List of practice Questions

Consider an art gallery whose walkways are shown as lines in the diagram. A black dot represents a junction of two walkways. A guard may be placed at a junction to watch over the walkways that join at that junction. The minimum number of guards needed to watch all the walkways is ________.
The 2nd of June is a Thursday in a certain year. Which day of the week is the 3rd of July in that year?
A coin with heads facing up is shown as (H) and a coin with tails facing up is shown as (T).
Six coins are placed in the Starting Arrangement, as shown in the figure below. A "step" is defined as interchanging a pair of adjacent coins without flipping them. The minimum number of steps needed to go from the Starting Arrangement to the Final Arrangement, as shown in the figure, is ________.
Exacerbate : Mitigate ::

Choose the option with the correct pair of words to fill the blank.
A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct?

In a population, patients who have high cholesterol also have high blood pressure (BP). Some patients with high BP also have diabetes. There are no patients who have both high cholesterol and diabetes. Furthermore,

1. the total number of patients with at least one of these conditions is 75,
2. the number of patients with high cholesterol is 10,
3. the number of patients with high BP is 45, and
4. the number of patients with only high BP and no other conditions is 20.

Then the number of patients who have both diabetes and high BP is
Four people P, Q, R, and S, of different ages, make the following observations.

P: I am younger than S.
Q: I am neither the youngest nor the oldest.
R: P is older than me.

Based on these observations, the youngest person is .
Circles \(C_1\), \(C_2\), and \(C_3\), with centers \(O_1\), \(O_2\), and \(O_3\), and radii \(r_1\), \(r_2\), and \(r_3\), respectively, touch each other as shown in the following figure. Given \(r_1 = 2\) cm, \(r_2 = 1\) cm and the angle \(\angle O_1O_3O_2\) is \(90^\circ\), \(r_3 = \) cm.

If \( I \) is an identity matrix, the polynomial equation that satisfies the Cayley-Hamilton theorem for the matrix \[ P = \begin{bmatrix} 2 & 1 \\ 0 & 3 \end{bmatrix} \] is
Let \( \hat{i} \) and \( \hat{j} \) be the unit vectors in the x and y direction, respectively. The divergence \( (\nabla . \vec{F}) \) of \( \vec{F} = x^2y\hat{i} + y^3x\hat{j} \) at the point \( (3,2) \) is
Which one of the following is a non-linear, second-order, and first-degree differential equation?
As per the Mohs scale of hardness, the correct sequence is
Match the distribution with its corresponding probability density/mass function.
Distribution typeProbability density/mass function
(P) Binomial Distribution(1) \( f(x) = \dfrac{1}{\sigma\sqrt{2\pi}}\exp\left(-\dfrac{1}{2}\left(\dfrac{x-\mu}{\sigma}\right)^2\right), \ \sigma>0 \)
(Q) Poisson Distribution(2) \( f(x) = \dbinom{n}{x}p^x(1-p)^{n-x}, \ x=0,1,2,...,n \)
(R) Normal Distribution(3) \( f(x) = \dfrac{\mu^x}{x!}\exp(-\mu), \ x=0,1,2,... \)
(S) Exponential Distribution(4) \( f(x) = \lambda\exp(-\lambda x), \ x>0 \)
As per the UNFC mineral resources classification system, the highest category of resource is indicated by
The best combination of explosive and initiation system for underwater blasting for rock breakage is
The firing sequence in a drivage is shown. The charge per hole for Sections 1, 2, and 3 are 2.0 kg, 3.0 kg, and 1.0 kg, respectively, and the delay between each section is 25 milliseconds. The maximum charge per delay, in \(kg\), is

The igneous intrusion along the bedding plane of the coal seam, as indicated by P, is known as

In remote sensing, the order of the wavelength bands of electromagnetic radiation used for data acquisition is
A simply supported beam is shown. The location at which the zero shear force is acting on the beam is
In a Slake Durability Index (SDI) test, a rock sample of 500 g undergoes two standard cycles of wetting and drying. The mass of the sample retained after the test is 400 g. The SDI of the sample, in %, is
Results from the permeability test of rock samples, E, F, and G are shown. The correct order of hydraulic conductivity (k) of the rock samples is

Note: Q is water flow rate, A is area of cross-section of the sample, h is water head, L is length of the sample.
The ideal load-deformation characteristic curve of a hydraulic prop is
A 20 m thick orebody is dipping at an angle of \(75^\circ\). The orebody and host rock are strong. It is proposed to deploy a 150-200 mm diameter drill for production. The suitable stoping method is
A gradually expanding duct fitted to the outlet of an exhaust fan is known as
The cobweb-like appearance in the radiograph of the lung of a miner can be diagnosed as