points of $y=\alpha \log x+\beta x^2+x$, then
  • A
    $\alpha=-6, \beta=\frac{1}{2}$
  • B
    $\alpha=-6, \beta=\frac{-1}{2}$
  • ✓
    $\alpha=2, \beta=\frac{-1}{2}$
  • D
    $\alpha=2, \beta=\frac{1}{2}$

Answer: C.

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Q 19Solve the Following Question.(3 Marks)3 Marks
A water tank in the form of an inverted cone is being emptied at the rate of 2 cubic feet per second. The height of the cone is 8 feet and the radius is 4 feet. Find the rate of change of the water level when the depth is 6 feet.
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Q 29Solve the Following Question.(5 Marks)5 Marks
A rectangular sheet of paper of fixed perimeter with the sides having their lengths in the ratio 8 : 15 converted into an open rectangular box by folding after removing the squares of the equal area from all comers. If the total area of the removed squares is 100, the resulting box has maximum volume. Find the lengths of the rectangular sheet of paper.
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Q 30Solve the Following Question.(5 Marks)5 Marks
A wire of length l is cut into two parts. One part is bent into a circle and the other into a square. Show that the sum of the areas of the circle and the square is the least if the radius of the circle is half of the side of the square.
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