List of top General Aptitude Questions

Consider the function \( f(x, y, z) = x^4 + 2y^3 + z^2 \). The directional derivative of the function at the point \( P(-1, -1, -1) \) along \( (\mathbf{i} + \mathbf{j}) \), where \( \mathbf{i} \) and \( \mathbf{j} \) are unit vectors in the \( x \)- and \( y \)-directions, respectively, rounded off to 2 decimal places, is:
Alumina particles with an initial moisture content of \( 5 \, \text{kg} \, \text{moisture}/\text{kg dry solid} \) are dried in a batch dryer. For the first two hours, the measured drying rate is constant at \( 2 \, \text{kg} \, \text{m}^{-2} \, \text{h}^{-1} \). Thereafter, in the falling-rate period, the rate decreases linearly with the moisture content. The equilibrium moisture content is \( 0.05 \, \text{kg}/\text{kg dry solid} \), and the drying area of the particles is \( 0.5 \, \text{m}^2/\text{kg dry solid} \). The total drying time, in hours, to reduce the moisture content to half its initial value is:
Let \( r \) and \( \theta \) be the polar coordinates defined by \( x = r \cos\theta \) and \( y = r \sin\theta \). The area of the cardioid \( r = a(1 - \cos\theta) \), \( 0 \leq \theta \leq 2\pi \), is: \includegraphics[width=0.3\linewidth]{q47 CE.PNG}
The temperatures of two large parallel plates of equal emissivity are \( 900 \, \text{K} \) and \( 300 \, \text{K} \). A reflective radiation shield of low emissivity and negligible conductive resistance is placed parallelly between them. The steady-state temperature of the shield, in \( \text{K} \), is:
Which of the following statements with reference to the petroleum/petrochemical industry is/are correct?
For the electrolytic cell in a chlor-alkali plant, which of the following statements is/are correct?
Consider a binary mixture of components \( A \) and \( B \) at temperature \( T \) and pressure \( P \). Let \( \bar{V}_A \) and \( \bar{V}_B \) be the partial molar volumes of \( A \) and \( B \), respectively. At a certain mole fraction of \( A \), \( x_A \): \[ \left( \frac{\partial \bar{V}_A}{\partial x_A} \right)_{T,P} = 22 \, \text{cm}^3 \, \text{mol}^{-1}, \quad \left( \frac{\partial \bar{V}_B}{\partial x_A} \right)_{T,P} = -18 \, \text{cm}^3 \, \text{mol}^{-1}. \] The value of \( x_A \), rounded off to 2 decimal places, is \_\_\_\_\_\_\_.
Consider a matrix \( A = \begin{bmatrix} -5 & a
-2 & -2 \end{bmatrix} \), where \( a \) is a constant. If the eigenvalues of \( A \) are \( -1 \) and \( -6 \), then the value of \( a \), rounded off to the nearest integer, is \_\_\_\_\_\_\_.
In an ammonia manufacturing facility, the necessary hydrogen is generated from methane. The facility consists of the following process units: \( P \): Methanator, \( Q \): CO shift convertor, \( R \): CO\(_2\) stripper, \( S \): Reformer, \( T \): Ammonia convertor. The correct order of these units, starting from methane feed, is:
If the Prandtl number \( \text{Pr} = 0.01 \), which of the following statements is/are correct?
Consider a linear homogeneous system of equations \( A\mathbf{x} = \mathbf{0} \), where \( A \) is an \( n \times n \) matrix, \( \mathbf{x} \) is an \( n \times 1 \) vector, and \( \mathbf{0} \) is an \( n \times 1 \) null vector. Let \( r \) be the rank of \( A \). For a non-trivial solution to exist, which of the following conditions is/are satisfied?
An infinitely long cylindrical water filament of radius \( R \) is surrounded by air. Assume water and air to be static. The pressure outside the filament is \( P_{\text{out}} \) and the pressure inside is \( P_{\text{in}} \). If \( \gamma \) is the surface tension of the water-air interface, then \( P_{\text{in}} - P_{\text{out}} \) is:
Consider a vapour-liquid mixture of components \( A \) and \( B \) that obeys Raoult’s law. The vapour pressure of \( A \) is half that of \( B \).The vapour phase concentrations of \( A \) and \( B \) are \( 3 \, \text{mol} \, \text{m}^{-3} \) and \( 6 \, \text{mol} \, \text{m}^{-3} \), respectively. At equilibrium, the ratio of the liquid phase concentration of \( A \) to that of \( B \) is:
The first non-zero term in the Taylor series expansion of \( (1 - x) - e^{-x \) about \( x = 0 \) is:}
Consider the normal probability distribution function \[ f(x) = \frac{4}{\sqrt{2\pi}} e^{-8(x+3)^2}. \] If \( \mu \) and \( \sigma \) are the mean and standard deviation of \( f(x) \) respectively, then the ordered pair \( (\mu, \sigma) \) is:
During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be \( 89.85^\circ \), the ratio of the Earth-Sun and Earth-Moon distances is closest to:
If \( z_1 = -1 + i \) and \( z_2 = 2i \), where \( i = \sqrt{-1} \), then \( \text{Arg}(z_1 / z_2) \) is:
In the 4 x 4 array shown below, each cell of the first three columns has either a cross (X) or a number, as per the given rule. Rule: The number in a cell represents the count of crosses around its immediate neighboring cells (left, right, top, bottom, diagonals). As per this rule, the maximum number of crosses possible in the empty column is: \includegraphics[width=0.5\linewidth]{q9 CE.PNG}
A homogeneous azeotropic distillation process separates an azeotropic AB binary feed using a heavy entrainer, \( E \), as shown in the figure. The loss of \( E \) in the two product streams is negligible, so \( E \) circulates around the process in a closed circuit. For a distillation column with fully specified feed(s), given operating pressure, a single distillate stream, and a single bottoms stream, the steady-state degrees of freedom equals 2. For the process in the figure with a fully specified AB feed stream and given column operating pressures, the steady-state degrees of freedom equals: \includegraphics[width=0.5\linewidth]{q14 CE.PNG}
The chart given below compares the Installed Capacity (MW) of four power generation technologies, T1, T2, T3, and T4, and their Electricity Generation (MWh) in a time of 1000 hours (h). The Capacity Factor of a power generation technology is: \[ \text{Capacity Factor} = \frac{\text{Electricity Generation (MWh)}}{\text{Installed Capacity (MW)} \times 1000 \, (\text{h})}. \] Which one of the given technologies has the highest Capacity Factor? \includegraphics[width=0.7\linewidth]{q8 CE.PNG}
On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time 12:05:00 hours to 12:55:00 hours?
For positive integers \( p \) and \( q \), with \( \frac{p}{q} \neq 1 \), \[ \left(\frac{p}{q}\right)^{\frac{p}{q}} = \left(\frac{p}{q}\right)^{(p - q)}. \] Then: (1) \( q^p = p^q \)
(2) \( q^p = p^{2q} \)
(3) \( \sqrt{q} = \sqrt{p} \)
(4) \( \sqrt[q]{q} = q\sqrt[p]{p} \)
In the given text, the blanks are numbered (i)—(iv). Select the best match for all the blanks. From the ancient Athenian arena to the modern Olympic stadiums, athletics \( (i) \) the potential for a spectacle. The crowd \( (ii) \) with bated breath as the Olympian artist twists his body, stretching the javelin behind him. Twelve strides in, he begins to cross-step. Six cross-steps \( (iii) \) in an abrupt stop on his left foot. As his body \( (iv) \) like a door turning on a hinge, the javelin is launched skyward at a precise angle.
Which one of the given options is a possible value of \( X \) in the following sequence? \[ 3, 7, 15, X, 63, 127, 255 \]
Three distinct sets of indistinguishable twins are to be seated at a circular table that has 8 identical chairs. Unique seating arrangements are defined by the relative positions of the people. How many unique seating arrangements are possible such that each person is sitting next to their twin?