Exams › GATE › Engineering Mathematics
The number of atoms per unit cell and the number of slip systems, respectively, for a face-centered cubic (FCC) crystal are
- 3, 3
- 3, 12
- 4, 12
- 4, 48
Correct answer: 4, 12
Solution
An FCC unit cell has 4 atoms per unit cell. The number of slip systems in FCC crystals is 12, arising from the {111}<110> combinations.
Related GATE Engineering Mathematics questions
- The smallest positive root of the equation $x^5 - 5x^4 - 10x^3 + 50x^2 + 9x - 45 = 0$ lies in the range
- The second-order differential equation in the unknown function $u(x,y)$ is defined as $\frac{\partial^2 u}{\partial x^2} = 2$. Assuming $f=f(y)$, $g=g(y)$, and $h=h(y)$, the general solution of the differential equation is
- What are the eigenvalues of the matrix \([2, 1, 1;\, 1, 4, 1;\, 1, 1, 2]\)?
- A vector field \(\mathbf{p}\) and a scalar field \(r\) are given by \[ \mathbf{p}=(2x^2-3xy+z^2)\hat{i}+(2y^2-3yz+x^2)\hat{j}+(2z^2-3xz+x^2)\hat{k} \] \[ r=6x^2+4y^2-z^2-9xyz-2xy+3xz-yz \] Consider the statements P and Q. P: Curl of the gradient of the scalar field \(r\) is a null vector. Q: Divergence of curl of the vector field \(\mathbf{p}\) is zero. Which one of the following options is correct?
- The sum of the following infinite series is: \(\frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \frac{1}{5!} + \cdots\)
- A circle with center at \((x,y)=(0.5,0)\) and radius \(0.5\) intersects another circle with center at \((x,y)=(1,1)\) and radius \(1\) at two points. One of the points of intersection is:
⚔️ Practice GATE Engineering Mathematics free + battle 1v1 →