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CBSE Questions for Class 11 Commerce Applied Mathematics Tangents And Its Equations Quiz 3 - MCQExams.com

Equation of the tangent to the parabola y2=4x+5 which is parallel to the line y=2x+7 is
  • y=2x+3
  • y=2x3
  • y=2x+5
  • y=2x5
For the parabola y2=8x, tangent and normal are drawn at P(2,4) which meet the axis of the parabola in A and B, then the length of the diameter of the circle through A,P,B is
  • 2
  • 4
  • 8
  • 6
If the curves y=x21, y=8xx29  touch each other at (2, 3) then equation of the common tangent is
  • 4xy=5
  • 4x+y=5
  • x4y=5
  • x+4y=14
The point on the hyperbola y=x1x+1 at which the tangents are parallel to y=2x+1 are
  • (0,1) only
  • (2,3) only
  • (0,1), (2,3)
  • (2,3), (5,4)
Assertion(A): The tangent to the curve y=x3x2x+2 at (1, 1) is parallel to the x axis.
Reason(R): The slope of the tangent to the above curve at (1, 1) is zero.
  • Both A and R are true R is the correct explanation of A
  • Both A and R are true but R is not correct explanation of A
  • A is true but R is false
  • A is false but R is true
Assertion A: The curves x2=y, x2=y  touch each other at (0, 0).
Reason R: The slopes of the tangents at (0, 0) for both the curves are equal.
  • Both A and R are true R is the correct explanation of A
  • Both A and R are true but R is not correct explanation of A
  • A is true but R is false
  • A is false but R is true
Observe the following statements for the curve y=2.ex3
I : The slope of the tangent to the curve where it meets y-axis is 23
II:The equation of normal to the curve where it meets y-axis is 3x+2y+4=0.
Which of the above statement is correct
  • only I
  • only II
  • both I and II
  • neither I nor II
Match the points on the curve  2y2=x+1 with the slope of normals at those points and choose 
the correct answer.
Point
Slope of normal
I : (7,2)

a)42

II: (0,12)

b)8
III : (1,1)
c)4
IV:  (3,2)


d)22



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The equation of the tangent to the curve y=e|x| at the point where the curve cuts the line x=1 is
  • x+y=e
  • e(x+y)=1
  • y+ex=1
  • x+ey=2
The equation of the normal at x = 2a for the curve y=8a34a2+x2 is
  • 2xy=3a
  • 2x+y=2a
  • x+2y=6a
  • x+y=a
The distance of the origin from the normal to the curve  y=e2x+x2 at x=0 is
  • 25
  • 25
  • 25
  • 52
Equation of the tangent line to y=bexa where it crosses y-axis is
  • ax+by=1
  • xa+yb=1
  • xb+ya=1
  • axby=1
The portion of the tangent to xy =a2 at any point on it between the axes is
  • Trisected at that point
  • bisected at that point
  • constant
  • with ratio 1:4 at the point
Area of the triangle formed by the normal to the curve x=esiny at (1, 0) with the coordinate axes is
  • 14
  • 12
  • 34
  • 1
The arrangment of the slopes of the normals to the curve  y=elog(cosx) in the ascending order at the points given below.
A)x=π6,B)x=7π4,C)x=11π6,D)x=π3
  • C,B,D,A
  • B,C,A,D
  • A,D,C,B
  • D,A,C,B
lf the normal at the point p(θ) of the curve x23+y23=a23 passes through the origin then
  • θ=π3
  • θ=π6
  • θ=π4
  • θ=π2
The equations of the tangents at the origin to the curve  y2=x2(1+x) are
  • y=±x
  • y=±2x
  • y=±3x
  • x=±2y
The equation of the common normal at the point of contact of the curves x2=y and x2+y28y=0
  • x=y
  • x=0
  • y=0
  • x+y=0
lf the chord joining the points where x=p, x=q on the curve y=ax2+bx+c is parallel to the tangent drawn to the curve at (α,β) then α=
  • 2pq
  • pq
  • p+q2
  • pq2
The arrangement of the following curves in the ascending order of slopes of their tangents at the given points.
A)y=11+x2 at x=0

B)y=2ex4, where it cuts the y-axis
C)y=cos(x) at x=π4
D)y=4x2 at x=1
  • DCBA
  • ACBD
  • ABCD
  • DBAC
Observe the following lists for the curve y=6+xx2 with the slopes of tangents at the given points; I, II, III, IV
Point
Tangent slope
I: (1,6)
a) 3
II: (2,4)
b) 5
III: (1,4)
c) 1
IV: (2,0)
d) 3
  • a,b,c,d
  • b,c,d,a
  • c,d,b,a
  • c,d,a,b
lf the tangent to the curve 2y3=ax2+x3 at the point (a, a) cuts off intercepts α and β on the coordinate axes such that α2+β2=61, then a is equal to
  • ±30
  • ±5
  • ±6
  • ±61
Assertion(A): If the tangent at any point P on the curve xy=a2 meets the axes at A and B then AP:PB=1:1
Reason(R): The tangent at P(x,y) on the curve Xm.Yn=am+n meets the axes at A and B. Then the ratio of P divides ¯AB is n:m.
  • Both A and R are true R is the correct explanation of A
  • Both A and R are true but R is not correct explanation of A
  • A is true but R is false
  • A is false but R is true
The point on the curve x+y=2a2, where the tangent is equally inclined to the axes, is
  • (a4,a4)
  • (0,4a4)
  • (4a4,0)
  • none of these
Match List-I with List-II and select the correct answer using the code given below. A B C D
List-I
List-II
a) Equation of tangent to the curve y=bex/a at x=0

1) x2y=2


b) Equation of tangent to the curve y=x2+1 at (1,2)
2) y=2x
c) Equation of normal to the curve y=2xx2at (2,0)

