CBSE Questions for Class 11 Commerce Applied Mathematics Tangents And Its Equations Quiz 2 - MCQExams.com

The equation of the tangent to the curve $$\displaystyle 6y=7-x^{3}$$ at point $$(1, 1)$$ is
  • $$2x + y = 3$$
  • $$x + 2y = 3$$
  • $$x + y = 1$$
  • $$x + y + 2 = 0$$
The slope of the curve $$\displaystyle y=\sin x+\cos ^{2}x $$ is zero at the point where -
  • $$\displaystyle x=\frac{\pi }{4}$$
  • $$\displaystyle x=\frac{\pi }{2}$$
  • $$\displaystyle x=\pi$$
  • No where
The equation of the tangent to the curve $$\displaystyle y=\cos x$$ at $$\displaystyle x=\dfrac {\pi }3$$ is -
  • $$\displaystyle 3x-2\sqrt{3}y=\pi +\sqrt{3}$$
  • $$\displaystyle 3x+2\sqrt{3}y=\pi +\sqrt{3}$$
  • $$\displaystyle 3x+2\sqrt{3}y=\pi -\sqrt{3}$$
  • None of these
The slope of the tangent to the curve $$\displaystyle y=\sin x$$ at point $$(0, 0)$$ is
  • $$1$$
  • $$0$$
  • $$\displaystyle \infty $$
  • None of these
If tangent at a point of the curve $$y = f(x)$$ is perpendicular to $$2x - 3y = 5$$ then at that point $$\displaystyle \dfrac{dy}{dx}$$ equals
  • $$\dfrac 2  3$$
  • $$-\dfrac 2  3$$
  • $$\dfrac 3  2$$
  • $$-\dfrac 3  2$$
The inclination of the tangent w.r.t. $$x$$ - axis to the curve $$\displaystyle x^{2}+2y=8x-7$$ at the point $$x = 5$$ is
  • $$\displaystyle\dfrac{ \pi }4$$
  • $$\displaystyle\dfrac{ \pi }3$$
  • $$\displaystyle\dfrac{3 \pi }4$$
  • $$\displaystyle\dfrac{ \pi }2$$
The equation of the tangent to the curve $$\displaystyle y=x^{2}+1$$ at point $$(1,2)$$ is
  • $$y = 2x$$
  • $$x + 2y = 5$$
  • $$2x + y = 4$$
  • None of these
The point on the curve $$\displaystyle y=x^{2}-3x+2$$ at which the tangent is perpendicular to the line $$y = x$$ is -
  • $$(0, 2)$$
  • $$(1, 0)$$
  • $$(-1, 6)$$
  • $$(2, -2)$$
The equation of normal to the curve $$\displaystyle y=x^{3}-2x^{2}+4$$ at the point $$x = 2$$ is-
  • $$x+ 4y = 0$$
  • $$4x - y = 0$$
  • $$x + 4y = 18$$
  • $$4x - y = 18$$
The sum of the intercepts made by a tangent to the  curve $$\displaystyle \sqrt{x}+\sqrt{y}=4 $$ at point $$(4, 4)$$ on coordinate axes is -
  • $$\displaystyle 4\sqrt{2}$$
  • $$\displaystyle 6\sqrt{3}$$
  • $$\displaystyle 8\sqrt{2}$$
  • $$\displaystyle \sqrt{256}$$
The equation of normal to the curve $$\displaystyle y=\tan x $$ at the point $$(0, 0)$$ is -
  • $$x + y = 0$$
  • $$x - y = 0$$
  • $$x + 2y = 0$$
  • None of these
The equation of normal to the curve $$\displaystyle x^{\tfrac 23}$$ + $$\displaystyle y^{\tfrac 23}$$ = $$\displaystyle a^{\tfrac 23}$$ at the point $$(a, 0)$$ is -
  • $$x = a$$
  • $$x = -a$$
  • $$y = a$$
  • $$y = -a$$
At what point the tangent to the curve $$\displaystyle \sqrt{x}+\sqrt{y}=\sqrt{a}$$ is perpendicular to the $$x$$ - axis
  • $$(0, 0)$$
  • $$(a, a)$$
  • $$(a, 0)$$
  • $$(0, a)$$
The equation of the normal to the curve $$\displaystyle 2y=3-x^{2}$$ at $$(1, 1)$$ is -
  • $$x + y = 0$$
  • $$x + y + 1 = 0$$
  • $$x - y + 1 = 0$$
  • $$x - y = 0$$
The normal at the point $$(1,1)$$ on the curve $$2y+{x}^{2}=3$$ is
  • $$x+y=0$$
  • $$x-y=0$$
  • $$x+y+1=0$$
  • $$x-y=1$$
  • answer required
The line $$y = x + 1$$ is a tangent to the curve $$ y^2 = 4x$$ at the point.
  • $$(1, 2)$$
  • $$(2, 1)$$
  • $$(1, 4)$$
  • $$( 2, 2)$$
If a tangent to the curve $$\displaystyle y=6x-{ x }^{ 2 }$$ is parallel to the line $$\displaystyle 4x-2y-1=0$$, then the point of tangency on the curve is:
  • (2, 8)
  • (8, 2)
  • (6, 1)
  • (4, 2)
The slope of the tangent to the curve $$y = \int_{0}^{x} \dfrac {dt}{1 + t^{3}}$$ at the point where $$x = 1$$ is
  • $$\dfrac {1}{4}$$
  • $$\dfrac {1}{3}$$
  • $$\dfrac {1}{2}$$
  • $$1$$
The equation of the tangent to the curve $$y=4xe^x$$ at $$\left(-1, \displaystyle\frac{-4}{e}\right)$$ is
  • $$y=-1$$
  • $$y=-\displaystyle\frac{4}{e}$$
  • $$x=-1$$
  • $$x=\displaystyle\frac{-4}{e}$$
The equation of the normal to the curve $${ y }^{ 4 }=a{ x }^{ 3 }$$ at $$\left( a,a \right) $$ is
  • $$x+2y=3a$$
  • $$3x-4y+a=0$$
  • $$4x+3y=7a$$
  • $$4x-3y=0$$
The slope of the tangent to the curve $$y=\displaystyle\int_{0}^{x}\dfrac{dt}{1+t^3}$$ at the point where x=1 is 
  • $$\dfrac{1}{4}$$
  • $$\dfrac{1}{3}$$
  • $$\dfrac{1}{2}$$
  • 1
Consider the curve $$y = e^{2x}$$.What is the slope of the tangent to the curve at (0, 1) ?
  • 0
  • 1
  • 2
  • 4
The gradient of the tangent line at the point $$(a cos \alpha, a sin \alpha)$$ to the circle $$x^2 + y^2 = a^2$$, is
  • $$tan (\pi - \alpha)$$
  • $$ tan \alpha$$
  • $$ cot \alpha$$
  • - $$ cot \alpha$$
If normal is drawn to $${ y }^{ 2 }=12x$$ making an angle $${45}^{o}$$ with the axis then the foot of the normal is
  • $$\left( 3,8 \right) $$
  • $$\left( 3,-6 \right) $$
  • $$\left( 12,-12 \right) $$
  • $$\left( 8,-8 \right) $$
Which one of the following be the gradient of the hyperbola $$xy=1$$ at the point $$\left(t,\dfrac{1}{t}\right)$$
  • $$-\dfrac{1}{t}$$
  • $$-\dfrac{1}{t^2}$$
  • $$\dfrac{1}{t}$$
  • $$-\dfrac{2}{t^2}$$
If the product of the slope of tangent to curve at $$(x,y)$$ and its y-co-ordinate is equal to the x-co-ordinate of the point, then it represent.
  • circle
  • parabola
  • ellipse
  • rectangular hyperbola
The slope of the tangent to the curve $$xy+ax-by=0$$ at the point $$(1,1)$$ is $$2$$, then value of $$a$$ and $$b$$ are respectively:
  • $$1,2$$
  • $$2,1$$
  • $$3,5$$
  • None of these
The Equation of the tangent to the curves $${y^2} = 8x$$ and $$xy = -1$$ is
  • $$3y=9x+2$$
  • $$y=2x+1$$
  • $$2y=x+1$$
  • $$y=x+2$$
The values of $$x$$ for which the tangents to the curves $$y=x\cos{x},y=\cfrac{\sin{x}}{x}$$ are parallel to the axis of $$x$$ are roots of  (respectively)
  • $$\sin{x}=x,\tan{x}=x$$
  • $$\cot{x}=x,\sec{x}=x$$
  • $$\cot{x}=x,\tan{x}=x$$
  • $$\tan{x}=x,\cot{x}=x$$
A curve with equation of the form $$y=a{x}^{4}+b{x}^{3}+cx+d$$ has zero gradient at the point $$(0,1)$$ and also touches the x-axis at the point $$(-1,0)$$ then
  • $$a=3$$
  • $$b=4$$
  • $$c+d=1$$
  • for $$x< -1$$ the curve has a negative gradient
The equation of the tangent to the curve $$y=2\sin{x}+\sin{2x}$$ at $$x=\cfrac{\pi}{3}$$ on it is
  • $$y-3=0$$
  • $$y+\sqrt{3}=0$$
  • $$2y-3=0$$
  • $$2y-3\sqrt{3}=0$$
The coordinates of the feet of the normals drawn from the point (14, 7) to the curve $$y^2 - 16 x - 8y = 0$$ are
  • (0, 0)
  • (3, 4)
  • (3, -4)
  • (8, 16)
The slope of the tangent to the curve $$y=sinx$$ where it crosses the $$x-axis$$ is 
  • $$1$$
  • $$-1$$
  • $$ \pm 1$$
  • $$ \pm 2$$
The equation of normal to the curve $$y=\left| { x }^{ 2 }-\left| x \right|  \right| $$ at $$x=-2$$ is
  • $$3y=2x+10$$
  • $$3y=x+8$$
  • $$2y=x+6$$
  • $$2y=3x+10$$
The equation of the normal at $$t=\dfrac{\pi}{2}$$ to the curve $$x=2\sin t, y=2\cos t$$ is?
  • $$x=0$$
  • $$y=0$$
  • $$y=2x+3$$
  • $$y=3$$
The intercept on x-axis made by tangent to the curve, $$\displaystyle y=\int _{ 0 }^{ x }{ \left| t \right|  } dt,x\in R$$, which are parallel to the line $$y=2x$$, are equal to
  • $$\pm 1$$
  • $$\pm 2$$
  • $$\pm 3$$
  • $$\pm 4$$
The Point (s) on the cure $${ y }^{ 3 }+{ 3x }^{ 2 }=12y$$ where the tangent is vertical (parallel to y-axis), is/are.
  • $$\left[ \pm \dfrac { 4 }{ \sqrt { 3 } } ,-2 \right] $$
  • $$\left( \pm \dfrac { \sqrt { 11 } }{ 3 } ,1 \right) $$
  • $$(0,0)$$
  • $$\left( \pm \dfrac { 4 }{ \sqrt { 3 } } ,2 \right) $$
Tangent drawn to $$y=ax^2+bx+c$$ at$$(5,4)$$ is parallel to $$x-axis.$$ If $$a$$ $$\epsilon $$ $$[2,4]$$. Then maximum value of c.
  • $$54$$
  • $$56$$
  • $$104$$
  • $$106$$
The angle made by the tangent line at (1, 3) on the curve $$y=4x-{ x }^{ 2 }$$ with $$\overset { - }{ OX } $$ is 
  • $${ tan }^{ -1 }(2)$$
  • $${ tan }^{ -1 }(1/3)$$
  • $${ tan }^{ -1 }(3)$$
  • $$\pi /4$$
The equation of normal to the curve $$2y=3-{ x }^{ 2 }$$ at the point $$\left(1,1\right)$$
  • $$x+y+1=0$$
  • $$x+y=0$$
  • $$x-y+1=0$$
  • $$x-y=0$$
equation of tangent at $$(0,0)$$ for the equation $$y^2=16x$$
  • $$y=0 $$
  • $$x=0$$
  • $$x+y=0$$
  • $$x-y=0$$
The area of triangle formed by tangent and normal at point $$(\sqrt{3}, 1)$$ of the curve $$x^2+y^2=4$$ and x-axis is?
  • $$\dfrac{4}{\sqrt{3}}$$
  • $$\dfrac{2}{\sqrt{3}}$$
  • $$\dfrac{8}{\sqrt{3}}$$
  • $$\dfrac{5}{\sqrt{3}}$$
The tangent to the curve $$y=e^{kx}$$ at a point (0, 1) meets the x-axis at (q, 0) where $$a \epsilon  \left [ -2,-1 \right ]$$ then $$k \epsilon $$ 
  • [-1/2,0]
  • [-1,-1/2]
  • [0,1]
  • [1/2, 1]
A curve $$y=me^{mx}$$ where $$m > 0$$ intersects y-axis at a point $$P$$.
What is the equation of tangent to the curve at $$P$$ ?
  • $$y=mx+m$$
  • $$y=-mx+2m$$
  • $$y=m^2x+2m$$
  • $$y=m^2x+m$$
If the slope of the tangent to the curve $$xy+ ax+ by=0$$ at the point $$(1, 1) $$ on it is $$2$$, then values of $$a$$ and $$b$$ are
  • $$1, 2$$
  • $$1, -2$$
  • $$-1, 2$$
  • $$-1, -2$$
If the slope of the tangent to the curve $$y = x^{3}$$ at a point on it is equal to the ordinate of the point then the point is
  • $$(27, 3)$$
  • $$(3, 27)$$
  • $$(3, 3)$$
  • $$(1, 1)$$
The area of the triangle formed by the tangent to the curve  $$\displaystyle y=\frac{8}{4+x^{2}}$$ at $$x=2$$ on it and the $$x$$-axis is
  • $$2$$ sq.units
  • $$4$$ sq.units
  • $$8$$ sq.units
  • $$16$$ sq.units
The two curves $$y=x^{2}-1$$ and $$y=8x-x^{2}-9$$ at the point $$(2, 3)$$ have common
  • tangent as $$4x-y-5=0$$
  • tangent as $$x+4y-14=0$$
  • normal as $$4x+y=11$$
  • normal as $$x-4y=10$$
Equation of the tangent to the curve  $$y(x-2)(x-3)-x+7=0$$ at the point where
the curve cuts x-axis is
  • $$x-20y=7$$
  • $$x-20y+7=0$$
  • $$x+20y-7=0$$
  • $$x+20y+7=0$$
P(1, 1) is a point on the parabola  $$y=x^{2}$$ whose vertex is A. The point on the curve at which the tangent drawn is parallel to the chord  $$\overline{AP}$$   is
  • $$(\displaystyle \frac{1}{2}, \frac{1}{4})$$
  • $$(\displaystyle \frac{-1}{2}, \frac{1}{4})$$
  • $$(2, 4)$$
  • $$(4, 2)$$
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