List of top Questions asked in GATE CS

The product of all eigenvalues of the matrix \[ \begin{bmatrix} 1 & 2 & 3
4 & 5 & 6
7 & 8 & 9 \end{bmatrix} is: \]
Let \( f: \mathbb{R} \to \mathbb{R} \) be a function such that \( f(x) = \max\{x, x^3\ \), \( x \in \mathbb{R} \), where \( \mathbb{R} \) is the set of all real numbers. The set of all points where \( f(x) \) is NOT differentiable is:}
The least number of squares to be added in the figure to make AB a line of symmetry is: \begin{center} \includegraphics[width=6cm]{10.png} \end{center}
A rectangular paper of 20 cm \( \times \) 8 cm is folded 3 times. Each fold is made along the line of symmetry, which is perpendicular to its long edge. The perimeter of the final folded sheet (in cm) is:
The pie chart presents the percentage contribution of different macronutrients to a typical 2,000 kcal diet of a person. The typical energy density (kcal/g) of these macronutrients is given in the table. \begin{center} \includegraphics[width=10cm]{8.png} \{0.5cm} \begin{tabular}{|c|c|} \hline Macronutrient & Energy density (kcal/g)
\hline Carbohydrates & 4
Proteins & 4
Unsaturated fat & 9
Saturated fat & 9
Trans fat & 9
\hline \end{tabular} \end{center} The total fat (all three types), in grams, this person consumes is:
A rectangular paper sheet of dimensions \( 54 \, \text{cm} \times 4 \, \text{cm} \) is taken. The two longer edges of the sheet are joined together to create a cylindrical tube. A cube whose surface area is equal to the area of the sheet is also taken. Then, the ratio of the volume of the cylindrical tube to the volume of the cube is:
In the given text, the blanks are numbered (i)–(iv). Select the best match for all the blanks.
Steve was advised to keep his head \_\_\_ (i) \_\_\_ before heading \_\_\_ (ii) \_\_\_ to bat; for, while he had a head \_\_\_ (iii) \_\_\_ batting, he could only do so with a cool head \_\_\_ (iv) \_\_\_ his shoulders.
The number of coins of Rs.1, Rs.5, and Rs.10 denominations that a person has are in the ratio 5:3:13. Of the total amount, the percentage of money in Rs.5 coins is:
Consider the following sample of numbers: \[ 9, \, 18, \, 11, \, 14, \, 15, \, 17, \, 10, \, 69, \, 11, \, 13 \] The median of the sample is:
If two distinct non-zero real variables \( x \) and \( y \) are such that \( (x + y) \) is proportional to \( (x - y) \), then the value of \( \frac{x}{y} \) is:
If \( \to \) denotes increasing order of intensity, then the meaning of the words [dry \( \to \) arid \( \to \) parched] is analogous to [diet \( \to \) fast \( \to \) \_\_\_\_\_].
A cube is to be cut into 8 pieces of equal size and shape Here each cut should be straight and it should not stop till it reaches the other end of the cube The minimum number of such cuts required?
Consider a disk with the following specifications: rotation speed of 6000 RPM, average seek time of 5 ms, 500 sectors/track, 512 B sectors. A file has content stored in 3000 sectors located randomly on the disk. Assuming average rotational latency, the total time (in secs, rounded to 2 places) to read the entire file from the disk is?
A processor with 16 GPR's uses a 32-bits instruction format. The instruction format consists of an op-code field, an addressing mode field, register operand fields, and a 16-bit scalar operand field. If 8 addressing modes are to be supported, the max. number of unique op-codes possible for every addressing mode is_______
log \([\frac{x+y}{2}]=\frac{1}{2}\) (log x+log y) the value of \(\frac{x}{y}+\frac{y}{x}\) is
The value of x in given series is
6, 9, 14, x, 30, 41
Increasing order of the intensity
Walk → Jog → Sprint
Bothered →? Daunted
If \(A_{n×n}\) such that A is real matrix and B is any matrix which is obtained from A by interchanging any two rows then pick the true statements?
The probability of getting a distinct number while throwing dice six times?
 
\(∫_{x=0}^a ∫^{y=1}_{y=\sqrt\frac{x}{a}}\)  \(e^{y^3}\) dy dx=(e-1) then the value of a is
 
Consider a non-pipeline processor with 2 GHz clock, average CPI of '6'. It is hence with a 5-stage pipeline processor with the same clock, consider 1 instructions per cycle and if 20% instructions have 2 cycle stalls due to control hazards and 20% of instructions have 3 cycles stalls due to data hazards. Speedup of pipeline over non-pipeline

Let \(A\) be the adjacency matrix of the given graph with vertices \(\{1,2,3,4,5\}\). 

Let \(\lambda_1, \lambda_2, \lambda_3, \lambda_4, \lambda_5\) be the eigenvalues of \(A\) (not necessarily distinct). Find: \[ \lambda_1 + \lambda_2 + \lambda_3 + \lambda_4 + \lambda_5 \;=\; \_\_\_\_\_\_ . \]

Consider the Deterministic Finite-state Automaton (DFA) A shown below. The DFA runs on the alphabet \(\{0, 1\}\), and has the set of states \(\{s, p, q, r\}\), with \(s\) being the start state and \(p\) being the only final state.

Which one of the following regular expressions correctly describes the language accepted by A?
 

The Lucas sequence $L_n$ is defined by the recurrence relation: \[ L_n = L_{n-1} + L_{n-2}, \text{for } n \geq 3, \] with $L_1 = 1$ and $L_2 = 3$. Which one of the options given is TRUE?
Which one of the options given below refers to the degree (or arity) of a relation in relational database systems?