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CBSE Questions for Class 11 Commerce Applied Mathematics Tangents And Its Equations Quiz 10 - MCQExams.com

If tangent at any point on the curve y2=1+x2 makes an angle θ with positive direction of the x-axis then
  • |tanθ|>1
  • |tanθ|<1
  • |tanθ|1
  • |tanθ|1
The equation of the normal to the curve y=(1+x)y+sin1(sin2x) at x=0 is.
  • x+y=1
  • xy+1=0
  • x+y=2
  • 2xy+1=0
If the line ax+y=c, touches both the curves x2+y2=1 and y2=42x, then |c| is equal to:
  • 1/2
  • 2
  • 2
  • 12
The equation of the normal to the curvey=\left( 1+x \right) ^{ y }+{ sin }^{ -1 }\left( { sin }^{ 2 }x \right) at\quad x=0 is
  • x+y=1
  • x-y+1=0
  • 2x+y=2
  • 2x-y+1
The sum of the length of sub tangent of sub tangent and tangent to the curve
x=c\left[ 2cos\theta -log\left( cos\quad ec\theta +cot\theta  \right)  \right] ,y=csin2\theta \quad at\quad \theta =\frac { \pi  }{ 3 } is
  • \dfrac { c }{ 2 }
  • 2c
  • \dfrac { 3c }{ 2 }
  • \dfrac { 5c }{ 2 }
If the tangent to the curve x=at^2, y=2at is perpendicular to x-axis, then its point of contact is
  • (a, a)
  • (0, a)
  • (0, 0)
  • (a, 0)
The slope of the tangent to the curve x=t^2+3t-8, y=2t^2-2t-5 at point (2, -1) is
  • \dfrac {22}{7}
  • \dfrac {6}{7}
  • -6
  • \dfrac {7}{6}
The equation of tangent at those points where the curve y=x^2-3x+2 meets x-axis are
  • x-y+2=0,x-y-1=0
  • x+y-1=0,x-y-2=0
  • x-y-1=0,x-y=0
  • x-y=0,x+y=0
The equation of the normal to the curve y=x+\sin x\cos x at x=\dfrac {\pi}{2} is
  • x=2
  • x=\pi
  • x+\pi =0
  • 2x=\pi
The point on the curve y=12x-x^2, where the slope of the tangent is zero will be
  • (0, 0)
  • (2, 16)
  • (3, 9)
  • (6, 36)
The slope of the tangent to the curve x=3t^2+1, y=t^3-1 at x=1 is
  • \dfrac {1}{2}
  • 0
  • -2
  • \infty
The point on the curve y=x^2-3x+2 where tangent is perpendicular to y=x is
  • (0, 2)
  • (1, 0)
  • (-1, 6)
  • (2, -2)
The equation of the normal to the curve y=x(2-x) at the point (2, 0) is
  • x-2y=2
  • x-2y+2=0
  • 2x+y=4
  • 2x+y-4=0
At what points the slope of the tangent to the curve x^2+y^2-2x-3=0 is zero?
  • (3, 0), (-1, 0)
  • (3, 0), (1, 2)
  • (-1, 0), (1, 2)
  • (1, 2), (1, -2)
Any tangent to the curve y=2x^7+3x+5
  • Is parallel to x-axis
  • Is parallel to y-axis
  • Makes an acute angle with x-axis
  • Makes an obtuse angle with x-axis
The normal to the curve x^2=4y passing through (1, 2) is
  • x+y=3
  • x-y=3
  • x+y=1
  • x-y=1
The equation of the normal to the curve x=a\cos^3\theta, y=a\sin^3\theta at the point \theta =\dfrac {\pi}{4} is
  • x=0
  • y=0
  • x=y
  • x+y=a
The number of tangents to the cure x^{3/2}+y^{3/2}=2a^{3/2}, a> 0, which are equally inclined to the axes, is 
  • 2
  • 1
  • 0
  • 4
The curve given by x + y = e^{xy} has a tangent parallel to the y-axis at the point
  • (0,1)
  • ( 1, 0 )
  • (1, 1)
  • None of these
Mark the correct alternative of the following.
The point on the curve 9y^2=x^3, where the normal to the curve makes equal intercepts with the axes is?
  • (4, \pm 8/3)
  • (-4, 8/3)
  • (-4, -8/3)
  • (8/3, 4)
Mark the correct alternative of the following.
The line y=mx+1 is a tangent to the curve y^2=4x, if the value of m is?
  • 1
  • 2
  • 3
  • 1/2
The slope of the tangent to the curve x=t^2+3t-8, y=2t^2-2t-5 at the point (2, -1) is
  • \dfrac {22}{7}
  • \dfrac {6}{7}
  • \dfrac {7}{6}
  • -\dfrac {6}{7}
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
Consider the equation x^y=e^{x-y}
What is \dfrac{d^2y}{dx^2} at x=1 equal to ?
  • 0
  • 1
  • 2
  • 4
Consider the equation x^y=e^{x-y}
What is \dfrac{dy}{dx} at x=1 equal to ?
  • 0
  • 1
  • 2
  • 4
A curve y=me^{mx} where m > 0 intersects y-axis at a point P.
How much angle does the tangent at P make with y-axis ? 
  • \tan^{-1}m^2
  • \cot^{-1}(a+m^2)
  • \sin^{-1}(\dfrac{1}{\sqrt{1+m^4}})
  • \sec^{-1}\sqrt{1+m^4}
A curve y=me^{mx} where m > 0 intersects y-axis at a point P.
What is the slope of the curve at the point of intersection P
  • m
  • m^2
  • 2m
  • 2m^2
For x > 1, y=\log_e x satisfies the inequality 
  • x-1 > y
  • x^2 -1 >y
  • y > x-1
  • \dfrac {x-1}{x} < y
The slope of the tangent to the curve y = \sqrt{4-x^{2}} at the point, where the ordinate and the abscissa are equal , is
  • -1
  • 1
  • 0
  • None of these
If m is the slope of a tangent to the curve e^{y}=1+x^{2}, then 
  • \left | m \right |> 1
  • m> 1
  • m> -1
  • \left | m \right |\leq 1
The abscissa of points P and Q in the curve y = e^{x}+e^{-x} such that tangents at P and Q make 60^{o} with the x-axis
  • ln \left ( \dfrac{\sqrt{3}+\sqrt{7}}{7} \right ) and ln \left ( \dfrac{\sqrt{3}+\sqrt{5}}{2} \right )
  • ln \left ( \dfrac{\sqrt{3}+\sqrt{7}}{2} \right )
  • ln \left ( \dfrac{\sqrt{7}+\sqrt{3}}{2} \right )
  • \pm ln \left ( \dfrac{\sqrt{3}+\sqrt{7}}{2} \right )
If x=4 y = 14 is a normal to the curve y^{2}=ax^{3}-\beta at (2,3) then the value of \alpha +\beta is 
  • 9
  • -5
  • 7
  • -7
At what points of curve y = \dfrac{2}{3}x^{3}+\dfrac{1}{2}x^{2}, the tangent makes the equal with the axis?
  • (\dfrac{1}{2},\dfrac{5}{24}) and \left ( -1,\dfrac{-1}{6} \right )
  • (\dfrac{1}{2},\dfrac{4}{9}) and ( -1,0)
  • \left ( \dfrac{1}{3},\dfrac{1}{7} \right ) and \left ( -3, \dfrac{1}{2} \right )
  • \left ( \dfrac{1}{3},\dfrac{4}{47} \right ) and \left ( -1, \dfrac{1}{2} \right )
The curve represented parametrically by the equations x = 2 in \cot t+1 and y=\tan t+\cot t 
  • tanfent and normal intersect at the point (2, 1)
  • normal at t = \pi /4 is parallel to the y-axis
  • tangent at t = \pi /4 is parallel to the line y = x
  • tangent at t = \pi /4 is parallel to the x-axis
If a variable tangent to the curve x^{2}y=c^{3} makes intercepts a, b on x-and y-axes, respectively, then the value of a^{2}b is
  • 27c^{3}
  • \dfrac{4}{27}c^{3}
  • \dfrac{27}{4}c^{3}
  • \dfrac{4}{9}c^{3}
The angle between the tangent to the curves y = x^{2} and x = y^{2} at (1, 1) is 
  • \cos ^{-1}\dfrac{4}{5}
  • \sin ^{-1}\dfrac{3}{5}
  • \tan ^{-1}\dfrac{3}{4}
  • \tan ^{-1}\dfrac{1}{3}
At the point P(a, a^{n}) on the graph of y = x^{n}(n \epsilon  n) in the first quadrant, a normal is drawn. the normal intersects the y-axis at the point (0, b) . if \underset{a\rightarrow b}{lim}b=\dfrac{1}{2}, then n equals
  • 1
  • 3
  • 2
  • 4
Point on the curve f(x)=\dfrac{x}{1-x^{2}} where the tangent is inclined at an angle of \dfrac{\pi }{4} ot the x-axis are 
  • (0, 0)
  • \left ( \sqrt{3},\dfrac{-\sqrt{3}}{2} \right )
  • \left ( -2 ,\dfrac{2}{3}\right )
  • \left (- \sqrt{3},\dfrac{\sqrt{3}}{2} \right )
The x-intercept of the tangent at any arbitrary point of the curve \dfrac{a}{x^{2}}+\dfrac{b}{y^{2}}=1 is proportion to
  • square of the abscissa of the point of tangency
  • square root of the abscissa of the point of tangency
  • cube of the abscissa pf the point of tangency
  • cube root of the abscissa of the point of tangency
If the tangent at any point P(4m^{2}, 8m^{3}) of x^{3}-y^{3}=0 is also a normal to the curve  x^{3}-y^{3}=0 , then value of m is
  • m = \dfrac{\sqrt{2}}{3}
  • m = -\dfrac{\sqrt{2}}{3}
  • m = \dfrac{3}{\sqrt{2}}
  • m = -\dfrac{3}{\sqrt{2}}
The slope of the tangent to the curve y = f(x) at \left [ x, f(x) \right ] is 2x +If the curve passes through the point (1, 2)then the area bounded by the curve, the x-axis and the line x = 1 is
  • \dfrac{5}{6}
  • \dfrac{6}{5}
  • \dfrac{1}{6}
  • 6
The normal to the curve x = a (\cos 0 + 0\sin 0), y= a (\sin 0- 0\cos 0) at any point 0 is such that
  • it makes a constant angle with x-axis
  • it passes through the origin
  • it is at a constant distance from the origin
  • none of these
A curve passes through (2,1) and is such that the square of the ordinate is twice the contained by the abscissa and the intercept of the normal. Then the equation of curve is
  • x^2 +y^2=9x
  • 4x^2 +y^2=9x
  • 4x^2 +2y^2=9x
  • None of these
The curve for which the ratio of the length of the segment by any tangent on the Y-axis to the length of the radius vector is constant (K), is
  • (y+\sqrt {x^2 -y^2})x^{k-1}=c
  • (y+\sqrt {x^2 +y^2})x^{k-1}=c
  • (y-\sqrt {x^2 -y^2})x^{k-1}=c
  • (y+\sqrt {x^2 +y^2})x^{k-1}=c
If f(x) = \displaystyle \int_{1}^{x} e^{t^2/2}(1-t^2)dt, then \dfrac{d}{dx} f(x) at x=1 is 
  • 0
  • 1
  • 2
  • -1
If y=\displaystyle \int_{x}^{x^2}t^2dt , then the equation of tangent at x=1 is 
  • x+y=1
  • y=x-1
  • y=x
  • y=x+1
The tangent to the curve y = e^{x} drawn at the point (c, e^{c}) intersects the line joining the points (c-1, e^{c-1}) and (c+1, e^{c+1})
  • on the left of x =c
  • on the right of x = c
  • at no point
  • at all point
If the line ax +by + c = 0 is a normal to the curve xy = 1, then 
  • a > 0, b> 0
  • a > 0, b < 0
  • a < 0, b > 0
  • a < 0, b < 0
The equation of the curves through the point (1,0) and whose slope is \dfrac{y -1}{x^{2} + x} is
  • (y - 1)(x + 1) + 2x = 0
  • 2x(y - 1) + x + 1 = 0
  • x(y - 1)(x + 1) + 2 = 0
  • None of these
The point(s) on the curve y^{3} + 3x^{2} = 12y, where the tangent is vertical, is (are)
  • \left ( \pm \dfrac{4}{\sqrt{3}}, -2 \right )
  • \left ( \pm \sqrt{\dfrac{11}{3}}, 1 \right )
  • (0, 0)
  • \left ( \pm \dfrac{4}{\sqrt{3}}, 2 \right )
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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers