Tangents and its Equations Test 57

Result

Tangents and its Equations Test 57

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
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 2
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 3
1 / -0

The equation of the curve $$y = be^{-x/a}$$ at the point where it crosses the y-axis is

A
$$\dfrac{x}{a}-\dfrac{y}{b}=1$$

B
$$ax = by = 1$$

C
$$ax-by=1$$

D
$$\dfrac{x}{a}+\dfrac{y}{b}=1$$

Solution
Question 4
1 / -0

A curve is represented by the equations $$x=sec^{2}t$$ and $$y=\cot t,$$ where t is a parameter. If the tangent at the point P on the curve, where $$t=\pi /4$$, meets the curve again at the point Q, then $$\left | PQ \right |$$ is equal to

A
$$\dfrac{5\sqrt{3}}{2}$$

B
$$\dfrac{5\sqrt{5}}{2}$$

C
$$\dfrac{2\sqrt{5}}{3}$$

D
$$\dfrac{3\sqrt{5}}{2}$$

Solution
Question 5
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 6
1 / -0

Let f be a continuous, differetiable and bijective function. If the tangent to y= f (x) at x = a is also the normal to y = f (x) at x = b then there exists at least one $$c \epsilon (a, b)$$ such that

A
f'(c) = 0

B
$$f (c)> 0$$

C
$$f (c)< 0$$

D
None of these

Solution
Question 7
1 / -0

Given the curves $$y=f(x)$$ passing through the point $$(0, 1)$$ and $$y=\displaystyle \int_{-\infty}^{x}{f(t)}$$ passing through the point $$\left( 0, \dfrac{1}{2}\right).$$ The tangents drawn to both the curves at the points with equal abscissae intersect on the $$x$$- axis. Then the curve $$y=f(x)$$ is

A
$$f(x)=x^2+x+1$$

B
$$f(x)=\dfrac{x^2}{e^x}$$

C
$$f(x)=e^{2x}$$

D
$$f(x)=x-e^x$$
Question 8
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 9
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 10
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