List of top Metallurgy Questions

The Newton-Raphson method is used to find the root of the equation f(x) \(\equiv\) x\(^2\) \(-\) x \(-\) 1 \(=\) 0. If the initial guess for the root is 1, then the estimate of the root after two iteration is

If the density function of X equals f(x) \(=\) \(\begin{cases} ce^{-2x}, & 0 \lt x \lt \infty \\ 0, & x \lt 0 \end{cases}\), then P(X \(\gt \) 2) is

Suppose that the average number of accidents occurring weekly on a particular stretch of a highway equals 3. The probability that there is at least two accidents in a week is

Under which one of the following conditions does the system of equations \(\begin{pmatrix} 1 & 2 & 4 \\ 2 & 1 & 2 \\ 1 & 2 & k-4 \end{pmatrix} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 6 \\ 4 \\ k \end{pmatrix}\) have a unique solution?

Let S be the surface of the cube bounded by x \(=\) 0, x \(=\) 1, y \(=\) 0, y \(=\) 1, z \(=\) 0, z \(=\) 1. The value of the surface integral \(\iint_S \vec{F} \cdot d\vec{s}\) of a vector field \(\vec{F} = 4xz \hat{i} - y^2 \hat{j} + yz \hat{k}\) over the entire surface S of the cube, is _____

The solution of the differential equation \(\frac{d^3y}{dx^3} - 5\frac{d^2y}{dx^2} + 8\frac{dy}{dx} - 4y = 0\) is

If y\(_1\) and y\(_2\) be two solutions of the differential equation \(\frac{d^2y}{dx^2} + 2y = f(x)\), then y\(_1\) + y\(_2\) is also solution of

If f(x, y) \(=\) x\(^3\)y \(+\) xy\(^3\) \(+\) e\(^{xy^2}\), then f\(_y\)(1, 1) is

If F(s) denotes the Laplace transform of some function f(t), then the Laplace transform of e\(^{-at}\)f(t), where a is a real constant, is

The modulus of resilience is equal to:

Alloy A has a narrow freezing range as compared to Alloy B. Considering both alloys solidify under identical conditions, which statement is correct regarding feeding?

Let A be a 3 \(\times\) 3 matrix such that the characteristic polynomial of A is f(x) \(=\) x\(^3\) \(-\) 4x\(^2\) \(-\) 11x \(+\) 30. If one of the eigenvalues of A is \(-\)3, then sum of the other two eigenvalues is

The fracture surface in ductile fracture generally shows

Heat transfer in vacuum occurs by:

The atomic packing factor (APF) of FCC structure is approximately

The formation of a passive layer decreases corrosion rate because it

The alumina obtained from Bayer process is converted to aluminium metal by:

The PCE (Pyrometric Cone Equivalent) value indicates:

Reverberatory furnaces are mainly used for:

The main purpose of vulcanization of rubber is to

In ferromagnetic materials, magnetic domains:

The coordination number of atoms in an FCC crystal structure is

The atomic packing factor (APF) for BCC structure is approximately

The rule of mixtures for composite modulus E\(_{\text{c}}\) in longitudinal loading is

Which of the following properties is most critical for a tool steel intended for high-speed machining applications?