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CBSE Questions for Class 11 Commerce Applied Mathematics Tangents And Its Equations Quiz 7 - MCQExams.com

If equation of normal at a point (m2,m3) on the curve x3y2=0isy=3mx4m3 then m2 equals
  • 0
  • 1
  • 29
  • 29
The coordinates of the points on the curve x=a(θ+sinθ),y=a(1cosθ) where tangent is inclined an angle π4 to the xaxis are -
  • (a,a)
  • (a(π21),a)
  • (a(π2+1),a)
  • (a,a(π2+1))
The line xa+yb=1 touches the curve y=bexa at the point -
  • (0,a)
  • (0.0)
  • (0,b)
  • (b,0)
At what values of a, the curve x4+3ax3+6x2+5 is not situated below any of its tangent lines
  • |a|>43
  • |a|<43
  • |a|>1
  • |a|<13
The points on the curve \displaystyle y^{2}=4a\left ( x+a\sin \frac{x}{a} \right ) at which the tangent is parallel to x axis lie on -
  • a straight line
  • a parabola
  • a circle
  • an ellipse
If the tangent at (1,\,1) on y^2=x(2-x)^2 meets the curve again at P(a,\,b) then a/b is equal to
  • 2
  • 4
  • 6
  • 8
The abcissa of the point on the curve \displaystyle ay^{2}=x^{3} the normal at which cuts off equal intercepts from the axes is -
  • 1
  • \dfrac {4a } 3
  • 3
  • \dfrac {4a } 9
The area of triangle formed by tangent to the hyperbola \displaystyle 2xy=a^{2} and coordinates axes is -
  • \displaystyle a^{2}
  • \displaystyle 2a^{2}
  • \displaystyle\dfrac{ a^{2} } 2
  • \displaystyle\dfrac{ 3a^{2} } 2
If the tangent at any point on the curve \displaystyle x^{4}+y^{4}=a^{4} cuts off intercept p and q on the axes, the value of \displaystyle p^{-\frac43}+q^{-\frac43} is
  • \displaystyle a^{-\frac43}
  • \displaystyle a^{-\frac13}
  • \displaystyle a^{-\frac12}
  • None of these
The equation of normal to the curve x+y=x^{y}, where it cuts x-axis is
  • y=x+1
  • y=-x+1
  • y=x-1
  • y=-x-1
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
If the tangent to the curve \displaystyle 2y^{3}=ax^{2}+x^{3} at a point (a, a) cuts off intercepts p and q on the coordinates axes where \displaystyle p^{2}+q^{2}=61 then a equals to
  • 30
  • -30
  • 0
  • \displaystyle \pm 30
The points on the curve \displaystyle 9y^2=x^{3} where the normal to the curve makes equal intercepts with coordinates axes is :
  • \displaystyle \left ( 4,\frac{8}{3} \right )\: \: or\: \: \left ( 4,-\frac{8}{3} \right )
  • \displaystyle \left ( -4,\frac{8}{3} \right )
  • \displaystyle \left ( -4,-\frac{8}{3} \right )
  • None of these
If the line x -y = 0 is tangent to f(x) = b \ln x - x, then b lies in the interval
  • (1, 3)
  • (0, 1)
  • (4, 6)
  • (6, 8)
If the curve y^2=ax^3-6x^2+b passes through (0,\,1) and has its tangent parallel to y-axis at x=2, then
  • a=2,\,b=1
  • a=\displaystyle\frac{23}{8},\,b=1
  • a=-\displaystyle\frac{8}{23},\,b=1
  • a=-\displaystyle\frac{23}{8},\,b=1
Let tangent at a point P on the curve \displaystyle { x }^{ 2m }={ y }^{ \tfrac { n }{ 2 }  }={ a }^{ \tfrac { 4m+n }{ 2 }  } meets the x-axis and y-axis at A and B respectively, If AP:PB is \displaystyle \frac { n }{ \lambda m } , where P lies between A and B, then find the value of \displaystyle \lambda 
  • 4
  • 3
  • -4
  • -3
The minimum value of the polynomial.
