Application of Derivatives Test

Result

Application of Derivatives Test - 68

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Weekly Quiz Competition

Question 1
1 / -0

The angle formed bt the positive y-axis and the tangent to $$y = x^{2}+4x-17$$ at $$(5/2, -3/4)$$ is

A
$$\tan ^{-1}(9)$$

B
$$\dfrac{\pi }{2}\tan ^{-1}(9)$$

C
$$\dfrac{\pi }{2}\tan ^{-1}(9)$$

D
None of these

Solution
Question 2
1 / -0

The abscissa of a point on the curve $$xy = (a+y)^{2}$$, the normal which cuts off numerically equal intercept from the coordinate axes, is

A
$$-\dfrac{a}{\sqrt{2}}$$

B
$$\sqrt{2a}$$

C
$$\dfrac{a}{\sqrt{2}}$$

D
$$-\sqrt{2a}$$

Solution
Question 3
1 / -0

The co-ordinates of the point (s) on the graph of the function $$f(x)= \dfrac{x^{3}}{3} - \dfrac{5x^{2}}{2} + 7x - 4$$, where the tangent drawn cuts off intercept from the co-ordinate axes which

A
(2, 8/3)

B
(3, 7/2)

C
(1, 5/6)

D
None of these

Solution
Question 4
1 / -0

The triangle by the tangent to the curve $$f(x) = x^{2} bx -b$$ at the point (1, 1) and the co-ordinate axes lies in the first quadrant. If its area is 2, then the value of b is

A
-1

B
3

C
-3

D
1

Solution
Question 5
1 / -0

If the normal to the curve y = f(x) at the point (3, 4) makes an angel $$\dfrac{3\pi }{4}$$ with the positive x-axis, then f'(3) is equal to

A
-1

B
$$-\dfrac{3 }{4}$$

C
$$\dfrac{4}{5}$$

D
1

Solution
Question 6
1 / -0

The curve possessing the property text the intercept made by the tangent at any point of the curve on the $$y-$$ axis is equal to square of the abscissa of the point of tangency, is given by

A
$$y^{2}=x+C$$

B
$$y=2x^{2}+C$$

C
$$y=-x^{2}+cx$$

D
$$None\ of\ these$$

Solution
Question 7
1 / -0

Let $$f(x, y)$$ be a curve in the $$x-y$$ plane having the property that distance from the origin of any tangent to the curve is equal to distance of point of contact from the $$y-$$ axis. Of $$f(1, 2)=0$$, then all such possible curves are

A
$$x^2+y^2=5x$$

B
$$x^2-y^2=5x$$

C
$$x^2y^2=5x$$

D
$$All\ of\ these$$

Solution
Question 8
1 / -0

The angle between the tangents at ant point P and the line joining P to the original, where P is a point on the curve in $$(x^{2}+y^{2})=c \tan ^{-1}\dfrac{y}{x},c$$ is a constnt, is

A
independent of x

B
independent of y

C
independent of x but dependent on y

D
independent of y but dependent on x

Solution
Question 9
1 / -0

Consider a curve $$y=f(x)$$ in $$xy$$- plane. The curve passes through $$(0,0)$$ and has the property that a segment of tangent drawn at any point $$P(x, f(x))$$ and the line $$y=3$$ gets bisected by the line $$x+y=1$$, then the equation of the curve is

A
$$y^2=9(x-y)$$

B
$$(y-3)^2=9(1-x-y)$$

C
$$(y+3)^2=9(1-x-y)$$

D
$$(y-3)^2-9(1+x+y)$$

Solution
Question 10
1 / -0

The percentage error in the $$11^{th}$$ root of the number $$28$$ is approximately _______ times the percentage error in $$28$$.

A
$$11$$

B
$$28$$

C
$$\dfrac{1}{28}$$

D
$$\dfrac{1}{11}$$

Solution

Given: To find percentage error in $$11th$$ root $$28$$ with respect to $$28$$
$$\therefore$$ As we know that if number $$=x^n$$
then $$\%$$ error in $$x^n$$=n times the ($$\%$$ error in $$x$$)
$$\therefore$$ We can say that percentage error of nth root of any number is approximately $$1/n$$ times percentage error in number.
$$\therefore 11th$$ root of $$28=28^{1/11}$$
here $$x=28,n=1/11$$
hence , $$1/11$$