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

The abscissa of the point on the curve 3y=6x5x3 the normal at which passes through origin is :
  • 1
  • 13
  • 2
  • 12
The point of the curve y2=x where the tangent makes an angle of π4 with x-axis is 
  • (12,14)
  • (14,12)
  • (4,2)
  • (1,1)
The curve y=x15 has at (0,0)
  • a vertical tangent (parallel to y-axis)
  • a horizontal tangent (parallel to x-axis)
  • an oblique tangent
  • no tangent
The tangent to the curve y=e2x at the point (0,1) meets x-axis at:
  • (0,1)
  • (12,0)
  • (2,0)
  • (0,2)
The equation of tangents to the curve y(1+x2)=2x, where it crosses x-axis is:
  • x+5y=2
  • x5y=2
  • 5xy=2
  • 5x+y=2
The slope of tangent to the curve x=t2+3t8,y=2t22t5 at the point (2,1) is:
  • 227
  • 67
  • 67
  • 6
The curve for which the slope of the tangent at any point is equal to the ratio of the abscissa to the ordinate of the point is :
  • an ellipse
  • parabola
  • circle
  • rectangular hyperbola
The line 5x2y+4k=0 is tangent to 4x2y2=36, then k is:
  • 94
  • 8116
  • 49
  • 23
The equation of the tangent to the curve y=1ex2 at the point of intersection with Y axis 
  • x+2y=0
  • 2x+y=0
  • xy=2
  • x+y=2
If the tangent at (1,1) on y2=x(2x)2 meets the curve again at P, then P is
  • (4,4)
  • (1,2)
  • (3,6)
  • (94,38)
The slope of the tangent to the curve x=t2+3t8,y=2t22t5 at the point (2,1) is
  • 227
  • 67
  • 76
  • 67
The line y=mx+1 is a tangent to the curve y2=4x if the value of m is .......
  • 1
  • 2
  • 3
  • 12
The normal at the point (1,1) on the curve 2y+x23 is .............
  • x+y=0
  • xy=0
  • x+y=1
  • xy=1
The intercepts on x-axis made by tangents to the curve, y=x0|t| dt, xR, which are parallel to the line y=2x, are equal to

  • ±2
  • ±3
  • ±4
  • ±1
The normal to the curve x2=4y passing (1,2) is
  • x+y=3
  • xy=3
  • x+y=1
  • xy=1
The slope of the normal to the curve y=2x2+3sinx at x=0 is 
  • 3
  • 1/3
  • 3
  • 1/3
The line y=x+1 is a tangent to the curve y2=4x at the point 
  • (1,2)
  • (2,1)
  • (1,2)
  • (1,2)
The points on the curve 9y2=x3, where the normal to the curve makes equal intercepts with the axes are ...........
  • (4,±83)
  • (4,83)
  • (4,+83)
  • (±4,83)
The point of contact of vertical tangent to the curve given by the equations x=32cosθ,y=2+3sinθ is
  • (1, 5)
  • (1, 2)
  • (5, 2)
  • (2, 5)
The coordinates of a point P(x, y) lying in the first quadrant of the ellipse x28+y218=1 so that the area of the triangle formed by the tangent at P and the axes is the smallest are
  • (3,2)
  • (-2,3)
  • (2,-3)
  • (2,3)
The greatest inclination between the tangents is
  • tan1(a+b2ab)
  • tan1(ab2ab)
  • tan1ab
  • tan1ba
If OT and ON are perpendiculars dropped from the origin to the tangent and normal to the curve x=asin3t,y=acos3t at an arbitrary point, then which of the following is/are correct?
  • 4OT2+ON2=a2
  • OT2+ON2=a2
  • OT2+ON2=2a2
  • OT2+2ON2=4a2
A function y=f(x) has a second order derivative f(x)=6(x1) .
If its graph passes through the point (2,1) and at that point the tangent to the graph is y=3x5, then the function is
  • (x1)2
  • (x+1)2
  • (x+1)3
  • (x1)3
The portion of the tangent to the curve x=a2y2+a2logaa2y2a+a2y2 intercepted between the curve and xaxis, is of length
  • a2
  • a
  • 2a
  • a4
A curve passes through (2,0) and the slope of the tangent at any point (x,y) is x22x for all values of x. The point of minimum ordinate on the curve where x>0 is (a,b)'
Then find the value of a+6b.
  • 2
  • 4
  • 2
  • 4
The value of x at which tangent to the curve y=x36x2+9x+4,0x5 has maximum slope is
  • 0
  • 2
  • 52
  • 5
The number of different points on the curve y2=x(x+1)2, where the tangent to the curve drawn at (1, 2) meets the curve again, is
  • 0
  • 1
  • 2
  • 3
Suppose a,b,c are such that the curve y=ax2+bx+c is tangent to y=3x3 at (1,0) and is also tangent to y=x+1 at (3,4) then the value of (2ab4c) equals
  • 7
  • 8
  • 9
  • 10
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
Let tangent at a point P on the curve x2mYn2=a4m+n2(m,nN,niseven), meets the x-axis and y-axis at A and B respectively, if AP:PBisnλm, where P lies between A and B, then find the value of λ
  • 2
  • 4
  • 6
  • 8
The equation of the normal to the curve y=e2|x| at the point where the curve cuts the line x=12 is
  • 2e(ex+2y)=e24
  • 2e(ex2y)=e24
  • 2e(ey2x)=e24
  • none of these
The  perpendicular  distance between the point (1, 1) and the tangent to the curve y  =e2x+x2 drawn at the point x = 0 is
  • 15
  • 35
  • 25
  • 45
The sum of the intercepts on the coordinate axis by any tangent to the curve x+y=2 is
  • 2
  • 4
  • 6
  • 8
For the curve represented parametrically by the equations, x=2lncot(t)+1 & y=tan(t)+cot(t)
  • tangent at t=π/4 is parallel to x - axis
  • normal at t=π/4 is parallel to y - axis
  • tangent at t=π/4 is parallel to the line y=x
  • tangent and normal intersect at the point (2,1)
The equation of the tangent to the curve y=92x2 at the point, where the ordinate & the abscissa are equal , is 
  • 2x+y3=0
  • 2x+y3=0
  • 2xy33=0
  • 2x+y33=0
The point on the curve y2=x, the tangent at which makes an angle of 450 with positive direction of x axis will be given by
  • (12,14)
  • (12,12)
  • (2,4)
  • (14,12)
At the point P(a,a) on the graph of y=xn, (nϵN), in the first quadrant , a normal is drawn. The normal intersects the y-axis at the point (0,b). If lima0b=12, then n equals
  • 1
  • 3
  • 2
  • 4
Let f(x)={x2,for x<0x2+8,for x0. Then x-intercept of the line, that is, the tangent to the graph of f(x) in both the intervals of its domain, is
  • zero
  • 1
  • 2
  • 4
A function y=f(x) has a second-order derivative f(x)=6(x1). If its graph passes through the point (2,1) and at the point tangent to the graph is y=3x5, then the value of f(0) is 
  • 1
  • 1
  • 2
  • 0
For the curve y=3sinθcosθ,x=eθsinθ,0θπ, the tangent is parallel to x-axis when θ is :
  • π4
  • π2
  • 3π4
  • π6
If the circle x2+y2+2gx+2fy+c=0 is touched by y=x at P such that OP = 62
then the value of c is
  • 36
  • 144
  • 72
  • None of these
The tangent of the acute angle between the curves y=|x21| and y=7x2 at their points of intersection is
  • 532
  • 352
  • 534
  • 354
The angle made by the tangent of the curve x=a(t+sintcost), y=a(1+sint)2 with the xaxis at any point on it is
  • 14(π+2t)
  • 1sintcost
  • 14(2tπ)
  • 1+sintcos2t
An equation for the line that passes through (10,1) and is perpendicular to y=x242 is
  • 4x+y=39
  • 2x+y=19
  • x+y=9
  • x+2y=8
The abscissas of points P and Q on the curve y=ex+ex such that tangents at P and Q make 60 with the x-axis are
  • ln(3+77) and ln(3+52)
  • ln(3+72)
  • ln(737)
  • ±ln(3+72)
If the curve represented parametrically by the equations x=2lncott+1 and y=tant+cott
  • tangent and normal intersect at the point (2,1)
  • normal at t=\displaystyle \frac{\pi}{4} is parallel to the y axis
  • tangent at t=\displaystyle \frac{\pi}{4} is parallel to the line y=x
  • tangent at t=\displaystyle \frac{\pi}{4} is parallel to the x axis
A curve is represented by the equations, \displaystyle x = \sec^2t and y =\cot t, where t is a parameter. If the tangent at the point P on the curve where \displaystyle t = \dfrac{\pi}{4} meets the curve again at the point Q then |PQ| is equal to
  • \displaystyle \frac {5\sqrt 3}{2}
  • \displaystyle \frac {5\sqrt 5}{2}
  • \displaystyle \frac {2\sqrt 5}{3}
  • \displaystyle \frac {3\sqrt 5}{2}
The real number \displaystyle '\alpha' such that the curve \displaystyle f(x) = e^x is tangent to the curve \displaystyle g(x) = \alpha x^2.
  • \displaystyle \frac{e^2}{4}
  • \displaystyle \frac{e^2}{2}
  • \displaystyle \frac{e}{4}
  • \displaystyle \frac{e}{2}
The x-intercept of the tangent at any arbitrary point of the curve \displaystyle \frac {a}{x^2} + \frac {b}{y^2} = 1 is proportional to:
  • square of the abscissa of the point of tangency
  • square root of the abscissa of the point of tangency
  • cube of the abscissa of the point of tangency
  • cube root of the abscissa of the point of tangency
The angle made by the tangent of the curve \displaystyle x = a(t + \sin t \cos t); y = a (1 + \sin t)^2 with the x-axis at any point on it is
  • \displaystyle \frac {1}{4} (\pi + 2t)
  • \displaystyle \frac {1 - \sin t}{ \cos t}
  • \displaystyle \frac {1}{4} (2t - \pi)
  • \displaystyle \frac {1 + \sin t}{\cos 2 t}
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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers