List of practice Questions

Which of the following equations is correct for the Pozzolanic reaction?
Four different soils are classified as CH, ML, SP, and SW, as per the Unified Soil Classification System. Which one of the following options correctly represents their arrangement in the decreasing order of hydraulic conductivity?
Let \( \sigma_{\nu}' \) and \( \sigma_{h}' \) denote the effective vertical stress and effective horizontal stress, respectively. Which one of the following conditions must be satisfied for a soil element to reach the failure state under Rankine's passive earth pressure condition?
Consider the following expression: \[ z = \sin(y + it) + \cos(y - it) \] where \( z \), \( y \), and \( t \) are variables, and \( i = \sqrt{-1} \) is a complex number. The partial differential equation derived from the above expression is
For the equation \[ \frac{d^3 y}{dx^3} + x \left( \frac{dy}{dx} \right)^{3/2} + x^2 y = 0 \] the correct description is

Let
 \(x = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}\) and \(A = \begin{bmatrix} -1 & 2 & 3 \\ 0 & 1 & 6 \\ 0 & 0 & -1 \end{bmatrix}\)
For k ∈ N, if X’AkX = 33, then k is equal to ____ .

Let $A B C$ be the triangle with $A B=1, A C=3$ and $\angle B A C=\frac{\pi}{2}$ If a circle of radius $r>0$ touches the sides $A B, A C$ and also touches internally the circumcircle of the triangle $A B C$, then the value of $r$ ___

If the given lines \(2x+ky=1\) and \(3x-5y=7\) are parallel, then the value of \(k\) is
A closed loop is made of a metal pipe and is rolling between two fixed pulleys as shown in the image on the left. What would be the path traced by point P when the loop completes one turn?
Figure 1 shows the skeleton of a T-rex dinosaur. Identify the correct distorted silhouette from the given options.
A virus has two variants P and Q. Two treatments L and M were developed against variant P and Q and tested through four independent trials. The table shows the results. Assuming that both variants are equally prevalent, and both treatments cost about the same, but a given patient can be treated with only one treatment, which of the options is/are true?
Which of the following rocking chairs will NOT topple while rocking 15 degree?
Shown on the left are the front and top views of a 3D object. Which option(s) can be the side view?
Figure P can be divided into four identical pieces. Assuming that the pieces can be rotated and flipped, which of the options will fit?
Eleven identical circles are linked together by line segments that connect the centres of adjoining circles as shown in the figure below. Which of the statements is TRUE?
Tile X was used to create a pattern which is seamless (without gaps) when arranged as shown in Y. Which tile(s) from the options will create a seamless pattern?
Shown on the left is a futon that becomes a mattress when opened and folds into a seat. Which option CANNOT be folded as a seat?
Which option resembles an angry person when flipped vertically?
Some configurations for the pair of scissors are shown below. If concentric circles represent hinges, which of the options will work?
A washbasin is to be installed in a college canteen in India. Which of the options can help derive the appropriate height of the washbasin from the floor?
Shown on the left is a woven mat using threads of two colours. The mat is flipped at the edge Q to reveal the back side. Identify the back side of the mat from the given options.
In the square ABCD, line XY is drawn parallel to the base as shown in the figure below. P and Q are any two arbitrary points on XY, forming triangles ABQ and CDP. What fraction of the area of the square is the total green shaded area?
Calyx,Corolla
A system of frictionless and massless pulleys is being used to pull up a load of 2520 N. What is the minimum force (in Newtons) required at the end of the rope (shown in dashed lines)?
A printed transparent sticker (as shown on the left) is applied onto a glass cylinder such that the vertical edges meet. Which option is the correct representation?