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CBSE Questions for Class 12 Commerce Maths Application Of Derivatives Quiz 4 - MCQExams.com

Let the parabolas y=x2+ax+b and y=x(cx) touch each other at the point (1,0). Then 
  • a=3
  • b=1
  • c=2
  • b+c=3
The curve xnan+ynbn=2 touches the line xa+yb=2 at the point
  • (b,a)
  • (a,b)
  • (1,1)
  • (1a,1b)
If the line joining the points (0,3) and (5,2) is the tangent to the curve y=cx+1 then the value of c is
  • 1
  • 2
  • 4
  • none of these
A point on the ellipse 4x2+9y2=36 where the tangent is equally inclided to the axes is
  • (913,413)
  • (913,413)
  • (913,413)
  • (413,913)
If error in  measuring the edge of a cube is k% then the percentage error in estimating its volume is
  • k
  • 3k
  • k3
  • none of these
The angle between two tangents to the ellipse x216+y29=1 at the points where the line y=1 cuts the curve is
  • π4
  • tan1627
  • π2
  • none of these
A tangent to the curve y=x0|t|dt, which is parallel to the line y=x, cuts off an intercept from the y-axis equal to
  • 1
  • 12
  • 12
  • 1
Angle between the tangents to the curve y=x25x+6 at the points (2,0) and (3,0) is
  • π2
  • π3
  • π6
  • π4
The number of tangents to the curve y=e|x| at the point (0,1) is
  • 2
  • 1
  • 4
  • 0
The curve y+exy+x=0 has a tangent parellel to y-axis at a point
  • (1,0)
  • (1,0)
  • (1,1)
  • (0,0)
The tangent to the curve y=ex drawn at the point (c,ec) intersects the line joining the points (c1,ec1)(c+1,ec+1)
  • on the left of x=c
  • on the right of x=c
  • at no point
  • at all points
For a[π,2π] and nZ, the critical points of f(x)=13sinatan3x+(sina1)tanx+a28a are 
  • x=nπ
  • x=2nπ
  • x=(2n+1)π
  • None of these
  • Assertion is true and Reason is true; Reason is a correct explanation for Assertion.
  • Assertion is True, Reason is true; Reason is not a correct explanation for Assertion.
  • Assertion is true, Reason is false
  • Assertion is false, Reason is true
y=4x2 and y=x2.
The two curves
  • intersect each other
  • touch each other
  • do not meet
  • represent parabola
If the normal to the curve y=f(x) at the point (3,4) makes an angle 3π4 with the positive x-axis then f(3) is equal to
  • 1
  • 34
  • 43
  • 1
Find the slopes of the tangents of the curve y=(x+1)(x3) at the points where it cuts the X-axis.
  • 4
  • 4
  • 2
  • 2
Find the points on the curve y=x3, the tangents at which are inclined at an angle of 60 to x-axis.
  • x=±13,y=13.13.
  • x=13,y=13.13.
  • x=±13,y=±13.13.
  • x=13,y=±13.13.
Find the points on the curve y=x/(1x2) where the tangents makes an angle of π/4 with x-axis
  • (3,23),(2,23)
  • (3,34),(3,34)
  • (3,32),(3,32)
  • none of these
Find the condition that the line Ax+By=1 may be a normal to the curve an1y=xn.
  • anB(B2+nA2)n=Annn.
  • an1B(B2+nA2)n1=Annn.
  • anB(B2+nA2)n1=Annn.
  • an1B(B2nA2)n1=Annn.
If the normal to the curve y=f(x) at the point (3,4) makes an angle 3π/4 with the positive x-axis, then f(3)=
  • 1
  • 0
  • 1
  • 3
The curve yexy+x=0 has a vertical tangent at the point 
  • (1, 1)
  • no point
  • (0, 1)
  • (1, 0)
The set of all values of x for which the function f(x)=(k23k+2)(cos2x4sin2x4)+(k1)x+sin1 does not posses critical points is 
  • (4,4)
  • (0,4)
  • (0,1)(1,4)
  • (0,2)(2,4)
 Determine the intervals of monotonicity of f(x)=log|x|. 
  • increasing for x>0
  • increasing for x<0
  • decreasing for x>0
  • decreasing for x<0
If xcosα+ysinα=p touches x2+a2y2=a2, then
  • p2=a2sin2α+cos2α
  • p2=a2cos2α+sin2α
  • 1/p2=sin2α+α2cos2α
  • 1/p2=cos2α+α2sin2α
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
Find the co-ordinates of the points on the curve y=x/(1+x2) where the tangent to the curve has greatest slope.
  • (3,34)
  • (0,0)
  • (3,34)
  • (1,12)
The line y=x is a tangent to the parabola y=ax2+bx+c at the point x=1.If the parabola passes through the point (1,0), then determine a,b,c.
  • a=12,b=14,c=13.
  • a=14,b=12,c=14.
  • a=2,b=1,c=4.
  • a=4,b=2,c=4.
Find dydx ify=[x+x+x]1/2, at x=1
  • 3+4282(1+2)
  • Not defined
  • 0
  • e
A and B are points (2,0) and (1,3) on the curve y=4x2. If the tangent at P on the curve be parallel to chord AB, then co-ordinates of point P are 
  • (13,53)
  • (12,154)
  • (12,154)
  • (13,15)
The line xa+yb=1 touches the curve y=bex/a at the point
  • (a,b/a)
  • (a,b/a)
  • (a,a/b)
  • None of these
If the line, ax+by+c=0 is a normal to the curve xy=2, then
  • a<0,b>0
  • a>0,b<0
  • a>0,b>0
  • a<0,b<0
The function f(x)=2log(x2)x2+4x+1  increases in the interval
  • (1,2)
  • (2,3)
  • (5/2,3)
  • (2,4)
The critical points of the function f(x)=|x1|x2 are
  • 0
  • 1
  • 2
  • -1
If f(0)=0 and f(x)>0 for all x>0, then f(x)x
  • decreases on (0,)
  • increases on (0,)
  • decreases on (1,)
  • neither increases nor decreases on (0,)
The interval(s) of decrease of  of the function f(x)=x2log276xlog27+(3x218x+24)log(x26x+8) is
  • (31+1/3e,2)
  • (4,3+1+1/3e)
  • (3,4+1+1/3e)
  • none of these
The slope of the tangent to the curve represented by x=t2+3t8 and y=2t22t5 at the point M(2,1) is

