Applications of Derivatives - Maharashtra Board STD 12 Science Maths Questions - Vidyadip

Question types

Applications of Derivatives question types

40 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

40

Questions

4

Question groups

5

Question types

MCQ

Solve the Following Question.(2 Marks)

Solve the Following Question.(3 Marks)

Solve the Following Question.(4 Marks)

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 1MCQ2 Marks

If $f(x)=x^3-6 x^2+9 x+18$, then $f(x)$ is strictly decreasing in $.........$

A
$(-\infty, 1)$
B
$[3, \infty)$
C
$(-\infty, 1] \cup[3, \infty)$
✓
$(1,3)$

Answer: D.

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Q 2MCQ2 Marks

The maximum value of the function $f(x)=\frac{\log x}{x}$ is $....... .$

A
$e$
✓
$\frac{1}{e}$
C
$e^2$
D
$\frac{1}{e^2}$

Answer: B.

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Q 3MCQ2 Marks

The function $f(x)=x^x$ is minimum at $x=$ ______

A
$e$
B
$-e$
C
$\frac{1}{e}$
D
$-\frac{1}{e}$

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Q 4MCQ2 Marks

The equation of tangent to the curve $y=3 x^2-x+1$ at $P (1,3)$ is $.......$

A
$y=5x+2$
✓
$y=5x-2$
C
$y=1/5x+2$
D
$y=1/5x-2$

Answer: B.

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Q 5MCQ2 Marks

The equation of tangent to the curve $y=x^2+4 x+1$ at $(-1,-2)$ is .....

A
$2 x-y=0$
B
$2 x+y-5=0$
C
$2 x-y-1=0$
D
$x+y-1=0$

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Q 6Solve the Following Question.(2 Marks)2 Marks

Show that function $f(x)=\tan x$ is increasing in $\left(0, \frac{\pi}{2}\right)$

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Q 7Solve the Following Question.(2 Marks)2 Marks

Find the equation of tangent to the curve $y=2 x^3-x^2+2$ at $\left(\frac{1}{2}, 2\right)$

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Q 8Solve the Following Question.(2 Marks)2 Marks

Test whether the function, $f(x)=x-\frac{1}{x}, x \in R, x \neq 0$, is increasing or decreasing.

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Q 9Solve the Following Question.(2 Marks)2 Marks

The displacement ' $s$ ' of a moving particle at time ' $t$ ' is given by $s=5+20 t-2 t^2$. Find its acceleration when the velocity is zero.

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Q 10Solve the Following Question.(2 Marks)2 Marks

Verify Rolle's theorem for the function $f(x)=x^2-5 x+9$ on $[1,4]$

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Q 11Solve the Following Question.(3 Marks)3 Marks

If $f^{\prime}(x)=k(\cos x-\sin x), f^{\ \prime}(0)=3$ and $f\left(\frac{\pi}{2}\right)=15$, find $f(x)$

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Q 12Solve the Following Question.(3 Marks)3 Marks

Find the equation of tangent to the curve $y=3 x^2-x+1$ at $P (1,3)$

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Q 13Solve the Following Question.(3 Marks)3 Marks

Find the approximate value of $\tan ^{-1}(1.001)$

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Q 14Solve the Following Question.(3 Marks)3 Marks

A wire of length 36 meters is bent to form a rectangle. Find its dimensions if the area of the rectangle is maximum.

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Q 15Solve the Following Question.(3 Marks)3 Marks

Find the approximate value of $e ^{1.005}$; given $e=2.7183$.

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Q 16Solve the Following Question.(4 Marks)4 Marks

Find the maximum and minimum values of the function $f(x)=x^3-9 x^2+24 x$

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Q 17Solve the Following Question.(4 Marks)4 Marks

Find the approximate value of $\cos \left(89^{\circ}, 30^{\prime}\right)$. [Given is : $1^{\circ}=0.0175^{\circ}c$ ]

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Q 18Solve the Following Question.(4 Marks)4 Marks

A rectangle has area $50 cm ^2$. Find its dimensions when its perimeter is the least.

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Q 19Solve the Following Question.(4 Marks)4 Marks

Verify Lagrange's mean value theorem for the function $f(x)=x+\frac{1}{x}, x \in[1,3]$

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Q 20Solve the Following Question.(4 Marks)4 Marks

A point source of light is hung 30 feet directly above a straight horizontal path on which a man of 6 feet in height is walking. How fast will the man's shadow lengthen and how fast will the tip of shadow move when he is walking away from the light at the rate of $100 ft / min$.

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