Statement I is correct, Statement II is also correct; Statement II is not the correct equation of Statement I

Statement I is correct, Statement II is also correct; Statement II is the correct explanation of Statement I

Statement I is correct, statement II is correct

Statement I is incorrect, Statement II is correct

The function f ( x ) = x 3 + a x 2 + b x + c, a 2 ≤ 3b has

one maximum and one minimum value

a local minima at x = 1 and a local maxima at x = - 1

a local maxima at x = 1 and a local minima at x = - 1

absolute maxima at x = 1 and absolute minima at x = -1

absolute minima at x = 1 and absolute maxima at x = -1

Both A and R are correct and R is the correct reason for A

Both A and r correct but R is not the correct reason for A

JEE Questions for Maths Applications Of Derivatives Quiz 4

Maths-Applications of Derivatives-9219.png

0%
Statement I is correct, Statement II is also correct; Statement II is the correct explanation of Statement I
0%
Statement I is correct, Statement II is also correct; Statement II is not the correct equation of Statement I
0%
Statement I is correct, statement II is correct
0%
Statement I is incorrect, Statement II is correct

The equation of the tangent of the curve y = x + 4/x² that is parallel to the X - axis is

0%
y = 0
0%
y = 1
0%
y = 2
0%
y = 3

The point in the interval [0, 2π], where f(x) = e^x sin x has maximum slope is

0%
π/4
0%
π/2
0%
π
0%
3π/2

The point on the curve x² + y² = a², y ≥ 0 at which the tangent is parallel to X - axis is

0%
(a, 0)
0%
(-a, 0)
0%
0%
(0, a)
0%
(0, a2)

The angle between the curves y = x² and y² - x = 0 at the point (1,is

0%
π/2
0%
tan-1 4/3
0%
π/3
0%
π4
0%
tan-1 3/4

The distance between the origin and the normal to the curve y = e^2x + x² at x = 0 is

0%
2
0%
2/√3
0%
2/√5
0%
1/2
0%
1/√5

Let P(x) = x⁴ + ax³ + bx² + cx + d such that x = 0 is the only real root of P'(x) = 0. If P(-1), then in the interval [-1, 1]

0%
P(-is the minimum and P(is the maximum of P
0%
P(-is not minimum but P(is the maximum of P
0%
P(-is minimum and P(is not maximum of P
0%
Neither P(-is the minimum and P(nor is the maximum of P

The shortest distance between the line y - x = 1 and the x = y² is

0%
0%
2)
0%
0%

The equation of the tangent to the curve y = 4e^x at (-1, -4/e) is

0%
y = - 1
0%
- (4/e)
0%
x = - 1
0%
x = -4/e

Maths-Applications of Derivatives-9234.png

0%
16
0%
12
0%
8
0%
4
0%
2

The equation of the tangent to the curve y = 4e^-x/4 at the point, where the curves crosses Y - axis is equal to

0%
3x + 4y = 16
0%
4x + y = 4
0%
x + y = 4
0%
4x - 3y = -12
0%
x - y = -4

The angle between the curves y = a^x and y = b^x is equal to

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

If a and b are positive numbers such that a > b, then the minimum value of a sec θ - b tan θ (where, 0 < θ < π/is

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

The angle between y² = x and x² = y at the origin is

0%
2 tan-1 (3/4)
0%
tan-1 (4/3)
0%
π/2
0%
π/4

The length of the normal to the curve x = a(θ + sin θ), y = a(1 - cos θ) at θ = π/2 is

0%
2a
0%
a/2
0%
a/√2
0%
√2a

The smallest circle with centre on Y - axis and passing through the point (7,has radius

0%
√58
0%
7
0%
3
0%
4

If sum of two numbers is 6, then the minimum value of the sum of their reciprocals is

0%
6/5
0%
3/4
0%
2/3
0%
1/2

The function f(x) = x³ + ax² + bx + c, a² ≤ 3b has

0%
one maximum value
0%
one minimum value
0%
no extreme value
0%
one maximum and one minimum value

If f(x) = x² + 4x + 1, then

0%
f(x) = f(-x), ∀ x
0%
f(x) ≠ 1, ∀ x = 0
0%
f ''(x) > 0, ∀ x
0%
f(x) > 1, for x ≤ 4

If the cubic equation x³ - px + q has three distinct real roots, where p > 0 and q < 0. Then, which one of the following is correct ?

0%
0%
2)
0%
0%

The slope of the tangent to the curves x = t² + 3t - 8, y = 2t² -2t - 5 at the point (2, -is

0%
22/7
0%
6/7
0%
-6
0%
-7

Maths-Applications of Derivatives-9262.png

0%
1
0%
2/e
0%
e
0%
1/e

Maths-Applications of Derivatives-9264.png

0%
x = 0
0%
x = 1
0%
x = 4
0%
x = 3

If m and M respectively denote the minimum and maximum of f(x) = (x - 1)² + 3 for x ϵ [-3, 1], then the ordered pair (m, M) is equal to

0%
(-3, 9)
0%
(3, 19)
0%
(-19, 3)
0%
(-19, -3)

The length of the subtangent at (2,to the curve x⁵ = 2y⁴ is

0%
5/2
0%
8/5
0%
2/5
0%
5/8

The equation of the normal to the curve y⁴ = ax³ at (a, a) is

0%
x + 2y = 3a
0%
3x - 4y + a = 0
0%
4x + 3y = 7a
0%
4x - 3y = 0

If y = 4x - 5 is a tangent to the curve y² = px³ + q at (2, 3), then

0%
p = 2, q = -7
0%
p = - 2, q = 7
0%
p = -2, q = -7
0%
p = 2, q = 7

Maths-Applications of Derivatives-9270.png

0%
a local maxima at x = 1 and a local minima at x = - 1
0%
a local minima at x = 1 and a local maxima at x = - 1
0%
absolute maxima at x = 1 and absolute minima at x = -1
0%
absolute minima at x = 1 and absolute maxima at x = -1

The normal to a curve at P(x, y) meets the X - axis at G. If the distance of G from the origin is twice the abscissa of P, then the curve is a

0%
ellipse
0%
parabolla
0%
circle
0%
hyperbola

The minimum value of 2x + 3y, when xy = 6 is

0%
9
0%
12
0%
8
0%
6

If the function f(x) = x² e^-2x, x > 0. Then, the maximum value of f(x) is

0%
1/e
0%
1/2e
0%
1/e2
0%
4/e4

The angle between the tangents at those points on the curve x = t² + 1 and y = t² - 1 - 6, where it meets X - axis is

0%
0%
2)
0%
0%

If the function f(x) = 2x³ - 9ax² + 12a²x + 1 attains its maximum and minimum at p and q respectively, such that p² = q, then a equals

0%
0
0%
1
0%
2
0%
None of these

The point on the curve y² = x, the tangent at which makes an angle 45^o with X - axis is

0%
0%
2)
0%
0%

A missile is fired from the ground level rises x metres vertically upwards in t sec, where x = 100t - (25/2)t². The maximum height reached is

0%
200 m
0%
125 m
0%
190 m
0%
300 m

The maximum slope of the curve y = x + 3x² + 2x - 27 is

0%
5
0%
-5
0%
1/5
0%
None of these

Maths-Applications of Derivatives-9288.png

0%
- (1/3)
0%
- (1/4)
0%
1/4
0%
1/6

Maths-Applications of Derivatives-9290.png

0%
(b, a)
0%
(-b, -a)
0%
(a, b)
0%
None of these

The length of tangent, subtangent, normal and subnormal for the curve y = x² + x - 1 at (1,are A, B C and D respectively, then their increasing order is

0%
B, D, A, C
0%
B, A, C, D
0%
A, B, C, D
0%
B, A, D, C

The condition f(x) = x³ + px² + qx + r (x ϵ R) to have no extreme value, is

0%
p2 < 3q
0%
2p2 < q
0%
p2 < 1/4q
0%
p2 > 3q

Maths-Applications of Derivatives-9294.png

0%
Both A and R are correct and R is the correct reason for A
0%
Both A and r correct but R is not the correct reason for A
0%
A is correct, R is incorrect
0%
A is incorrect, R is correct

Maths-Applications of Derivatives-9296.png

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

On the interval [0, 1], the function x²⁵ (1 - x)⁷⁵ takes its maximum value at the point

0%
0
0%
1/4
0%
1/2
0%
1/3

Maths-Applications of Derivatives-9299.png

0%
a local maximum
0%
a local minimum
0%
no local extremum
0%
no local maximum

Maths-Applications of Derivatives-9301.png

0%
x = - 2
0%
x= 0
0%
x = 1
0%
x = 2

Angle between the tangents to the curve y = x² - 5x + 6 at the points (2,and (3,is

0%
π/2
0%
π/6
0%
π/4
0%
π/3

If the curve y = 2x³ + ax² + bx + c passes through the origin and the tangent drawn to it at x = - 1 and x = 2 are parallel to the X - axis, then the values of a, b and c are respectively

0%
12, -3 and 0
0%
-3, -12 and 0
0%
-3, 12 and 0
0%
3, -12 and 0

The tangent and the normal drawn to the curve y = x² - x + 4 at P(1,cut the X - axis at A and B, respectively. If the length on the subtangent drawn to the curve at P is equal to the length of the subnormal, then the area of the ∆PAB(in sq units) is

0%
4
0%
32
0%
8
0%
16

If the line ax + by + c = 0 is a normal to the curve xy = 1, then

0%
a > 0, b > 0
0%
a > 0, b < 0
0%
a < 0, b < 0
0%
Data is insufficient

The maximum value of x^1/x is

0%
1/ee
0%
e
0%
e1/e
0%
1/e

JEE Questions for Maths Applications Of Derivatives Quiz 4 - MCQExams.com

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Practice Maths Quiz Questions and Answers

JEE Questions for Maths Applications Of Derivatives Quiz 4 - MCQExams.com

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Practice Maths Quiz Questions and Answers

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