Statement I is correct, statement II is correct, statement II is correct, Statement II is correct explanation for Statement I

Statement I is incorrect, Statement II is correct

statement I is correct, statement II is correct ; Statement II is correct explanation for statement I

Statement I is incorrect, statement II is incorrect

neither minima nor maxima at x = 0

JEE Questions for Maths Applications Of Derivatives Quiz 1

For the function f(x) = xe^x the point

0%
x = 0 is a maximum
0%
x = 0 is a minimum
0%
x = -1 is a maximum
0%
x = -1 is a minimum

The equation e^{x – 8} + 2x − 17 = 0 has :

0%
one real root
0%
two real roots
0%
eight real roots
0%
four real roots

The minimum value of sin x + cos x is

0%
0%
2)
0%
0%
0%
1

If there is an error of k% in measuring the edge of a cube, then the percent error in estimating its volume is

0%
k
0%
3k
0%
k/3
0%
None of these

Maths-Applications of Derivatives-8986.png

0%
2.0000
0%
2.1001
0%
2.0125
0%
2.0500

If the diagonal of a square is changing at the rate of 0.5 cms^-1 . Then, the rate of change of area, when the area is 400 cm², is

0%
0%
2)
0%
0%
0%

A spherical iron ball of radius 10 cm, coated with a layer of ice of uniform thickness, melts at a rate of 100 it cm³/min. The rate at which the thickness layer decreases, when the thickness of ice is 5 cm, is

0%
1 cm/min
0%
2 cm/min
0%
1/376 cm/min
0%
5 cm/min
0%
3 cm/min

A man of 2 m height walks at a uniform speed of 6 km/h, away from a lamp post of 6 m height. The rate at which the length of his shadow increase is

0%
2 km/h
0%
1 km/h
0%
3 km/h
0%
6 km/h

The radius of a cylinder is increasing at the rate of 3 m/s and its altitude is decreasing at the rate of 4 m/s. The rate of change of volume, when radius is 4 m and altitude is 6 m, is

0%
80 π cu m/s
0%
144 π cu m/s
0%
80 cu m/s
0%
64 cu m/s

A point on the parabola y² = 18x at which the ordinate increases at twice the rate of the abscissa is

0%
(2, 4)
0%
(2, -4)
0%
(-9/8, 9/2)
0%
(9/8, 9/2)

If the distance s covered by a particle in time t is proportional to the cube root of its velocity, then the acceleration is

0%
a constant
0%
proportional to s3
0%
proportional to 1/s3
0%
proportional to s5
0%
proportional to 1/s5

The distance travelled by a motorcar in t sec after the breakes are applied is s feet, where s = 22t — 12t². The distance travelled by the car before it stops is

0%
10.08 ft
0%
10 ft
0%
11 ft
0%
11.5 ft

If the radius of a circle is increasing at a uniform rate of 2 cm/s. The area of increasing of area of circle, at the instant when the radius is 20 cm, is

0%
70 π cm2 / s
0%
70 cm2 / s
0%
80 π cm2 / s
0%
80 cm2 / s

The circumference of a circle is measured as 56 cm with an error 0.02 cm. The percentage error in its area is

0%
1/7
0%
1/28
0%
1/14
0%
1/56

A particle moves in a straight line, so that s = √t then its acceleration is proportional to

0%
(velocity)3
0%
velocity
0%
(velocity)2
0%
(velocity)3/2

If the radius of a circular plate is increasing at the rate of 0.01cm /s, when the radius is 12 cm. Then, the rate at which the area increases is

0%
0.24 π sq cm/s
0%
60 π sq cm/s
0%
24 π sq cm/s
0%
1.2 π sq cm/s

If a stone thrown upwards, has equation of motion s = 490t - 4.9t² . Then, the maximum height reached by it is

0%
24500
0%
12500
0%
12250
0%
25400

The rate of change of the surface area of the sphere of radius r, when the radius is increasing at the rate of 2 cm/s is proportional to

0%
1/r2
0%
1/r
0%
r2
0%
r

The equation of normal of the curve y = (1 + x)^y + sin^-1 (sin² x) at x = 0 is

0%
x + y = 1
0%
x - y = 1
0%
x + y = - 1
0%
x - y = - 1

Maths-Applications of Derivatives-9007.png

0%
1
0%
2
0%
3
0%
infinitely many

The triangle formed by the tangent to the curve f (x) = x² + bx - b at the point (1,and the ordinate axes lies in the first quadrant. If its area is 2, then the value of b is

0%
-1
0%
3
0%
-3
0%
1

Maths-Applications of Derivatives-9010.png

0%
0%
2)
0%
0%

The minimum radius vector of the curve
Maths-Applications of Derivatives-9016.png

0%
a - b
0%
a + b
0%
2a + b
0%
None of these

The local minimum value of the function f ' given by f (x) = 3 + |x|, x ϵ R is

0%
-1
0%
3
0%
1
0%
0

The angle of intersection between the curves y = [|sin x| + |cos x| ] and x² + y² = 10, where [x] denotes the greatest integer ≤ x , is

