List of practice Questions

Translate the following passage into English: % Passage text \begin{center} \includegraphics[width=0.7\textwidth]{01.png} \end{center}
The welding process commonly used for fabricating tailor-welded blanks of dissimilar thickness for automotive applications is:
Find the odd word:
A 1 cm segment of a wire lying along the x-axis carries a current of 0.5 A along the \( +x \)-direction. A magnetic field \( \vec{B} = (0.4 \, \text{mT} \hat{j}) + (0.6 \, \text{mT} \hat{k}) \) is switched on. The force acting on the segment is:
A final year student appears for placement interview in two companies, S and T. Based on her interview performance, she estimates the probability of receiving job offers from companies S and T to be 0.8 and 0.6, respectively. Let \( p \) be the probability that she receives job offers from both the companies. Select the most appropriate option.

P and Q play chess frequently against each other. Of these matches, P has won 80% of the matches, drawn 15% of the matches, and lost 5% of the matches.
If they play 3 more matches, what is the probability of P winning exactly 2 of these 3 matches?

A shopkeeper increases the price of an article by 25% and then offers a discount of 20%. What is the net percentage change in the price?
A longwall panel is to be developed in a flat seam at a depth of \( H \) m. The surface subsidence profile (\( s \)) of the area with the horizontal distance \( x \) is estimated as \[ s = \frac{S_{{max}}}{2} \left[ 1.002 - \tanh \left( \frac{4.8x}{H} \right) \right], \] where \( S_{{max}} \) is the maximum subsidence at the centre of the panel, \( x \) is measured from the inflection point. The value of \( x \) is negative towards the panel centre and positive towards the panel boundary. The ratio between the critical width of the panel and the depth is:
In a group of 100 people, 30 speak only English, another 50 speak only Telugu, and another 20 speak both. How many speak at least one language?
If \(y=(\tan^{-1} x)^2\), show that \((x^2+1)^2 \frac{d^2y}{dx^2} + 2x(x^2+1)\frac{dy}{dx} = 2\).

Consider the following hierarchical cache system with the following access times:

\[ \begin{array}{|c|c|c|} \hline \textbf{Cache Level} & \textbf{Hit Rate} & \textbf{Access Time} \\ \hline L1 & 90\% & 1 \text{ ns} \\ L2 & 80\% & 10 \text{ ns} \\ L3 & 100\% & 100 \text{ ns} \\ \hline \end{array} \]

Find \( T_{avg} \) for hierarchical or simultaneous access.

Ruma reached the metro station and found that the escalator was not working. She walked up the stationary escalator with velocity \( v_1 \) in time \( t_1 \). On another day, if she remains stationary on the escalator moving with velocity \( v_2 \), the escalator takes her up in time \( t_2 \). The time taken by her to walk up with velocity \( v_1 \) on the moving escalator will be:
Let \(E_1: \frac{x^2}{9} + \frac{y^2}{4} = 1\) be an ellipse. Ellipses \(E_i\) are constructed such that their centers and eccentricities are the same as that of \(E_1\), and the length of the minor axis of \(E_{i+1}\) is the length of the major axis of \(E_i\). If \(A_i\) is the area of the ellipse \(E_i\), then \(\frac{5}{\pi} \sum_{i=1}^{\infty} A_i\) is equal to:

How many triangles are there in the figure given below? 

A bag contains 4 red and 6 blue balls. Two balls are drawn at random without replacement. What is the probability that both are red?

Assertion (A): The shaded portion of the graph represents the feasible region for the given Linear Programming Problem (LPP).
Reason (R): The region representing \( Z = 50x + 70y \) such that \( Z < 380 \) does not have any point common with the feasible region.

Three thin uniform rods each of mass \( M \) and length \( L \) are placed along the three axes of a Cartesian coordinate system with one end of all the rods at origin. The moment of inertia of the system of the rods about z-axis is
Observe the following statements
Statement-I: Hybridisation is not same in both SF₆ and BrF₅.
Statement-II: BrF₅ is Square pyramidal while SF₆ is octahedral in shape
The correct answer is
A person is Head of two independent selection committees I and II. If the probability of making a wrong selection in committee I is 0.03 and in committee II is 0.01, then find the probability that the person makes the correct decision of selection: (i) in both committees (ii) in only one committee
The emf of the cell \(\mathrm{Ni}_{(s)} \left| \mathrm{Ni}^{2+}(0.16 \, \mathrm{M}) \right| \mathrm{Ag}^{+}(0.002 \, \mathrm{M}) \left| \mathrm{Ag}_{(s)} \right.\) is (\(E^0_{\text{cell}} = 1.05 \, \mathrm{V}\)):
How did Indians react to the Jallianwala Bagh massacre? Explain.
Two infinitely long conductors kept along XX' and YY' axes are carrying current \( I_1 \) and \( I_2 \) along -X axis and -Y axis respectively. Find the magnitude and direction of the net magnetic field produced at point P(X, Y).
Prove that \(\int_0^{\pi/2} \log(\cos x) \, dx = -\frac{\pi}{2} \log 2\).
If \(A = \begin{bmatrix} 2 & -3 & 5
3 & 2 & -4
1 & 1 & -2 \end{bmatrix}\), find \(A^{-1}\). Using \(A^{-1}\) solve the following system of equations:
2x - 3y + 5z = 11
3x + 2y - 4z = -5
x + y - 2z = -3.
A bar magnet is initially at right angles to a uniform magnetic field. The magnet is rotated till the torque acting on it becomes one-half of its initial value. The angle through which the bar magnet is rotated is: