List of top Questions asked in GATE CS- 2024

The product of all eigenvalues of the matrix \[ \begin{bmatrix} 1 & 2 & 3
4 & 5 & 6
7 & 8 & 9 \end{bmatrix} is: \]
Consider a system that uses 5 bits for representing signed integers in 2’s complement format. In this system, two integers \( A \) and \( B \) are represented as \( A = 01010 \) and \( B = 11010 \). Which one of the following operations will result in either an arithmetic overflow or an arithmetic underflow?
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:
Consider the following sample of numbers: \[ 9, \, 18, \, 11, \, 14, \, 15, \, 17, \, 10, \, 69, \, 11, \, 13 \] The median of the sample is:
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:
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.
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