0%
tan-1 3
0%
tan-1 (-3)
0%
tan-1 (√3)
0%
tan-1 (1/√3)

If y = 4x + 3 is parallel to the tangent of the parabola y² = 12x, then is distance from the normal parallel to the given line is

0%
0%
2)
0%
0%

Maths-Applications of Derivatives-9025.png

0%
neither maximum nor minimum
0%
only one maximum
0%
only one minimum
0%
None of the above

Maths-Applications of Derivatives-9027.png

0%
Statement I is incorrect, Statement II is correct
0%
statement I is correct, statement II is correct ; Statement II is correct explanation for statement I
0%
Statement I is correct, statement II is correct, statement II is correct, Statement II is correct explanation for Statement I
0%
Statement I is incorrect, statement II is incorrect

The maximum value of the function
Maths-Applications of Derivatives-9029.png

0%
1
0%
9/8
0%
13/12
0%
17/8

The least value of the function f(x) = ax + b/x, a > 0, b > 0, x > 0 is

0%
0%
2)
0%
0%

If f(x) = x³ e^-3x, x > 0. then, the maximum value of f(x) is

0%
e-3
0%
3e-3
0%
27e-9
0%
∞

The length of the normal to the curve y = a cosh (x/a) at any point varies as

0%
ordinate
0%
abscissa
0%
Square of the abscissa
0%
square of the ordinate

If the normal to the curve y = f(x) at the point (3,make an angle 3π/4 with the positive X - axis, then f '(is

0%
1
0%
-1
0%
- (3/4)
0%
3/4

The coordinates of the point on the curve y = x² - 3x + 2, where the tangent is perpendicular to the straight line y = x are

0%
(0, 2)
0%
(1, 0)
0%
(-1, 6)
0%
(2, -2)

Maths-Applications of Derivatives-9040.png

0%
1
0%
0
0%
-(1/2)
0%
-1

If the line ax + by + c = 0 is a tangent to the curve xy = 4, then

0%
a < 0, b > 0
0%
a ≤ 0, b > 0
0%
a < 0, b < 0
0%
a ≤ 0, b < 0

The minimum value of f(x) = e^{(x⁴ - x³ + x²)} is

0%
e
0%
-e
0%
1
0%
-1

The equation of the tangent to the curve x² - 2xy + y² + 2x + y = 6 = 0 at (2,is

0%
2x + y - 6 = 0
0%
2y + x - 6 = 0
0%
x + 3y - 8 = 0
0%
3x + y - 8 = 0
0%
x + y - 4 = 0

Maths-Applications of Derivatives-9045.png

0%
minimum at x = 0
0%
maxima at x = 0
0%
neither minima nor maxima at x = 0
0%
None of the above

The maximum value of function f(x) = sinx(1 + cosx) x ϵ R is

0%
0%
2)
0%
0%

The normal at point (1,of the curve y² = x³ is parallel to the line

0%
3x - y - 2 = 0
0%
2x + 3y - 7 = 0
0%
2x - 3y + 1 = 0
0%
2y - 3x + 1 = 0

The abscissae of the points, where the tangent to curve y = x³ - 3x² - 9x + 5 is parallel to X - axis, are

0%
x = 0 and 0
0%
x = 1 and -1
0%
x = 1 and -3
0%
x = -1 and 3

The point of the curve y² = 2(x -at which the normal is parallel to the line y - 2x + 1 = 0 is

0%
(5, 2)
0%
(-(1/2), -2)
0%
(5, -2)
0%
(3/2, 2)

Divide 12 into two parts such that the product of the square of one part and the fourth power of the second part is maximum are

0%
6, 6
0%
5, 7
0%
4, 8
0%
3, 9

The stone is thrown vertically upwards and the height x feet reached by the stone in t sec, is given by x = 80t - 16t². the stone reaches the maximum height in

0%
2 s
0%
2.5 s
0%
3 s
0%
1.5 s

If ax² + bx + 4 attains its minimum value - 1 at x = 1, then the values of a and b are respectively

0%
5, -10
0%
5, -5
0%
10, -5
0%
10, 10

Maths-Applications of Derivatives-9058.png

0%
y - 2x = 6 + log 2
0%
y + 2x = 6 + log 2
0%
y + 2x = 6 - log 2
0%
y + 2x = -6 + log 2
0%
y - 2x = -6 + log 2

The minimum value of e^{(2x² - 2x + 1)sin²x} is

0%
0
0%
1
0%
2
0%
3

If θ is angle between the curves xy = 2 and x² + 4y = 0, then tan θ is equal to

0%
1
0%
-1
0%
2
0%
3

The abscissa of the point on the curve y = a(e^x/a + e^-x/a ), where the tangent is parallel to the X - axis is

0%
0
0%
a
0%
2a
0%
-2a

JEE Questions for Maths Applications Of Derivatives Quiz 1 - MCQExams.com

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Practice Maths Quiz Questions and Answers

JEE Questions for Maths Applications Of Derivatives Quiz 1 - MCQExams.com

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Practice Maths Quiz Questions and Answers

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