3) xy=π


d) Equation of normal to the curve y=sinx at x=π
4) xa+yb=1

  • 4 1 2 3
  • 4 2 1 3
  • 1 2 3 4
  • 1 4 3 2
Area of the triangle formed by the tangent, normal at (1,1) on the curve x+y=2 and the y axis is (in sq. units)
  • 1
  • 2
  • 12
  • 4
A curve with equation of the form y=ax4+bx3+c+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 the x for which the curve has a negative gradient are :
  • x>1
  • x<1
  • x<1
  • 1x1
Assertion (A): The points on the curve y=x33x at which the tangent is parallel to x-axis are (1,2) and (1,2).
Reason (R): The tangent at (x1,y1) on the curve y=f(x) is vertical then dydx at (x1,y1) is not defined.
  • Both A and R are true and R is the correct explanation for A
  • Both A and R are true but R is not the correct explanation for A
  • A is true but R is false
  • A is false but R is true
lf the tangent at any point on the curve x4+y4=c4 cuts off intercepts a and b on the coordinate axes, the value of a4/3+b4/3 is
  • c4/3
  • c1/2
  • c1/2
  • c4/3
I. lf the curve y=x2+bx+c touches the straight line y=x at the point (1,1) then b and c are given by 1,1.
II. lf the line Px+my+n=0 is a normal to the curve xy=1, then P>0, m<0.
Which of the above statements is correct
  • only I
  • only II
  • both I and II
  • Neither I nor II
At origin the curve  y2=x3+x
  • Touches the x-axis
  • Touches the y-axis
  • Bisects the angle between the axes
  • touches both the axes
Observe the following statements
I: If p and q are the lengths of perpendiculars from the origin on the tangent and normal at any point on the curve x23+y23=1 then 4p2+q2=1.
II: If the tangent at any point P on the curve x3.y2=a5 cuts the coordinate axes at A and B then AP:PB=3:2
  • only I
  • only II
  • both I and II
  • neither I nor II
Observe the following statements for the curve x=at3, y=at4 at t=1.
I : The equation of the tangent to the curve is 4x3ya=0
II : The equation of the normal to the curve is 3x+4y7a=0
III: Angle between tangent and normal at any point on the curve is π2
Which of the above statements are correct.
  • I and II
  • II and III
  • I and III
  • I, II, III
Assertion (A): The normal to the curve ay2=x3(a0,x0) at a point (x,y) on it makes equal intercepts on the axes, then x=4a9.
Reason (R): The normal at (x1,y1) on the curve y=f(x) makes equal intercepts on the coordinate axes, then dydx|(x1,y1)=1
  • Both (A) and (R) are true and (R) is the correct explanation for (A).
  • Both (A) and (R) are true but (R) is not the correct explanation for (A).
  • (A) is true but (R) is false.
  • (A) is false but (R) is true.
Given the curves y=f(x) passing through the point (0,1) and y=xf(t) passing through the point (0,12). The tangents drawn to both the curves at the points with equal abscissae intersect on the x- axis. Then the curve y=f(x) is 
  • f(x)=x2+x+1
  • f(x)=x2ex
  • f(x)=e2x
  • f(x)=xex
The point of intersection of the tangents drawn to the curve x2y=1y at the points where it is met by the curve xy=1y is given by
  • (0,1)
  • (1,1)
  • (0,1)
  • (1,)
The number of tangents to the curve x3/2+y3/2=a3/2, where the tangents are equally inclined to the axes, is
  • 2
  • 1
  • 0
  • 4
The points on the hyperbola x2y2=2 closest to the point (0, 1) are
  • (±32,12)
  • (12,±32)
  • (12,12)
  • (±34±32)
lf the tangent to the curve f(x)=x2 at any point (c,f(c)) is parallel to the line joining points (a,f(a)) and (b,f(b)) on the curvel then a, c, b are in
  • AP
  • GP
  • HP
  • AGP
A curve is given by the equations x=sec2θ,y=cotθ. If the tangent at P where θ=π4 meets the curve again at Q, then length PQ, is
  • 52
  • 352
  • 10
  • 20
lf the parametric equation of a curve given by x=etcost, y=etsint, then the tangent to the curve at the point t=π4 makes with axis of x the angle.
  • 0
  • π4
  • π3
  • π2
The normal to the curve x=a(1+cosθ), y=asinθ at any point θ always passes through the fixed point: 
  • (a,0)
  • (0,a)
  • (0,0)
  • (a,a)
lf the curve y=px2+qx+r passes through the point (1, 2) and the line y=x touches it at the origin, then the values of p, q and r are
  • p=1,q=1,r=0
  • p=1,q=1,r=0
  • p=1,q=1,r=0
  • p=1,q=2,r=3
For the curve y=3sinθcosθ,x=eθsinθ,0θπ; the tangent is parallel to x -axis when θ is
  • 0
  • π2
  • π4
  • 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
If x+4y=14 is a normal to the curve y2=αx3β at (2,3), then the value of α+β is
  • 9
  • 5
  • 7
  • 7
The number of tangents to the curve x3/2+y3/2=2a3/2, a>0, which are equally inclined to the axes, is
  • 2
  • 1
  • 0
  • 4
If m is the slope of a tangent to the curve ey=1+x2, then 
  • |m|>1
  • m>1
  • m>1
  • |m|1
If the circle x2+y2+2gx+2fy+c=0 is touched by y = x at P in the first quadrant, such that OP=62, then the value of c is
  • 36
  • 144
  • 72
  • None of these
The equations of the tangents to the curve y=x4 from the point (2, 0) not on the curve, are given by
  • y=0
  • y1=5(x1)
  • y409881=204827(x83)
  • y32243=8081(x23)
0:0:2


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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers