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Calculus
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Q141

Open question

For a small value of h, the Taylor series expansion for f(x + h) is

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Q142

Open question

The divergence of the vector field

3xz i^+ 2 xy j^- y z^{2} k^

at a point (1, 1, 1) is equal to

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Q143

Open question

The right circular cone of largest volume that can be enclosed by a sphere of 1 m radius has a height of

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Q144

Open question

The area enclosed between the curves y² = 4x and x² = 4y is

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Q145

Open question

It is known that two roots of the nonlinear equation x³ - 6x² + 11x - 6 = are 1 and 3. The third root will be

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Q146

Open question

The derivative of f(x) = cos x can be estimated using the approximation

f^{'} (x) = \frac{f ( x + h ) - f ( x - h )}{2 h} .

The percentage error is calculated as

(\frac{Exact value - Approx value}{Exact value} \times 100)

The percentage error in the derivative of f(x) at

x = \frac{π}{6}

radian choosing h = 0.1 radian is

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Q147

Open question

A = xy a^_{x} + x^{2} a^_{y}, c \oint A \cdot d l

over the path shown in the figure is
Calculus mcq question image

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Q148

Open question

The expression

α \to 0 lim \frac{x ^{α} - 1}{α}

is equal to

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Q149

Open question

It is known that two roots of the non-linear equation x³ - 6x² + 11x - 6 = 0 and 1 and 3. The third root will be

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Q150

Open question

Consider the function y = x² - 6x + 9. The maximum value of y obtained when x varies over the interval 2 to 5 is

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Q151

Open question

If Z = e^{ax + by} F(ax - by); the value of

b \cdot \frac{\partial Z}{\partial x} + a \cdot \frac{\partial Z}{\partial y}

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Q152

Open question

Curl of vector V(x, y, z) = 2x²i + 3z²j + y³k at x = y = z = 1 is

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Q153

Open question

For a scalar function f(x, y, z) = x² + 3y² + 2z², the directional derivative at the point P(1, 2, -1) in the direction of a vector

i - j + 2 k

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Q154

Open question

The directional derivative of the function f(x, y) = x² + y² along a line directed from (0, 0) to (1, 1), evaluated at point x = 1, y = 1 is

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Q155

Open question

Value of the integral

c \oint (xydy - y^{2} dx)

, where c is the square cut from the first quadrant by the lines x = 1 and y = 1 will be (Use Green's theorem to change the line integral into double integral)

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Q156

Open question

The tangent to the curve represented by y = x

l

nx is required to have 45° inclination with the x-axis. The coordinates of the tangent point would be

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Q157

Open question

Consider the function f(x) = sin (x) in the interval

x \in [\frac{π}{4}, \frac{7 π}{4}] .

The number and location(s) of the local minima of this function are

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Q158

Open question

Euclidean norm (length) of the vector [4 -2 -6]^T is

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Q159

Open question

∇ × ∇ × P where P is a vector is equal to

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Q160

Open question

A parabolic cable is held between two supports at the same level. The horizontal span between the supports is L. The sag at the mid-span is h. The equation of the parabola is

y = 4 h (\frac{x ^{2}}{L ^{2}})

, where x is the horizontal coordinate and y is the vertical coordinate with the origin at the centre of the cable. The expression for the total length of the cable is

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Calculus
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