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CBSE Questions for Class 11 Commerce Applied Mathematics Tangents And Its Equations Quiz 6 - MCQExams.com

The points of contact of the vertical tangents x=23sinθ, y=3+2cosθ are
  • (2,5),(2,1)
  • (1,3),(5,3)
  • (2,5),(5,3)
  • (1,3),(2,1)
Tangent is drawn to ellipse x227+y2=1 at (33cosθ,sinθ) (where θ(0,π2)). Then the value of θ such that sum of intercepts on axes made by this tangent is least is
  • π3
  • π6
  • π8
  • π4
The tangent to the curve 3xy22x2y=1  at (1,1) meets the curve again at the point
  • (165,120)
  • (165,120)
  • (120,165)
  • (120,165)
The angle at which the curve y=kekx intersects the y -axis is
  • tan1(k2)
  • cot1(k2)
  • sin1(1/1+k4)
  • sec1(1/1+k4)
The lines tangent to the curves y3x2y+5y2x=0 and x4x3y2+5x+2y=0 at the origin intersect at an angle θ equal to
  • π6
  • π4
  • π3
  • π2
Let f(x)=x3+ax+b with ab and suppose the tangent lines to the graph of f at x=a and x=b have the same gradient Then the value of f(1) is equal to
  • 0
  • 1
  • 13
  • 23
A curve with equation of the form y=ax4+bx3+cx+d has zero gradient at the point (0, 1) and also touches the x-axis at the point (-1, 0) then the values of x for which the curve has a negative gradient are
  • x > -1
  • x < 1
  • x < -1
  • 1×1
For the curve represented parametrically by the equations x=2lncott+1 and y=tant+cott
  • normal at t=π4 is parallel to y=axis
  • tangent at t=π4 is parallel to x-axis
  • tangent at t=π4 is parallel to the line y=x
  • normal at t=π4 is parallel to the line y=x
If a variable tangent to the curve x2y=c3 makes intercepts a,b on x and y axis respectively then the value of x2 is
  • 27c3
  • 427c3
  • 274c3
  • 49c3
The coordinates of the point(s) on the graph of the function f(x)=x335x22+7x4 where the tangent drawn cut off intercepts from the coordinate axes which are equal in magnitude but opposite in sign is
  • (2,83)
  • (3,72)
  • (1,56)
  • none
The number of values of c such that the straight line 3x+4y=c touches the curve x42=x+y is
  • 0
  • 1
  • 2
  • 4
Find all the tangents to the curve y=cos(x+y),2π×2π that are parallel to the line x+2y=0
  • x+2y=π2 & x+2y=3π2
  • x+2y=π2 & x+2y=π2
  • x+2y=3π2 & x+2y=3π2
  • x+2y=3π2 & x+2y=3π2
The angle at which the curve y=kekx intersects the y - axis is
  • tan1k2
  • cot1(k2)
  • sin1(11+k4)
  • sec1(1+k4)
The abscissa of the point on the curve xy=a+x the tangent at which cuts off equal intercepts from the co-ordinate axes is (a > 0)
  • a2
  • a2
  • a2
  • a2
Consider the curve f(x)=x1/3 then
  • the equation of tangent at (0, 0) is x = 0
  • the equation of normal at (0, 0) is y = 0
  • normal to the curve does not exist at (0, 0)
  • f(x) and its inverse meet at exactly 3 points
Equation of the line through the point (1/2,2) and tangent to the parabola y=x22+2 and secant to the curve y=4x2 is
  • 2x+2y5=0
  • 2x+2y9=0
  • y2=0
  • none
Equation of a trangent to the curve ycotx=y3tanx at the point where the abscissa is π4 is 
  • 4x+2y=π+2
  • 4x2y=π+2
  • x = 0
  • y = 0
If the curve (xa)n+(yb)n=2 touches the straight line xa+yb=2, then find the value of n.
  • 2
  • 3
  • 4
  • any real number
Find the equation of the normal to the curve y=(1+x)y+sin1(sin2x) at x=0
  • x+y1=0
  • x+y2=0
  • x+y3=0
  • x+y4=0
Find the equation of normal to the curve x2=4y passing through the point (1,2)
  • x+y=3
  • xy=3
  • 2xy=4
  • 2x3y=1
A function is defined parametrically by the equations
x= 2t+t2sin1t   if t0;    0,   otherwise
  and 
y = 1tsint2   if t0;    0,   otherwise
Find the equation of the tangent and normal at the point for t = 0 if they exist
  • Tangent ;2yx=0; Normal: 2x+y=0
  • Tangent ;3yx=0; Normal: 2x+y=0
  • Tangent ;2yx=0; Normal: 3x+y=0
  • Tangent ;3yx=0; Normal: 3x+y=0
The curve \displaystyle y=ax^{3}+bx^{2}+cx+5 touches the x - axis at P(-2, 0) and cuts the y-axis at a point Q, where its gradient is 3. Find a, b, c.
