List of top Engineering Mathematics Questions on Number Systems

In the given diagram, ovals are marked at different heights (h) of a hill. Which one of the following options P, Q, R, and S depicts the top view of the hill?

A ‘frabjous’ number is defined as a 3 digit number with all digits odd, and no two adjacent digits being the same. For example, 137 is a frabjous number, while 133 is not. How many such frabjous numbers exist?
Residency is a famous housing complex with many well-established individuals among its residents. A recent survey conducted among the residents of the complex revealed that all of those residents who are well established in their respective fields happen to be academicians. The survey also revealed that most of these academicians are authors of some best-selling books. Based only on the information provided above, which one of the following statements can be logically inferred with certainty?
Ankita has to climb 5 stairs starting at the ground, while respecting the following rules: 1. At any stage, Ankita can move either one or two stairs up. 2. At any stage, Ankita cannot move to a lower step. Let $F(N)$ denote the number of possible ways in which Ankita can reach the $N^{th}$ stair. For example, $F(1) = 1$, $F(2) = 2$, $F(3) = 3$. The value of $F(5)$ is ..............
The activities of a project are given in the following table along with their durations and dependency.
The total float of the activity \( E \) (in days) is _________ (in integer).
The error in measuring the radius of a 5 cm circular rod was 0.2%. If the cross-sectional area of the rod was calculated using this measurement, then the resulting absolute percentage error in the computed area is _________ % . (round off to two decimal places).
A simply supported beam is loaded with a uniformly distributed load (UDL). Which statements about strain energy are TRUE?
Following observation equations are obtained in a survey task.
\[ x + y = 3 \\ 2x + y = 6 \\ x + 2y = 4 \] Using least square method, the most probable values of x and y will be
Using the following regression equations, the correlation coefficient between two survey quantities x and y will be __________________ (round off to 2 decimal places). \[ 2x - 5y + 98 = 0 \] \[ 6x - 7y + 114 = 0 \]
If population variance is 14.8, sample variance is 15.4 and the number of degrees of freedom is 10, then Chi-square value is __________________ (round off to 2 decimal places).
Most probable value of a quantity

The root of the equation \( \sin x - 4x + 1 = 0 \) after its first iteration, using the Newton-Raphson method with an initial guess of \( x_0 = 0.2 \), is _____.\( \textit{[Round off to three decimal places.]}\)

Work done by a moving particle in the force field \( \mathbf{F} = 6x^2 \hat{i} + (3xz + y) \hat{j} + 4z \hat{k} \), moving along the straight line from (0,0,0) to (1,2,3) is _____. \(\textit{[Answer in integer]}\)

Function \( f(x) \) by Maclaurin's series (as an infinite series) can be expressed as:
In a cosmopolitan city, the population comprises of 30% female and 70% male. Suppose that 5% of females and 30% of males in the population are foreigners. A person is selected at random from this population. Given that the selected person is a foreigner, the probability that the person is a female is ________ (round off to three decimal places).
If the quadrature rule \[ \int_{-1}^1 f(x) \, dx \approx f(\alpha) + \gamma f(\beta), \] where \( \alpha, \beta \) and \( \gamma \) are real constants, is exact for all polynomials of degree \( \leq 3 \), then \( \gamma + 3 (\alpha^2 + \beta^2) + (\alpha^3 + \beta^3) \) is equal to ________.