GATE Quantitative Aptitude Questions

A shop has 4 distinct flavors of ice-cream. One can purchase any number of scoops of any flavor. The order in which the scoops are purchased is inconsequential. If one wants to purchase 3 scoops of ice-cream, in how many ways can one make that purchase?

A box contains 5 coins: 4 regular coins and 1 fake coin. When a regular coin is tossed, the probability $P(head)=0.5$ and for a fake coin, $P(head)=1$. You pick a coin at random and toss it twice, and get two heads. The probability that the coin you have chosen is the fake coin is ______. (rounded off to two decimal places)

In the diagram, the lines QR and ST are parallel to each other. The shortest distance between these two lines is half the shortest distance between the point P and line QR. What is the ratio of the area of the triangle PST to the area of the trapezium SQRT?

Note: The figure shown is representative.

Consider a probability distribution given by the density function $P(x)$.

$P(x)=\{\begin{array}{ll}C{x}^2,& \text{for }1\le x\le 4\\ 0,& \text{for }x<1\text{ or }x>4\end{array}$

The probability that $x$ lies between 2 and 3, i.e., $P(2\le x\le 3)$ is ________. (rounded off to three decimal places)

Let $p_1$ and $p_2$ denote two arbitrary prime numbers. Which one of the following statements is correct for all values of $p_1$ and $p_2$?

A fair six-faced dice, with the faces labelled 1, 2, 3, 4, 5, and 6, is rolled thrice. What is the probability of rolling 6 exactly once?

In the given figure, PQRS is a square of side 2 cm and PLMN is a rectangle. The corner L of the rectangle is on the side QR. Side MN of the rectangle passes through the corner S of the square.

What is the area (in cm^2) of the rectangle PLMN?

Note: The figure shown is representative.

The average marks obtained by a class in an examination were calculated as 30.8. However, while checking the marks entered, the teacher found that the marks of one student were entered incorrectly as 24 instead of 42. After correcting the marks, the average becomes 31.4. How many students does the class have?

g(.) is a function from A to B, f(.) is a function from B to C, and their composition defined as f(g(.)) is a mapping from A to C.

If f(.) and f(g(.)) are onto (surjective) functions, which ONE of the following is TRUE about the function g(.)?

Consider the given system of linear equations for variables $x$ and $y$, where $k$ is a real-valued constant. Which of the following option(s) is/are CORRECT?

$x+ky=1$

$kx+y=-1$

Let $A$ be a $2\times 2$ matrix as given.

$A=\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right]$

What are the eigenvalues of the matrix $A^{13}$ ?

If $P{e}^x=Q{e}^{-x}$ for all real values of $x$, which one of the following statements is true?