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Answers by Suraj / GATE Overflow for GATE CSE
3.3k
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4 votes
Derive the expressions for the number of operations required to solve a system of linear equations in $n$ unknowns using the Gaussian Elimination Method. Assume that one ...
27.3k
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0 votes
Let $G$ be a simple undirected graph. Let $T_D$ be a depth first search tree of $G$. Let $T_B$ be a breadth first search tree of $G$. Consider the following statements.No...
969
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2 votes
Two unsorted arrays of size m and n are to be sorted into a single array, what is best case time complexity?
652
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9 votes
38.7k
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127 votes
Consider a $2$-way set associative cache with $256$ blocks and uses $\text{LRU}$ replacement. Initially the cache is empty. Conflict misses are those misses which occur d...
44.5k
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49 votes
Let $A$ be $n\times n$ real valued square symmetric matrix of rank $2$ with $\sum_{i=1}^{n}\sum_{j=1}^{n}A^{2}_{ij} = 50.$ Consider the following statements.One eigenvalu...
14.0k
views
25 votes
Let $u$ and $v$ be two vectors in $\mathbf{R}^{2}$ whose Euclidean norms satisfy $\left \| u \right \| = 2\left \| v \right \|$. What is the value of $\alpha$ such that $...
20.3k
views
83 votes
Let $c_{1}.....c_{n}$ be scalars, not all zero, such that $\sum_{i=1}^{n}c_{i}a_{i}$ = 0 where $a_{i}$ are column vectors in $R^{n}$.Consider the set of linear equations$...
2.4k
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12 votes
Consider a 3 x 3 real symmetric matrix S such that two of its eigen values are a ≠ 0 , b ≠ 0 with respective Eigen vectors [ x1 x2 x3 ] , [ y1 y2 y3 ] . If a &ne...
6.8k
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10 votes
In the summer of $2012$, in New Delhi, the mean temperature of Monday to Wednesday was $41°C$ and of Tuesday to Thursday was $43°C$. If the temperature on Thursday was ...
4.5k
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0 votes
A is a 4-square matrix and A_5 (a raised to the power of 5) = 0. Then A_4 =a) Ib) -Ic) 0d) A
697
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4 votes
963
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0 votes
1 0 0 0 0 20 1 0 0 2 00 0 1 2 0 00 0 2 1 0 00 2 0 0 1 02 0 0 0 0 1
10.2k
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39 votes
Suppose that the expectation of a random variable $X$ is $5$. Which of the following statements is true?There is a sample point at which $X$ has the value $5$.There is a ...
500
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4 votes
4.2k
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4 votes
The head of newly formed government desires to appoint five of the six selected members $P, Q, R, S, T$ and $U$ to portfolios of Home, Power, Defense, Telecom, and Financ...
11.6k
views
70 votes
Let $G$ be a simple graph with $20$ vertices and $100$ edges. The size of the minimum vertex cover of G is $8$. Then, the size of the maximum independent set of $G$ is:$1...
16.0k
views
2 votes
Consider a pipelined processor with the following four stages:IF: Instruction FetchID: Instruction Decode and Operand FetchEX: ExecuteWB: Write BackThe IF, ID and WB stag...
4.7k
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15 votes
Let $X$ be a set of size $n$. How many pairs of sets (A, B) are there that satisfy the condition $A\subseteq B \subseteq X$ ?$2^{n+1}$$2^{2n}$$3^{n}$$2^{n} + 1$$3^{n + 1}...
901
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2 votes
Which of the following multiplier pattern of boothe algo gives better performance and how:1..011111111102..11111000111113..0111110111114..111111111000
34.3k
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69 votes
Consider a $4$ stage pipeline processor. The number of cycles needed by the four instructions $I1, I2, I3, I4$ in stages $S1, S2, S3, S4$ is shown below:$$\begin{array}{|...
2.3k
views
5 votes
Suppose the probability that x is the ith element in a list of n distinct integers is i/[n(n + 1)]. Find the average number of comparisons used by the linear search algor...
3.4k
views
6 votes
How many solutions are there to the equation $x+y+z=17$ in positive integers?$120$$171$$180$$121$
21.0k
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98 votes
A function $f(x)$ is continuous in the interval $[0,2]$. It is known that $f(0) = f(2) = -1$ and $f(1) = 1$. Which one of the following statements must be true?There exis...
13.3k
views
32 votes
For the undirected, weighted graph given below, which of the following sequences of edges represents a correct execution of Prim's algorithm to construct a Minimum Span­...
34.3k
views
104 votes
Consider the following pseudo code. What is the total number of multiplications to be performed?D = 2 for i = 1 to n do for j = i to n do for k = j + 1 to n do D = D * 3H...
3.7k
views
1 votes
What is the complexity of finding $50^{th}$ smallest element in an already constructed binary min-heap?$\Theta(1)$$\Theta (\log n)$$\Theta (n)$$\Theta (n \log n)$
13.0k
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48 votes
A CPU has $32-bit$ memory address and a $256 \ KB$ cache memory. The cache is organized as a $4-way$ set associative cache with cache block size of $16$ bytes.What is the...