Application of Derivatives PYQs - Last 5 Years

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Practice 227 MHT CET Mathematics questions from Application of Derivatives. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 5 Years Application of Derivatives Questions

Showing 27 of 227 filtered questions.

1Application Of Derivatives

A ladder, 5 meters long, rests against a vertical wall. If its top slides downwards at the rate of \(10 \mathrm{~cm} / \mathrm{s}\), then the angle between the ladder and the floor is decreasing at the rate of __________ radians/second when...

2Application Of Derivatives

If the curves \(y^2=6 x\) and \(9 x^2+b y^2=16\) intersect each other at right angle, then value of '\(b\)' is

3Application Of Derivatives

The equation of the normal to the curve \(3 x^2-y^2=8\), which is parallel to the line \(x+3 y=10\), is

4Application Of Derivatives

A poster is to be printed on a rectangular sheet of paper of area \(18 \mathrm{~m}^2\). The margins at the top and bottom of \(75 \mathrm{~cm}\) each and at the sides \(50 \mathrm{~cm}\) each are to be left. Then the dimensions i.e. height ...

5Application Of Derivatives

If \(\mathrm{f}(x)=x \mathrm{e}^{x(1-x)}, x \in \mathrm{R}\), then \(\mathrm{f}(x)\) is

6Application Of Derivatives

Value of \(c\) satisfying the conditions and conclusions of Rolle's theorem for the function \(\mathrm{f}(x)=x \sqrt{x+6}, x \in[-6,0]\) is

7Application Of Derivatives

At present a firm is manufacturing 1000 items. It is estimated that the rate of change of production \(\mathrm{P}\) w.r.t. additional number of worker \(x\) is given by \(\frac{\mathrm{dp}}{\mathrm{d} x}=100-12 \sqrt{x}\).

If the firm empl...

8Application Of Derivatives

The equation of the tangent to the curve \(y=\sqrt{9-2 x^2}\), at the point where the ordinate and abscissa are equal, is

9Application Of Derivatives

\(A\) rod \(A B, 13\) feet long moves with its ends \(A\) and \(B\) on two perpendicular lines \(O X\) and \(O Y\) respectively. When \(A\) is 5 feet from \(O\), it is moving away at the rate of \(3 \mathrm{feet} / \mathrm{sec}\). At this i...

10Application Of Derivatives

If \(a\) and \(b\) are positive number such that \(a>b\), then the minimum value of \(a \sec \theta-b \tan \theta\left(0 < \theta < \frac{\pi}{2}\right)\) is

11Application Of Derivatives

If the function \(f\) is given by \(f(x)=x^3-3(a-2) x^2+3 a x+7\), for some \(\mathrm{a} \in \mathbb{R}\), is increasing in \((0,1]\) and decreasing in \([1,5)\), then a root of the equation \(\frac{\mathrm{f}(x)-14}{(x-1)^2}=0(x \neq 1)\) ...

12Application Of Derivatives

A kite is \(120 \mathrm{~m}\) high and \(130 \mathrm{~m}\) of string is out. If the kite is moving away horizontally at the rate of \(39 \mathrm{~m} / \mathrm{sec}\), then the rate at which the string is being out, is

13Application Of Derivatives

If the line \(a x+b y+c=0\) is a normal to the curve \(x y=1\), then

14Application Of Derivatives

A ladder of length \(17 \mathrm{~m}\) rests with one end against a vertical wall and the other on the level ground. If the lower end slips away at the rate of \(1 \mathrm{~m} / \mathrm{sec}\)., then when it is \(8 \mathrm{~m}\) away from th...

15Application Of Derivatives

A square plate is contracting at the uniform rate \(4 \mathrm{~cm}^2 / \mathrm{sec}\), then the rate at which the perimeter is decreasing, when side of the square is \(20 \mathrm{~cm}\), is

16Application Of Derivatives

An open metallic tank is to be constructed, with a square base and vertical sides, having volume 500 cubic meter. Then the dimensions of the tank, for minimum area of the sheet metal used in its construction, are

17Application Of Derivatives

In a certain culture of bacteria, the rate of increase is proportional to the number of bacteria present at that instant. It is found that there are 10,000 bacteria at the end of 3 hours and 40,000 bacteria at the end of 5 hours, then the n...

18Application Of Derivatives

The value of \(\alpha\), so that the volume of parallelopiped formed by \(\hat{i}+\alpha \hat{j}+\hat{k}, \hat{j}+\alpha \hat{k}\) and \(\alpha \hat{\mathrm{i}}+\hat{\mathrm{k}}\) becomes minimum, is

19Application Of Derivatives

If the surface area of a spherical balloon of radius \(6 \mathrm{~cm}\) is increasing at the rate \(2 \mathrm{~cm}^2 / \mathrm{sec}\), then the rate of increase in its volume in \(\mathrm{cm}^3 / \mathrm{sec}\) is

20Application Of Derivatives

The displacement '\(\mathrm{S}\)' of a moving particle at a time \(t\) is given by \(S=5+\frac{48}{t}+t^3\). Then its acceleration when the velocity is zero, is

21Application Of Derivatives

Let \(\mathrm{f}(x)=\mathrm{e}^x-x\) and \(\mathrm{g}(x)=x^2-x, \forall x \in \mathrm{R}\), then the set of all \(x \in \mathrm{R}\), where the function \(\mathrm{h}(x)=(\mathrm{fog})(x)\) is increasing is

22Application Of Derivatives

The value of \(\mathrm{c}\) for the function \(\mathrm{f}(x)=\log x\) on [\(1\), e] if LMVT can be applied, is

23Application Of Derivatives

A spherical iron ball of \(10 \mathrm{~cm}\) radius is coated with a layer of ice of uniform thickness that melts at the rate of \(50 \mathrm{~cm}^3 / \mathrm{min}\). If the thickness of ice is \(5 \mathrm{~cm}\), then the rate at which the...

24Application Of Derivatives

If the function \(f(x)=x^3-3(a-2) x^2+3 a x+7\), for some \(a \in I R\) is increasing in \((0,1]\) and decreasing in \([1,5)\), then a root of the equation \(\frac{f(x)-14}{(x-1)^2}=0(x \neq 1)\) is

25Application Of Derivatives

A firm is manufacturing 2000 items. It is estimated that the rate of change of production \(P\) with respect to additional number of workers \(x\) is given by \(\frac{\mathrm{d} P}{\mathrm{~d} x}=100-12 \sqrt{x}\). If the firm employs 25 mo...

26Application Of Derivatives

If \(y=\cos \left(\sin x^2\right)\), then \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) at \(x=\sqrt{\frac{\pi}{2}}\) is

27Application Of Derivatives

If the normal to the curve \(y=f(x)\) at the point \((3,4)\) makes an angle \(\left(\frac{3 \pi}{4}\right)^c\) with positive \(X\)-axis, then \(f^{\prime}(3)\) is equal to