  • \displaystyle a=-\frac{1}{5}, b=1,c=3
  • \displaystyle a=-\frac{1}{4}, b=-1,c=4
  • \displaystyle a=-\frac{1}{4}, b=0,c=3
  • \displaystyle a=-\frac{1}{3}, b=1,c=-3
The slope of the normal to the curve \displaystyle x=a\left ( \theta -\sin \theta  \right ),\: \: y=a\left ( 1-\cos \theta  \right ) at point \displaystyle \theta =\dfrac{\pi }2 is
  • 0
  • 1
  • -1
  • \dfrac 1{\displaystyle \sqrt{2}}
The equation of the normal to the curve \displaystyle y^{2}=4ax at point (a, 2a) is
  • x - y + a = 0
  • x + y - 3a = 0
  • x + 2y + 4a = 0
  • x + y + 4a = 0
The tangent at a point P of a curve meets the y- axis at A and the line parallel to y- axis at A, and the line parallel to y- axis through P meets the x- axis at B. If area of \Delta OAB is constant (O being the origin). Then the curve is
  • cx^2-xy+k=0
  • x^{2}+y^{2}=cx
  • 3x^{2}+4y^{2}=k
  • xy-x^{2}y^{2}+kx=0
A tangent to the hyperbola \displaystyle y=\frac { x+9 }{ x+5 } passing though the origin is
  • x+25y=0
  • 5x+y=0
  • 5x-y=0
  • x-25y=0
asymptotes of the graph
  • \displaystyle x=\frac{3\pi }{2}
  • \displaystyle x=-\frac{\pi }{2}
  • \displaystyle x=\frac{\pi }{2}
  • \displaystyle x=-\frac{3\pi }{2}
Let f be a continuous, differentiable and bijective function. If the tangent to y=f\left( x \right) at x=b, then there exists at least one c\in \left( a,b \right) such that 
  • f'\left( c \right) =0
  • f'\left( c \right) >0
  • f'\left( c \right) <0
  • none of these
The slope of normal to the curve \displaystyle y^{2}=4ax at a point \displaystyle \left ( at^{2},2at \right ) is
  • \dfrac 1  t
  • t
  • -t
  • -\dfrac 1  t
The coordinates of the point P on the graph of the function \displaystyle y=e^-{\left | x \right |}, where area of triangle made by tangent and the coordinate axis has the greatest area, is
  • \displaystyle \left ( 1,\frac{1}{e} \right )
  • \displaystyle \left ( -1,\frac{1}{e} \right )
  • \displaystyle \left ( e,e^{-e} \right )
  • none
On the ellipse, 4x^2\, +\, 9y^2\, =\, 1, the points at which the tangents are parallel to the line 8x = 9y are
  • \left ( \displaystyle \frac{2}{5},\,\frac{1}{5} \right )
  • \left ( -\displaystyle \frac{2}{5},\,\frac{1}{5} \right )
  • \left ( -\displaystyle \frac{2}{5},\,-\frac{1}{5} \right )
  • \left ( \displaystyle \frac{2}{5},\,-\frac{1}{5} \right )
The slope of the tangent to the curve xy + ax - by = 0 at the point (1, 1) is 2 then values of a and b are respectively -
  • 1, 2
  • 2, 1
  • 3, 5
  • None of these
It \displaystyle x=t^{2} and y = 2t then equation of normal at t = 1 is -
  • x + y + 3 = 0
  • x + y + 1 = 0
  • x + y - 1 = 0
  • x + y - 3 = 0
The equation of the tangent to the curve \displaystyle \frac{1}{\sqrt{x}}+\frac{1}{\sqrt{y}}=\frac{2}{\sqrt{a}} at point (a, a) is
  • \displaystyle \frac{a}{\sqrt{x}}+\frac{a}{\sqrt{y}}={2}\sqrt a
  • x + y = 2a
  • \displaystyle \sqrt{x}+\sqrt{y}=2\sqrt{a}
  • None of these
Consider the curved mirror y=f(x) passing through (0, 6) having the property that all light rays emerging from origin, after getting reflected from the mirror becomes parallel to x- axis, then the equation of curve is
  • y^2=4(x-y) or y^2=36(9+x)
  • y^2=4(1-x) or y^2=36(9-x)
  • y^2=4(1+x) or y^2=36(9-x)
  • None\ of\ these
The point where the tangent line to the curve \displaystyle y=e^{2x} at (0, 1) meets x - axis is -
  • (1, 0)
  • (-1, 0)
