List of top Quantitative Aptitude Questions asked in GATE CE

A remote village has exactly 1000 vehicles with sequential registration numbers starting from 1000. Out of the total vehicles, 30% are without pollution clearance certificate. Further, even- and odd-numbered vehicles are operated on even- and odd-numbered dates, respectively.
If 100 vehicles are chosen at random on an even-numbered date, the number of vehicles expected without pollution clearance certificate is\underline{\hspace{2cm}.}
Three husband–wife pairs are to be seated at a circular table that has six identical chairs. Seating arrangements are defined only by the relative position of the people. How many seating arrangements are possible such that every husband sits next to his wife?
There are $4$ red, $5$ green, and $6$ blue balls inside a box. If $N$ number of balls are picked simultaneously, what is the smallest value of $N$ that guarantees there will be at least two balls of the same colour? One cannot see the colour of the balls until they are picked.
In how many ways can cells in a $3 \times 3$ grid be shaded, such that each row and each column have exactly one shaded cell? An example of one valid shading is shown. \includegraphics[width=0.25\linewidth]{image1.png}
The probabilities of occurrences of two independent events \( A \) and \( B \) are 0.5 and 0.8, respectively. What is the probability of occurrence of at least \( A \) or \( B \) (rounded off to one decimal place)?
A square of side length 4 cm is given. The boundary of the shaded region is defined by one semi-circle on the top and two circular arcs at the bottom, each of radius 2 cm, as shown. The area of the shaded region is \underline{\hspace{1cm} cm$^2$.} \includegraphics[width=0.5\linewidth]{image2.png}
In the given figure, PQRSTV is a regular hexagon with each side of length 5 cm. A circle is drawn with its centre at V such that it passes through P. What is the area (in cm$^2$) of the shaded region? (The diagram is representative) \includegraphics[width=0.5\linewidth]{image37.png}
If \(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}....\frac{1}{29} =\frac{N}{29!}\) Find the remainder when N is divided by 19.