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CBSE Questions for Class 12 Commerce Maths Application Of Derivatives Quiz 1 - MCQExams.com

The tangent at the point (2,2) to the curve, x2y22x=4(1y) does not pass through the point.
  • (8,5)
  • (4,13)
  • (2,7)
  • (4,9)
If the tangent to the conic, y6=x2 at (2, 10) touches the circle, x2+y2+8x2y=k (for some fixed k) at a point (α,β); then (α,β) is;
  • (417,117)
  • (717,617)
  • (617,1017)
  • (817,217)
Let b be a nonzero real number. Suppose f:RR is a differentiable function such that f(0)=1.
If the derivative f' of f satisfies the equation f(x)=f(x)b2+x2 for all xR, then which of the following statements is/are TRUE?
  • If b>0, then f is an increasing function
  • If b<0, then f is a decreasing function
  • f(x)f(x)=1 for all xR
  • f(x)f(x)=0 for all xR
What is the x-coordinate of the point on the curve f(x)=x(7x6), where the tangent is parallel to x-axis?
  • 13
  • 27
  • 67
  • 12
Consider the following statements in respect of the function f(x)=x31,xϵ[1,1]
I. f(x) is increasing in [1,1]
II. f(x) has no root in (1,1).
Which of the statements given above is/ are correct?
  • Only I
  • Only II
  • Both I and II
  • Neither I nor II
If x2f(4a)=y2f(a25) respresents and ellipse with major axis as y-axis and f is a decreasing function, then 
  • a(,1)
  • a(5,)
  • a(1,4)
  • a(1,5)
The values of x at which f(x)=sinx is stationary are given by
  • nπ, nZ
  • (2n+1)π2, nZ
  • nπ4, nZ
  • nπ2, nZ

The number of stationary points of f(x)=sinx in [0,2π] are
  • 1
  • 2
  • 3
  • 4
Find the equation of a line passing through (2,3) and parallel to tangent at origin for the circle x2+y2+xy=0
  • x2y+5=0
  • x4y+3=0
  • xy+5=0
  • 2xy+6=0

