List of practice Questions

Check dams are constructed in association with main dam in the

A geological formation neither containing nor transmitting water is termed as

The characteristic rock of contact metamorphism is

The volcanic equivalent of nepheline syenite is

Identify the correct match between mineral/ore and its physical property.

A helically coiled ammonite Turrilites is differentiated from externally resembling Gastropoda Turritella by

The facial suture of trilobites running through the genal angle is known as

Which one of the following statements is correct for Class 1B (Parallel) folds?

En-echelon sigmoidal ‘gash’ veins indicate

Which one of the following primary sedimentary structures is NOT used for palaeocurrent analysis?

The age of the Patcham Formation is

Rivers that receive water from groundwater seepage are termed as

Conservative plate boundary is represented by

Which one of the following prismatic crystal forms belongs to the hexagonal crystal system?

Which one of the following minerals exhibits luminescence when exposed to ultraviolet light?

In which one of the following mass extinction periods trilobites became extinct?

Let \[ f(x, y) = \frac{xz y}{x^2 + y^2 + z^2}, \quad (x, y) \neq (0, 0). \] Then \[ \frac{\partial f}{\partial x} \text{ and } f \text{ are bounded and unbounded.} \]

Let \( 0<a_1<b_1 \), For \( n \geq 1 \), define \[ a_{n+1} = \sqrt{a_n b_n} \quad \text{and} \quad b_{n+1} = \frac{a_n + b_n}{2}. \] Then which one of the following is NOT TRUE?

The area of the surface \[ z = \frac{xy}{3} \] intercepted by the cylinder \[ x^2 + y^2 \leq 16 \] lies in the interval \[ \left( 20\pi, 22\pi \right) \]

For \( a>0, b>0 \), let \[ \mathbf{F} = \frac{xj - yk}{b x^2 + a y^2}. \] Let \[ C = \{(x, y) \in \mathbb{R}^2 | x^2 + y^2 = a^2 + b^2\}. \] Then the line integral \[ \oint_C \mathbf{F} \cdot d\mathbf{r} = \]

If \( \lim_{t \to \infty} \int_0^t e^{-x^2} dx = \frac{\sqrt{\pi}}{2} \), then \[ \lim_{t \to \infty} \int_0^t x^2 e^{-x^2} dx = \]

The flux of the vector field \[ \mathbf{F} = \left( \frac{2\pi x + 2x^2 y^2}{\pi} \right) \hat{i} + \left( \frac{2\pi x y - 4y}{\pi} \right) \hat{j} \] along the outward normal, across the ellipse \( x^2 + 16y^2 = 4 \) is equal to

The number of generators of the additive group \( \mathbb{Z}_{36} \) is equal to

Find the limit: \[ \lim_{n \to \infty} \sum_{k=1}^{n} \sin \left( \frac{\pi}{2} + \frac{5\pi}{2} \cdot \frac{k}{n} \right) = \]

Evaluate the integral: \[ \int_0^1 \int_x^1 \sin(y^2) \, dy \, dx \]