if `a=b ne c` and `alpha=beta=gamma=90^(@)`, the crystal system is

Options

A. cubic
B. rhombic
C. tetragonal
D. monoclinic

Explanation

To determine the crystal system based on the provided parameters, we will analyze the given conditions step by step.

### Given:
- \( a = b \neq c \)
- \( \alpha = \beta = \gamma = 90^\circ \)

### Step 1: Identify the conditions for the crystal systems
We need to recall the definitions of the various crystal systems based on the lengths of the axes and their angles:

1. **Cubic**: \( a = b = c \) and \( \alpha = \beta = \gamma = 90^\circ \)
2. **Tetragonal**: \( a = b \neq c \) and \( \alpha = \beta = \gamma = 90^\circ \)
3. **Orthorhombic**: \( a \neq b \neq c \) and \( \alpha = \beta = \gamma = 90^\circ \)
4. **Hexagonal**: \( a = b \neq c \) and \( \alpha = \beta = 90^\circ \), \( \gamma = 120^\circ \)
5. **Rhombohedral**: \( a = b = c \) and \( \alpha = \beta = \gamma \neq 90^\circ \)
6. **Monoclinic**: \( a \neq b \neq c \) and two angles are \( 90^\circ \) while one is not.
7. **Triclinic**: \( a \neq b \neq c \) and all angles are not equal to \( 90^\circ \).

### Step 2: Analyze the given parameters
From the given conditions:
- \( a = b \) indicates that two axes are equal.
- \( c \) is not equal to \( a \) (or \( b \)).
- All angles \( \alpha, \beta, \gamma \) are equal to \( 90^\circ \).

### Step 3: Match with the crystal systems
The only crystal system that matches the conditions \( a = b \neq c \) and \( \alpha = \beta = \gamma = 90^\circ \) is the **Tetragonal** system.

### Conclusion
Thus, the crystal system is **Tetragonal**.

---