  • 7/6
  • 2/3
  • 3/2
  • 6/7
The number of critical points of the fuction f(x), where f(x)=|x2|x3 are
  • 0
  • 1
  • 3
  • 4
The value of a for which the function f(x)=(4a3)(x+log5)+2(a7)cot(x/2)sin2(x/2) does not possess critical points is
  • (,4/3)
  • (,1)
  • (1,)
  • (2,)
The critical points of the function f(x)=(x2)2/3(2x+1) are
  • 1,2
  • 1
  • 1,12
  • 1,2
The coordinates of the point on the curve (x2+1)(y3)=x where a tangent to the curve has the greatest slope are given by
  • (3,3+3/4)
  • (3,33/4)
  • (0,3)
  • none of these
The angle at which the curve y=kekx intersects the y -axis is
  • tan1(k2)
  • cot1(k2)
  • sin1(1/1+k4)
  • sec1(1/1+k4)
The lines tangent to the curves y3x2y+5y2x=0 and x4x3y2+5x+2y=0 at the origin intersect at an angle θ equal to
  • π6
  • π4
  • π3
  • π2
Let f(x)=x3+ax+b with ab and suppose the tangent lines to the graph of f at x=a and x=b have the same gradient Then the value of f(1) is equal to
  • 0
  • 1
  • 13
  • 23
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 the values of x for which the curve has a negative gradient are
  • x > -1
  • x < 1
  • x < -1
  • 1×1
If f(x)=g(x)(xa)2, where g(a)0 and g is continuous at x=a then
  • f is increasing near a if g(a)>0
  • f is increasing near a if g(a)<0
  • f is decreasing near a if g(a)>0
  • f is decreasing near a if g(a)<0
The curve y=ax3+bx2+cx+8  touches x-axis at P(2,0) and cuts the y-axis at a point Q(0,8) where its gradient isThe values of a, b, c are respectively

  • 12,34,3
  • 3,12,4
  • 12,74,2
  • none of these
Suppose f(x) exists for each x and h(x)=f(x)(f(x))2+(f(x))3 for every real number x. Then
  • h is increasing whenever f is increasing
  • h is increasing whenever f is decreasing
  • h is decreasing whenever f is decreasing
  • nothing can be said in general.
The critical points of the function f(x)=(x2)2/3(2x+1) are
  • 1 and 2
  • 1 and 12
  • 1 and 2
  • 1
The graph a function f is given. On what interval is f increasing ?
255196.png
  • (1,3]
  • (3,1)
  • (3,1]
  • none of these
The points of contact of the vertical tangents x=23sinθ, y=3+2cosθ are
  • (2,5),(2,1)
  • (1,3),(5,3)
  • (2,5),(5,3)
  • (1,3),(2,1)
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Practice Class 12 Commerce Maths Quiz Questions and Answers