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

The equation of the tangent to the curve 6y=7x3 at point (1,1) is
  • 2x+y=3
  • x+2y=3
  • x+y=1
  • x+y+2=0
The slope of the curve y=sinx+cos2x is zero at the point where -
  • x=π4
  • x=π2
  • x=π
  • No where
The equation of the tangent to the curve y=cosx at x=π3 is -
  • 3x23y=π+3
  • 3x+23y=π+3
  • 3x+23y=π3
  • None of these
The slope of the tangent to the curve y=sinx at point (0,0) is
  • 1
  • 0
  • None of these
If tangent at a point of the curve y=f(x) is perpendicular to 2x3y=5 then at that point dydx equals
  • 23
  • 23
  • 32
  • 32
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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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers