List of practice Questions

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: \[ \int_0^1 \int_x^1 \sin(y^2) \, dy \, dx \]
If for a suitable \( \alpha>0 \), \[ \lim_{x \to 0} \left( \frac{1}{e^{2x} - 1} - \frac{1}{\alpha x} \right) \] exists and is equal to \( l \) (\( |l|<\infty \)), then \( \alpha = 2, l = -\frac{1}{2} \) is given by
Let \[ P = \int_0^1 \frac{dx}{\sqrt{8 - x^2 - x^3}}. \] Which of the following statements is TRUE?
Let \( X \) be a random variable having a probability density function \( f \in \{ f_0, f_1 \} \), where
\[ f_0(x) = \begin{cases} 1, & 0 \leq x \leq 1 \\ 0, & \text{otherwise} \end{cases} \quad \text{and} \quad f_1(x) = \begin{cases} \frac{1}{2}, & 0 \leq x \leq 2 \\ 0, & \text{otherwise} \end{cases} \] For testing the null hypothesis \( H_0 : f = f_0 \) against \( H_1 : f = f_1 \), based on a single observation on \( X \), the power of the most powerful test of size \( \alpha = 0.05 \) equals