 Stationary point of y=logxx(x>0) is
  • (1,0)
  • (e,1e)
  • (1e,e)
  • (1e1e)
I: lf f(a)<0 then the function f is decreasing at x=a
II: lf f is decreasing at x=a then f(a)<0 
Which of the above statements are true ?
  • onlyI
  • only II
  • both I and II
  • neither I nor II
The slope of tangent to the curve y=x0dx1+x3 at the point where x=1 is
  • 12
  • 1
  • 14
  • none of these
The value of x at which f(x)= cosx is stationary are given by
  • nπ, nZ
  • (2n+1)π2, nZ
  • nπ4, nZ
  • nπ2, nZ
The number of stationary points of f(x)=cosx in [0,2π] are
  • 1
  • 2
  • 3
  • 4
The curve yexy+x=0 has a vertical tangent at
  • (1,1)
  • (0,1)
  • (1,0)
  • (0,0)
The stationary point of f(x)=x210x+43 is
  • (5, 18)
  • (18, 5)
  • (5, 5)
  • (5, 15)
The point on the curve y=x23x+2 at which the tangent is perpendicular to the line y=x is -
  • (0,2)
  • (1,0)
  • (1,6)
  • (2,2)
If tangent to curve at a point is perpendicular to x - axis then at that point -
  • dydx=0
  • dxdy=0
  • dydx=1
  • dydx=1
If y=f(x) be the equation of a parabola which is touched by the line y=x at the point where x=1 Then
  • f(1)=1
  • f(0)=f(1)
  • 2f(0)=1f(0)
  • f(0)+f(0)+f"(0)=1
The slope of the curve y=sinx+cos2x is zero at the point where -
  • x=π4
  • x=π2
  • x=π
  • No where
The slope of the tangent to the curve y=sinx at point (0,0) is
  • 1
  • 0
  • None of these
If tangent at a point of the curve y=f(x) is perpendicular to 2x3y=5 then at that point dydx equals
  • 23
  • 23
  • 32
  • 32
The inclination of the tangent w.r.t. x - axis to the curve x2+2y=8x7 at the point x=5 is
  • π4
  • π3
  • 3π4
  • π2
The slope of the tangent to the curve y=x3+3x2+9x27 is maximum when x equals.
  • 1
  • 3
  • 12
  • 12
At what point the tangent to the curve x+y=a is perpendicular to the x - axis
  • (0,0)
  • (a,a)
  • (a,0)
  • (0,a)
If xa+yb=1 is a tangent to the curve x=Kt,y=Kt,K>0 than
  • a>0,b>0
  • a>0,b<0
  • a<0,b>0
  • a<0,b<0
The line y=x+1 is a tangent to the curve y2=4x at the point.
  • (1,2)
  • (2,1)
  • (1,4)
  • (2,2)
If a tangent to the curve y=6xx2 is parallel to the line 4x2y1=0, then the point of tangency on the curve is:
  • (2, 8)
  • (8, 2)
  • (6, 1)
  • (4, 2)
The slope of the tangent to the curve y=x0dt1+t3 at the point where x=1 is
  • 14
  • 13
  • 12
  • 1
If 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 normal to the curve y=2x2+3sinx at x=0 is. 
  • 3
  • 13
  • 3
  • 13
The slope of the tangent to the curve y=x0dt1+t3 at the point where x=1 is 
  • 14
  • 13
  • 12
  • 1
Consider the curve y=e2x.What is the slope of the tangent to the curve at (0, 1) ?
  • 0
  • 1
  • 2
  • 4
The gradient of the tangent line at the point (acosα,asinα) to the circle x2+y2=a2, is
  • tan(πα)
  • tanα
  • cotα
  • - cotα
The function xx is increasing, when
  • x>1e
  • x<1e
  • x<0
  • For all x
Find the approximate error in the volume of a cube with edge x cm, when the edge is increased by 2%
  • 4%
  • 2%
  • 6%
  • 8%
Which one of the following be the gradient of the hyperbola xy=1 at the point (t,1t)
  • 1t
  • 1t2
  • 1t
  • 2t2
If the product of the slope of tangent to curve at (x,y) and its y-co-ordinate is equal to the x-co-ordinate of the point, then it represent.
  • circle
  • parabola
  • ellipse
  • rectangular hyperbola
The slope of the tangent to the curve xy+axby=0 at the point (1,1) is 2, then value of a and b are respectively:
  • 1,2
  • 2,1
  • 3,5
  • None of these
The graph of the function f(x)=2x37 goes :
  • up to the right and down to the left
  • down to the right and up to the left
  • up to the right and up to the left
  • down to the right and down to the left
  • none of these ways.
A curve with equation of the form y=ax4+bx3+cx+d has zero gradient at the point (0,1) and also touches the x-axis at the point (1,0) then
  • a=3
  • b=4
  • c+d=1
  • for x<1 the curve has a negative gradient
The local maximum value of x(1x)2,0x2 is
  • 2
  • 427
  • 5
  • 2,427
Function f(x)=xnx is decreasing, when
  • x(0,1)
  • x(1,1)
  • x(1,)
  • None of these
If the curves y2=6x,9x2+by2=16 intersect each other at right angles, then the values of b is
  • 6
  • 72
  • 4
  • 92
The interval in which the  function f(x)=x3 increases less rapidly than g(x)=6x2+15x+5 is :
  • (,1)
  • (5,1)
  • (1,5)
  • (5,)
The values of x for which the tangents to the curves y=xcosx,y=sinxx are parallel to the axis of x are roots of  (respectively)
  • sinx=x,tanx=x
  • cotx=x,secx=x
  • cotx=x,tanx=x
  • tanx=x,cotx=x
Among all the critical points of a function f(x)=(4-x)|2-x|. Let 'a' and 'b' be the maximum and minimum values of their abscissate respectively then match the correct option. 
  • a+2b=7
  • 2a+b=7
  • 2a+b=5
  • 2a-b=5
The slope of the tangent to the curve y=sinx where it crosses the xaxis is 
  • 1
  • 1
  • ±1
  • ±2
The equation of normal to the curve y=|x2|x|| at x=2 is
  • 3y=2x+10
  • 3y=x+8
  • 2y=x+6
  • 2y=3x+10
The Point (s) on the cure y3+3x2=12y where the tangent is vertical (parallel to y-axis), is/are.
  • [±43,2]
  • (±113,1)
  • (0,0)
  • (±43,2)
0:0:1


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