p(x)=3{ x }^{ 2 }-5x+2
  • -\frac { 1 }{ 6 }
  • \frac { 1 }{ 6 }
  • \frac { 1 }{ 12 }
  • -\frac { 1 }{ 12 }
If the tangent to the curve x = a(8 + sin \theta), y = a(1 + cos \theta ) at \theta = \displaystyle \frac{\pi}{3} makes an angle \alpha with x-axis, then \alpha is equal to
  • \displaystyle \frac{\pi}{3}
  • \displaystyle \frac{2\pi}{3}
  • \displaystyle \frac{\pi}{6}
  • \displaystyle \frac{5\pi}{6}
The curve which passes through (1, 2) and whose tangent at any point has a slope that is half of slope of the line joining origin to the point of contact, is -
  • A rectangle hyperbola
  • A circle
  • A parabola
  • A straight line through origin
  • Answer required
The lines tangent to the curve x^3-y^3+x^2y-yx^2+3x-2y=0 and x^5-y^4+2x+3y=0 at the origin intersect at an angle \theta equal to
  • \displaystyle\frac{\pi}{6}
  • \displaystyle\frac{\pi}{4}
  • \displaystyle\frac{\pi}{3}
  • \displaystyle\frac{\pi}{2}
A curve \displaystyle y=f\left( x \right) ;\left( y>0 \right)   passes thorugh (1,1) and at point \displaystyle P(x,y) tangents cuts x-axis and y-axis at A and B respectively. If P divides AB  internally in the ratio 3 : 2, then the value of \displaystyle f\left( \frac { 1 }{ 8 }  \right)  is
  • 4
  • \displaystyle \frac { 1 }{ 4 }
  • \displaystyle 16\sqrt { 2 }
  • \displaystyle \frac { 1 }{ 16\sqrt { 2 } }
The slope of the tangent to the curve x={t}^{2}+3t-8, y=2{t}^{2}-2t-5 at the point (2,-1) is
  • \cfrac{22}{7}
  • \cfrac{6}{7}
  • \cfrac{7}{6}
  • \cfrac{-6}{7}
  • answer required
The line y=mx+1 is a tangent to the curve {y}{^2}=4x, if the value of m is
  • 1
  • 2
  • 3
  • \cfrac{1}{2}
  • answer required
Let y=e^{x^2} and y=e^{x^2}\sin\, x be two given curves. Then, angle between the tangents to the curves at any point their intersection is 
  • 0
  • \pi
  • \dfrac{\pi}{2}
  • \dfrac{\pi}{4}
The abscissa of the points, where the tangent to curve y={x}^{3} - 3{x}^{2} - 9x+5 is parallel to x-axis, are
  • x=0 and 0
  • x=1 and -1
  • x=1 and -3
  • x=-1 and 3
The equation of normal of x^2+y^2-2x+4y-5=0 at (2,\,1) is
  • y=3x-5
  • 2y=3x-4
  • y=3x+4
  • y=x+1
If the tangent at a point P, with parameter t, on the curve x = 4t^{2} + 3, y = 8t^{3} - 1, t\epsilon R meets the curve again at a point Q, then the coordinates of Q are:
  • (t^{2} + 3, -t^{3} - 1)
  • (4t^{2} + 3, -8t^{3} - 1)
  • (16t^{3} + 3, -64 t^{3} - 1)
  • (t^{2} + 3, t^{3} - 1)
Suppose that the equation f\left( x \right) ={ x }^{ 2 }+bx+c=0 has two distinct real roots \alpha and \beta . The angle between the tangent to the curve y=f\left( x \right) at the point \left( \dfrac { \alpha +\beta  }{ 2 } ,f\left( \dfrac { \alpha +\beta  }{ 2 }  \right)  \right) and the positive direction of the x-axis is
  • { 0 }^{ }
  • { 30 }^{ }
  • { 60 }^{ }
  • { 90 }^{ }
The points on the curve 9{y}^{2}={x}^{3}, where the normal to the curve makes equal intercepts with the axes are
  • \left( 4,\pm \cfrac { 8 }{ 3 } \right)
  • \left( 4,\cfrac { -8 }{ 3 } \right)
  • \left( 4,\pm \cfrac { 3 }{ 8 } \right)
  • \left( \pm 4,\cfrac { 3 }{ 8 } \right)
  • answer required
The normal to the curve {x}^{2}=4y passing (1,2) is
  • x+y=3
  • x-y=3
  • x+y=1
  • x-y=1
  • answer required
The coordinates of the point P on the curve x = a(\theta + \sin \theta), y = a(1 - \cos \theta) where the tangent is inclined at an angle \dfrac {\pi}{4} to the x-axis, are
  • \left (a\left (\dfrac {\pi}{2} - 1\right ), a\right )
  • \left (a\left (\dfrac {\pi}{2} + 1\right ), a\right )
  • \left (a \dfrac {\pi}{2}, a\right )
  • (a, a)
Angle between { y }^{ 2 }=x and { x }^{ 2 }=y at the origin is
  • 2\tan ^{ -1 }{ \left( \dfrac { 3 }{ 4 } \right) }
  • \tan ^{ -1 }{ \left( \dfrac { 4 }{ 3 } \right) }
  • \dfrac { \pi }{ 2 }
  • \dfrac { \pi }{ 4 }
Equation of normal to the circle \displaystyle x=6\cos { \theta  } ,y=6\sin { \theta  }  at \displaystyle p\left( \frac { 2\pi  }{ 3 }  \right)  is
  • \displaystyle \sqrt { 3x } -y=0
  • \displaystyle \sqrt { 3x } +y=0
  • \displaystyle x+\sqrt { 3y } =0
  • \displaystyle x-\sqrt { 3y } =0
If the line \alpha\,x+by+c=0 is a tangent to the curve xy=4, then
  • a < 0,\,b > 0
  • a \le o,\,b > 0
  • a < 0,\,b < 0
  • a \le 0,\,b < 0
The slope at any point of a curve y=f\left( x \right) is given by \dfrac { dy }{ dx } =3{ x }^{ 2 } and it passes through \left( -1,1 \right) . The equation of the curve is
  • y={ x }^{ 3 }+2
  • y=-{ x }^{ 3 }-2
  • y=3{ x }^{ 3 }+4
  • y=-{ x }^{ 3 }+2
The equation of one of the curves whose slope at any point is equal to y+2x is
  • y=2(e^x+x-1)
  • y=2(e^x-x-1)
  • y=2(e^x-x+1)
  • y=2(e^x+x+1)
The slope of the normal to the curve y = 3x^2 at the point whose x-coordinate 2 is
  • \dfrac{1}{13}
  • \dfrac{1}{14}
  • \dfrac{-1}{12}
  • \dfrac{1}{12}
If \Delta is the area of the triangle formed by the positive x-axis and the normal and tangent to the circle x^{2} + y^{2} = 4 at (1, \sqrt {3}), then \Delta =
  • \dfrac {\sqrt {3}}{2}
  • \sqrt {3}
  • 2\sqrt {3}
  • 6
If the tangent to the curve 2y^{3} = ax^{2} + x^{3} at the point (a, a) cuts off intercepts \alpha and \beta on the coordinate axes where \alpha^{2} + \beta^{2} = 61 then the value of 'a' is equal to
  • 25
  • 36
  • \pm 30
  • \pm 40
The tangent to the curve y=x^3+1 at (1, 2) makes an agnle \theta with y axis, then the value of tan \theta is.
  • 3
  • \frac{1}{3}
  • -\frac{1}{3}
  • -3
The slope of the tangent to the curve y=3{ x }^{ 2 }+3\sin { x } at x=0 is
  • 3
  • 2
  • 1
  • -1
What is the slope of the tangent to the curve y=sin^{-1}(sin^2x) at x=0 ?
  • 0
  • 1
  • 2
  • None of the above
Find the slope of the normal to the curve 4x^3+6x^2-5xy-8y^2+9x+14=0T the point -2, 3.
  • \infty
  • 11
  • \displaystyle\frac{9}{19}
  • \displaystyle-\frac{19}{9}
A mirror in the first quadrant is in the shape of a hyperbola whose equation is xy =A light source in the second quadrant emits a beam of light that hits the mirror at the point (2,1/2). If the reflected ray is parallel to the y-axis the slope of the incident beam is 
631253_bb2ecc0476db46a5bd709f62d7b4e000.png
  • \dfrac{13}{8}
  • \dfrac{7}{4}
  • \dfrac{15}{8}
  • 2
What is the slope of the tangent to the curve x = t^2 + 3t - 8, y = 2t^2 - 2t - 5 at t = 2 ?
  • \dfrac{7}{6}
  • \dfrac{6}{7}
  • 1
  • \dfrac{5}{6}
If the tangent to the function y = f(x) at (3, 4) makes an angle of \dfrac {3\pi}{4} with the positive direction of x-axis in anticlockwise direction then f'(3) is
  • -1
  • 1
  • \dfrac {1}{\sqrt {3}}
  • \sqrt {3}
How many tangents are parallel to x-axis for the curve y = x^2 - 4x + 3 ?
  • 1
  • 2
  • 3
  • No tangent is parallel to x-axis.
Consider the curve y = e^{2x}.Where does the tangent to the curve at (0, 1) meet the x-axis ? 
  • (1, 0)
  • (2, 0)
  • \left(-\dfrac{1}{2}, 0\right)
  • \left(\dfrac{1}{2}, 0\right)
The slope of the tangent to the curve given by x = 1 - \cos { \theta  }, y = \theta -\sin { \theta  } at \theta = \dfrac { \pi  }{ 2 } is
  • 0
  • -1
  • 1
  • Not defined
Let f(x)=2{ x }^{ 3 }-5{ x }^{ 2 }-4x+3,\cfrac { 1 }{ 2 } \le x\le 3. The point at which the tangent to the curve is parallel to the X-axis is
  • (1,-4)
  • (2,-9)
  • (2,-4)
  • (2,-1)
  • (2,-5)
0:0:2


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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers