List of top Engineering Mathematics Questions

An exhibition was held in a hall on 15 August 2022 between 3 PM and 4 PM during which any person was allowed to enter only once. Visitors who entered before 3:40 PM exited the hall exactly after 20 minutes from their time of entry. Visitors who entered at or after 3:40 PM, exited exactly at 4 PM. The probability distribution of the arrival time of any visitor is uniform between 3 PM and 4 PM. Two persons \(X\) and \(Y\) entered the exhibition hall independent of each other. Which one of the following values is the probability that their visits to the exhibition overlapped with each other?

Which one of the following is the CORRECT value of \(y\), as defined by the expression given below?
\[ y = \lim_{x \to 0} \frac{2x}{e^x - 1} \]

The vector \(\vec{v}\) is defined as \[ \vec{v} = zx\,\hat{i} + 2xy\,\hat{j} + 3yz\,\hat{k}. \] Which one of the following is the CORRECT value of divergence of \(\vec{v}\), evaluated at the point \((x,y,z) = (3,2,1)\)?

For a two-dimensional plane, the unit vectors \((\hat{e}_r,\hat{e}_\theta)\) of the polar coordinate system and \((\hat{i},\hat{j})\) of the cartesian coordinate system are related by \[ \hat{e}_r=\cos\theta\,\hat{i}+\sin\theta\,\hat{j}, \qquad \hat{e}_\theta=-\sin\theta\,\hat{i}+\cos\theta\,\hat{j}. \] Which one of the following is the CORRECT value of \(\dfrac{\partial(\hat{e}_r+\hat{e}_\theta){\partial\theta}\)?}

Given that \( F=\dfrac{|z_1+z_2|}{|z_1|+|z_2|} \), where \(z_1=2+3i\) and \(z_2=-2+3i\) with \(i=\sqrt{-1}\), which one of the following options is CORRECT?

If \(A=\begin{pmatrix}1 & 2 \\ 3 & 5\end{pmatrix}\), the value of \(\left|A^{4}+3A^{2}-5A+6I\right|\) is ________________.

If \(f(2)=5\) and \(f(x)\,f(x+1)=3\) for all real \(x\), the value of \(f(10)\) is ________________.

Ten playing cards numbered \(1,\ldots,10\) are drawn with replacement. What is the probability that the second number is greater than the first (rounded to two decimal places)?

If \(7^{3x}=216\), the value of \(7^{-x}\) (rounded off to three decimal places) is __________________.

The value of \(\displaystyle \lim_{x\to 0}\left[\frac{\cos 2x-\cos 4x}{x^2}\right]\) is __________________.

A series \(S\) is given as \(S=1+3+5+7+9+\dots\). The sum of the first 50 terms of \(S\) is __________________.

Two fair six-sided dice are thrown. The probability of getting \(12\) as the product of the numbers on the dice (rounded off to two decimal places) is __________________.

The distance between the two points of intersection of \(x^{2}+y=7\) and \(x+y=7\) (rounded off to two decimal places) is __________________.

To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand and that of cement are in the ratio of 1:2.
If the total cost of sand and cement to construct the wall is 1000 rupees, then what is the cost (in rupees) of cement used?

The coefficient of \(x^4\) in the polynomial \((x-1)^3(x-2)^3\) is equal to __________.

Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without leaving any empty spaces in between them? The copies of the shape used to tile are identical and are not allowed to overlap.

In the given figure, PQRS is a parallelogram with \(PS=7\) cm, \(PT=4\) cm and \(PV=5\) cm. What is the length of \(RS\) in cm? (The diagram is representative.)

A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line. The given figure consists of 16 unit squares arranged as shown. In addition to the three black squares, what is the minimum number of squares that must be coloured black, such that both \(PQ\) (vertical) and \(MN\) (the bottom-left to top-right diagonal) form lines of symmetry? (The figure is representative)

Calculate the reciprocal of the coefficient of \(z^3\) in the Taylor series expansion of the function \(f(z)=\sin(z)\) around \(z=0\). (Provide the answer as an integer.)

For the function \(f(x) = x^4 - x^2\), which of the following statements is/are TRUE?