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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=(1+x)y+sin1(sin2x)atx=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[2cosθlog(cosecθ+cotθ)],y=csin2θatθ=π3is
  • c2
  • 2c
  • 3c2
  • 5c2
If the tangent to the curve x=at2,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=t2+3t8,y=2t22t5 at point (2,1) is
  • 227
  • 67
  • 6
  • 76
The equation of tangent at those points where the curve y=x23x+2 meets x-axis are
  • xy+2=0,xy1=0
  • x+y1=0,xy2=0
  • xy1=0,xy=0
  • xy=0,x+y=0
The equation of the normal to the curve y=x+sinxcosx at x=π2 is
  • x=2
  • x=π
  • x+π=0
  • 2x=π
The point on the curve y=12xx2, 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=3t2+1,y=t31 at x=1 is
  • 12
  • 0
  • 2
The point on the curve y=x23x+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(2x) at the point (2,0) is
  • x2y=2
  • x2y+2=0
  • 2x+y=4
  • 2x+y4=0
At what points the slope of the tangent to the curve x2+y22x3=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=2x7+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 x2=4y passing through (1,2) is
  • x+y=3
  • xy=3
  • x+y=1
  • xy=1
The equation of the normal to the curve x=acos3θ,y=asin3θ at the point θ=π4 is
  • x=0
  • y=0
  • x=y
  • x+y=a
The number of tangents to the cure x3/2+y3/2=2a3/2,a>0, which are equally inclined to the axes, is 
  • 2
  • 1
  • 0
  • 4
The curve given by x+y=exy 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 9y2=x3, where the normal to the curve makes equal intercepts with the axes is?
  • (4,±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 y2=4x, if the value of m is?
  • 1
  • 2
  • 3
  • 1/2
The slope of the tangent to the curve x=t2+3t8,y=2t22t5 at the point (2,1) is
  • 227
  • 67
  • 76
  • 67
The normal at the point (1,1) on the curve 2y+x2=3 is
  • x+y=0
  • xy=0
  • x+y+1=0
  • xy=1
Consider the equation xy=exy
What is d2ydx2 at x=1 equal to ?
  • 0
  • 1
  • 2
  • 4
Consider the equation xy=exy
What is dydx at x=1 equal to ?
  • 0
  • 1
  • 2
  • 4
A curve y=memx where m>0 intersects y-axis at a point P.
How much angle does the tangent at P make with y-axis ? 
  • tan1m2
  • cot1(a+m2)
  • sin1(11+m4)
  • sec11+m4
A curve y=memx where m>0 intersects y-axis at a point P.
What is the slope of the curve at the point of intersection P
  • m
  • m2
  • 2m
  • 2m2
For x>1,y=logex satisfies the inequality 
  • x1>y
  • x21>y
  • y>x1
  • x1x<y
The slope of the tangent to the curve y=4x2 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 ey=1+x2, then 
  • |m|>1
  • m>1
  • m>1
  • |m|1
The abscissa of points P and Q in the curve y=ex+ex such that tangents at P and Q make 60o with the x-axis
  • ln (3+77) and ln (3+52)
  • ln (3+72)
  • ln (7+32)
  • ± ln (3+72)
If x=4 y = 14 is a normal to the curve y2=ax3β at (2,3) then the value of α+β is 
  • 9
  • -5
  • 7
  • -7
At what points of curve y=23x3+12x2, the tangent makes the equal with the axis?
  • (12,524) and (1,16)
  • (12,49) and (1,0)
  • (13,17) and(3,12)
  • (13,447) and (1,12)
The curve represented parametrically by the equations x = 2 in cott+1 and y=tant+cott 
  • tanfent and normal intersect at the point (2, 1)
  • normal at t=π/4 is parallel to the y-axis
  • tangent at t=π/4 is parallel to the line y = x
  • tangent at t=π/4 is parallel to the x-axis
If a variable tangent to the curve x2y=c3 makes intercepts a, b on x-and y-axes, respectively, then the value of a2b is
  • 27c3
  • 427c3
  • 274c3
  • 49c3
The angle between the tangent to the curves y=x2 and x=y2 at (1, 1) is 
  • cos145
  • sin135
  • tan134
  • tan113
At the point P(a,an) 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 limabb=12, then n equals
  • 1
  • 3
  • 2
  • 4
Point on the curve f(x)=x1x2 where the tangent is inclined at an angle of π4 ot the x-axis are 
  • (0, 0)
  • (3,32)
  • (2,23)
  • (3,32)
The x-intercept of the tangent at any arbitrary point of the curve ax2+by2=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(4m2,8m3) of x3y3=0 is also a normal to the curve  x3y3=0 , then value of m is
  • m=23
  • m=23
  • m=32
  • m=32
The slope of the tangent to the curve y=f(x) at [x,f(x)] 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
  • 56
  • 65
  • 16
  • 6
The normal to the curve x=a(cos0+0sin0),y=a(sin00cos0) 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
  • x2+y2=9x
  • 4x2+y2=9x
  • 4x2+2y2=9x
  • None of these
The curve for which the ratio of the length of the segment by any tangent on the Yaxis to the length of the radius vector is constant (K), is
  • (y+x2y2)xk1=c
  • (y+x2+y2)xk1=c
  • (yx2y2)xk1=c
  • (y+x2+y2)xk1=c
If f(x)=x1et2/2(1t2)dt, then ddxf(x) at x=1 is 
  • 0
  • 1
  • 2
  • 1
If y=x2xt2dt, then the equation of tangent at x=1 is 
  • x+y=1
  • y=x1
  • y=x
  • y=x+1
The tangent to the curve y=ex drawn at the point (c,ec) intersects the line joining the points (c1,ec1) and (c+1,ec+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 y1x2+x is
  • (y1)(x+1)+2x=0
  • 2x(y1)+x+1=0
  • x(y1)(x+1)+2=0
  • None of these
The point(s) on the curve y3+3x2=12y, where the tangent is vertical, is (are)
  • (±43,2)
  • (±113,1)
  • (0, 0)
  • (±43,2)
0:0:1


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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers