List of practice Questions

Find \(x\): \(4(x - 2) = 3(x + 5)\).
Find the missing number in the series: \(2,\,6,\,12,\,20,\,30,\,?\)
Which of the following noble gas compounds has a square planar geometry: \(XeF_2\), \(XeF_4\), or \(XeF_6\)?
Let \[ \alpha= \left(1-2\cos\frac{\pi}{11}\right) \left(1-2\cos\frac{3\pi}{11}\right) \left(1-2\cos\frac{9\pi}{11}\right) \left(1-2\cos\frac{27\pi}{11}\right) \left(1-2\cos\frac{81\pi}{11}\right) \] Then the value of \[ 5-\alpha^2 \] is ________.
Two cylinders, both fitted with frictionless pistons, are filled with mixtures of He and Ar gases. In the first cylinder, the masses of He and Ar are \(m_1\) and \(m_2\), respectively. In the second cylinder, the masses of He and Ar are \(m_2\) and \(m_1\), respectively. The molar mass of Ar is \(10\) times the molar mass of He. The external pressure applied by the piston on the first cylinder needs to be \(5\) times that on the second cylinder so that the volume of the gas mixtures in both the cylinders are equal at the same temperature. Assuming He and Ar behave like ideal gases, the value of \(\left(\dfrac{m_1}{m_2}\right)\) is ____.
A nuclear reactor starts producing a radioactive nuclide $X$ from $t = 0$, at a constant rate of $\alpha$ per second. Each decay of $X$ produces energy $E_0$, which is utilized to heat a liquid of mass $m$ and specific heat $s$. Assuming no heat loss from the liquid and taking $\lambda$ as the decay constant of $X$, the rate of increase in the temperature of the liquid is:
Let \(P\) be the plane such that it contains the straight line \[ \frac{x-1}{2}=\frac{y-3}{3}=\frac{z+2}{1} \] and is perpendicular to the plane \[ x+2y+3z=4 \] Let \(P_1\) be the plane which passes through the point \((4,2,2)\) and is parallel to \(P\). Then which of the following statements is (are) TRUE?
Statement I: The structure of Maltose is given below: Maltose is a non-reducing sugar.

Statement II: The structure of Lactose is given below: Lactose is a reducing sugar.
In the light of the above statements, choose the correct answer:
'The team ______ more than 300 runs in 20 overs ___________ rains. However, some players needed to improve their batting skills.'
Choose the option with the correct sequence of words to fill the blanks.
If a positive real \(x\) satisfies the following equation
\[ \log_2 x + \log_{\sqrt{2}} x = 48, \]
then the value of \(x\) is _________________
The next figure (indicated by '?') in the sequence is shown below. Three grid panels are given, each a grid with a small arrow in the top-left corner and one dot and one filled triangle placed in different cells; the positions of the dot, the triangle, and the arrow orientation change from panel to panel following a consistent rule. The fourth panel (marked '?') must be chosen from the given options.
'All the mangoes in the basket are good.'
If the above statement is false, then which one of the following statements is necessarily true?
Consider the following statements about four numbers:
(S1) The average of the four numbers is 25
(S2) Each number is at most 40
(S3) Each number is at least 20
Choose the option that is necessarily correct.
'People are crowding around ___ pit into which ___ elephant has fallen. I have never seen an elephant looking more bewildered ___ miserable. Here it is in a most undignified position, thrust into a pit and made to look up ___ a vast, curiosity-stricken crowd.'

Choose the option with the correct sequence of words to fill the blanks.
The table lists the unit selling price of five products P, Q, R, S, and T. On a particular day, 250 items were sold with the average selling price of Rs. 60. The following observations were made:
(i) The quantity of S sold was twice that of T.
(ii) The quantity of R sold was thrice that of T.
(iii) The quantity of Q sold was four times that of T.

ProductPQRST
Unit selling price (Rs.)10050406060

What is the quantity of product P sold on that day?
Consider a string P of length \(l\) that is laid out as a straight-line segment. Another string K is laid out as a semicircular arc with string P as its diameter, as represented in Figure (i). When both the strings are shortened by a length \(x\) they can be re-arranged such that the shortened string K forms a full circle with the shortened string P as its diameter, as represented in Figure (ii). The value of \(x/l\) is ___________
The Roman senator Meritorius, his brother, his son, and his daughter have varying oratory skill levels. They are seated in rows and columns as shown in the figure with exactly one person sitting in each box. It is known that
(i) Meritorius' daughter and his brother are seated in the same column.
(ii) His son is seated diagonally across the sibling of the worst orator.
(iii) The best and worst orators are seated in the same row.

Who is the best orator?

Column 1Column 2
Row 1
Row 2
Which one of the patterns labelled P, Q, R, and S is used to generate the following figure?


Given a function \(f(t) = e^{-at}\), where \(a\) is a constant. The Laplace transform of the function is \(\mathcal{L}[f(t)] = F(s)\). Which one of the following options is correct?
Select the correct pair of eigenvectors for the following symmetric matrix.
\[ A = \begin{bmatrix} 1 & 2 \\ 2 & 4 \end{bmatrix} \]
Choose one correct option.
Given \(w = f(ax+by)\), where \(a\) and \(b\) are constants. The value of
\[ \left(b\frac{\partial w}{\partial x} - a\frac{\partial w}{\partial y}\right) \] is:
Which one of the following fusion welding techniques results in least Heat-Affected Zone (HAZ)?
During metallography, Nital is the most commonly used for etching _____________.
Which one of the following options is correct?
In a face-centered cubic metal, Shockley partial is:
Deformation mechanism map of a given material is used for determining which one of the following properties?