  • \displaystyle \left ( -\dfrac12,0 \right )
  • None of these
The slope of the tangents to the curve y = (x + 1) (x - 3) at the points where it crosses x - axis are
  • \displaystyle \pm 2
  • \displaystyle \pm 3
  • \displaystyle \pm 4
  • None of these
The equation of tangent at the point \displaystyle \left ( at^{2},at^{3} \right ) on the curve \displaystyle ay^{2}=x^{3} is
  • \displaystyle 3tx-2y=at^{3}
  • \displaystyle tx-3y=at^{3}
  • \displaystyle 3tx+2y=at^{3}
  • None of these
The equation of the normal to the curve  \left (\displaystyle x=at^{2} \right ), \left (y=2at \right ) at 't' point is -
  • \displaystyle ty=x+at^{2}
  • \displaystyle y+tx-2at-at^{3}=0
  • \displaystyle y=tx-2at-at^{3}
  • None of these
The equation of the tangent to the curve is \displaystyle y=2\sin x+\sin 2x at the point \displaystyle x=\dfrac {\pi }3 is -
  • \displaystyle 2y=\sqrt{3}
  • \displaystyle 3y=\sqrt{2}
  • \displaystyle 2y=3\sqrt{3}
  • 2y = 3
The equation of the tangent to the curve \displaystyle \sqrt{x}+\sqrt{y}=\sqrt{a} at the point \displaystyle \left ( x_{1},y_{1} \right ) is -
  • \displaystyle \frac{x}{\sqrt{x_{1}}}+\frac{y}{\sqrt{y_{1}}}=\frac{1}{\sqrt{a}}
  • \displaystyle \frac{x}{\sqrt{x_{1}}}+\frac{y}{\sqrt{y_{1}}}=\sqrt{a}
  • \displaystyle x\sqrt{x_{1}}+y\sqrt{y_{1}}=\sqrt{a}
  • None of these
The coordinates of the point on the curve \displaystyle y=x^{2}+3x+4 the tangent at which passes through the origin are -
  • (-2, 2), (2, 14)
  • (1, -1), (3, 4)
  • (2, 14), (2, 2)
  • (1, 2), (14, 3)
At what point the tangent line to the curve \displaystyle y=\cos \left ( x+y \right ),\left ( -2\pi \leq x\leq 2\pi  \right ) is parallel to x + 2y = 0
  • \displaystyle \left ( \dfrac {\pi }2, 0 \right )
  • \displaystyle \left ( -\dfrac {\pi }2, 0 \right )
  • \displaystyle \left (\dfrac{ 3\pi }2, 0 \right )
  • \displaystyle \left (-\dfrac{ 3\pi }2,\dfrac { \pi }2 \right )
The point at which the tangent to the curve \displaystyle y=x^{3}+5 is perpendicular to the line x + 3y = 2 are
  • (6, 1), (-1, 4)
  • (6, 1) (4, -1)
  • (1, 6), (1, 4)
  • (1, 6), (-1, 4)
A normal  P(x,y) on a curve meets the X-axis at Q and N is the ordinate at P
If NQ=\dfrac {x(1+y^2)}{1+x^2} .
Then the equation of curves passing through (3,1) is
  • 5(1+y^2)=(1+x^2)
  • 5(1+y^2)=5(1+x^2)
  • 5(1+x^2)=(1+y^2)
  • None of these
At what point of the curve \displaystyle y=2x^{2}-x+1 tangent is parallel to y = 3x + 4
  • (0, 1)
  • (1, 2)
  • (-1, 4)
  • (2, 7)
Tangents are drawn from origin to the curve \displaystyle y=\sin x then point of contect lies on -
  • \displaystyle x^{2}=y^{2}
  • \displaystyle x^{2}y^{2}=0
  • \displaystyle x^{2}y^{2}=x^{2}-y^{2}
  • None of these
A tangent to the curve \displaystyle y=x^{2}+3x passes through a point (0, -9) if it is drawn at the point -
  • (-3, 0)
  • (1, 4)
  • (0, 0)
  • (-4, 4)
The equation of the normal to the curve \displaystyle y^{2}=x^{3} at the point whose abscissa is 8 is -
  • \displaystyle x\pm \sqrt{2}y=104
  • \displaystyle x\pm 3\sqrt{2}y=104
  • \displaystyle 3\sqrt{2}x\pm y=104
  • None of these
The normal to the curve \displaystyle \sqrt{x}+\sqrt{y}=\sqrt{a} is perpendicular to x axis at the point
  • (0, a)
  • (a, 0)
  • (\dfrac a  4, \dfrac a  4)
  • No where
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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers