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Mere Teacher · Previous Year Questions
JEE Main Mathematics · Application of Derivatives · Set 5 (Q121-150)
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121.
Equation of tangent to the curve y=x+x24 which is parallel to x-axis is
(1)y=8
(2)y=0
(3)y=3
(4)y=2
122.
The rate at which the population of a city increses varies as the population present. Within the period of 30 years, the population grew from 20 lakhs to 40 lakhs. Then, the population after a further period of 15 years will be (Take 2=1.41 )
(1)56 lakhs
(2)57.4 lakhs
(3)56.4 lakhs
(4)60 lakhs
123.
x1,x2,∈N. If a line having slope 2 is a tangent to the curve y=x4−6x3+13x2−10x+5 at points P(x1,y1) and Q(x2,y2), then x1x2+y1y2=
(1)17
(2)-5
(3)13
(4)-10
124.
Let the function f(x)=3x+x3+3,x=0 be strictly increasing in (−∞,α1)∪(α2,∞) and strictly decreasing in (α3,α4)∪(α4,α5). Then ∑i=15αi2 is equal to
(1)48
(2)40
(3)36
(4)28
125.
If x and y are two positive numbers such that x+y=32, then the minimum value of x2+y2 is,
(1)500
(2)256
(3)1024
(4)512
126.
If the curve y=ax2+bx+c,x∈R, passes through the point (1,2) and the tangent line to this curve at origin is y=x, then the possible values of a,b,care :
(1)a=1,b=1,c=0
(2)a=−1,b=1,c=1
(3)a=1,b=0,c=1
(4)a=21,b=21,c=1
127.
Let f:(−1,∞)⟶R be defined by f(0)=1 and f(x)=x1loge(1+x),x=0 Then the function f:
(1)increases in (−1,∞)
(2)increases in (−1,0) and decreases in (0,∞)
(3)decreases in (−1,0) and increases in (0,∞)
(4)decreases in (−1,∞)
128.
The interval in which the function f(x)=x3−6x2+9x+10 is increasing in
(1)(−∞,1)∪(3,∞)
(2)[1,3]
(3)(−∞,1]∪[3,∞)
(4)(−∞,−1]∪[3,∞)
129.
Let a be a fixed positive real number and n be an arbitrary constant. For the curve y=an−1xn, if the length of the subnormal at any point (α,β) is proportional to a2, then n=
(1)2
(2)1
(3)0
(4)23
130.
The function f(x) is defined by f(x)=(x+2)e−x is
(1)decreasing in (−∞,−1) and increasing in (−1,∞)
(2)decreasing for all x
(3)increasing for all x
(4)monotonically decreasing in (−1,∞) and monotonically increasing in (−∞,−1)
131.
The diameter and altitude of a right circular cone, at a certain instant, were found to be 10cm and 20cm respectively. If its diameter is increasing at a rate of 2cm/s, then at what rate must its altitude change, in order to keep its volume constant?
(1)4cm/s
(2)6cm/s
(3)−4cm/s
(4)−8cm/s
132.
For the function f(x)=(cosx)−x+1,x∈R, between the following two statements (S1) f(x)=0 for only one value of x in [0,π]. (S2) f(x) is decreasing in (0,2π) and increasing in (2π,π).
(1)Both (S1) and (S2) are correct.
(2)Both (S1) and (S2) are incorrect.
(3)Only (S2) is correct.
(4)Only (S1) is correct.
133.
The local maximum of y=x3−3x2+5 is attained at
(1)x=0
(2)x=2
(3)x=1
(4)x = -1
134.
The function, f(x)=(3x−7)x2/3,x∈R is increasing for all x lying in:
(1)(−∞,0)∪(1514,∞)
(2)(−∞,0)∪(73,∞)
(3)(−∞,−1514)∪(0,∞)
(4)(−∞,1514)
135.
Let f(x)=2x+tan−1x and g(x)=loge(1+x2+x), x∈(0,3). Then
(1)Three exists x∈0,3 such f’(x)<g’(x)
(2)max f(x)>fmaxg(x)
(3)Three exists 0<x1<x2<3 such that f(x)<f(x),⩝∈(x1,x2)
(4)min f’(x)=1+maxg’(x)
136.
The lengths of the sub-tangent, ordinate and the sub-normal are in
(1)A.G.P.
(2)A.P.
(3)H.P
(4)G.P.
137.
If f(x)=x2+1x is increasing function, then the value of x lies in
(1)R
(2)(−∞,−1)
(3)(1,∞)
(4)(−1,1)
138.
Let g:R→R be a non constant twice differentiable such that g’(21)=g’(23). If a real valued function f is defined as f(x)=21[g(x)+g(2−x)], then
(1)f’’(x)=0 for atleast two x in (0,2)
(2)f’’(x)=0 for exactly one x in (0,1)
(3)f’’(x)=0 for no x in (0,1)
(4)f’(23)+f’(21)=1
139.
The function f(x)=x2−6x−16x,x∈R−-2,8
(1)decreases in (−2,8) and increases in (-∞,-2)∪(8,∞)
(2)decreases in (−∞,−2)∪(−2,8)∪(8,∞)
(3)decreases in (−∞,−2) and increases in (8,∞)
(4)increases in (−∞,−2)∪(−2,8)∪(8,∞)
140.
The angle between the curves x2=8y and xy=8 is
(1)tan−1(3−1)
(2)tan−1(−3)
(3)tan−1(−3)
(4)tan−1(3−1)
141.
The point on the curve y=x−1 where the tangent is perpendicular to the line 2x+y−5=0 is
(1)(2,−1)
(2)(10,3)
(3)(2,1)
(4)(5,−2)
142.
If 5f(x)+4f(x1)=x2−2,∀x=0 and y=9x2f(x), then y is strictly increasing in :
(1)(0,51)∪(51,∞)
(2)(−51,0)∪(51,∞)
(3)(−51,0)∪(0,51)
(4)(−∞,51)∪(0,51)
143.
If a curve passes through the point (1,1) and at any point (x,y) on the curve, the product of the slope of its tangent and x co-ordinate of the point is equal to the y co-ordinate of the point, then the curve also passes through the point
(1)(−1,2)
(2)(2,2)
(3)(3,0)
(4)(3,0)
144.
The rate of change of volume of a sphere with respect to its surface area when the radius is 4cm is
(1)2cm3/cm2
(2)4cm3/cm2
(3)8cm3/cm2
(4)6cm3/cm2
145.
Let f:(0,1)→R be a function defined byf(x)=1−e−x1, and g(x)=(f(−x)−f(x)). Consider two statements (I)g is an increasing function in (0,1) (I)Ig is one – one in (0,1) Then
(1)Only (I) is true
(2)Only (II) is true
(3)Neither (I) nor (II) is true
(4)Both (I) and (II) are true
146.
V is the set of points on the curve y3−3xy+2=0 where the tangent is vertical then V=
(1)Φ
(2){(1,0)}
(3){(1,1)}
(4){(0.0)(1.1)}
147.
The local maximum value of the function f(x)=−(x−2)3(x+2)2 is
(1)0
(2)55123⋅82
(3)125
(4)5629⋅32
148.
If the equation of the normal to the curve y=(x+b)(x−2)x−a at the point (1,−3) is x−4y=13, then the value of a+b is equal to ______
149.
Let the normals at all the points on a given curve pass through a fixed point (a,b). If the curve passes through (3,−3) and (4,−22), and given that a−22b=3, then (a2+b2+ab) is equal to
150.
Let the tangent to the curve x2 + 2x -4y + 9 = 0 at the point P(1, 3) on it meet the y-axis at A. Let the line passing through P and parallel to the line x - 3y = 6 meet the parabola y2 = 4x at B. If B lies on the line 2x-3y = 8, then (AB)2 is equal to_______.
