1
Let the function $f(x)$ be defined as $f(x)=\mid x-1 \mid + \mid x-2 \:\mid$. Then which of the following statements is true? $f(x)$ is differentiable at $x=1$ $f(x)$ is differentiable at $x=2$ $f(x)$ is differentiable at $x=1$ but not at $x=2$ none of the above
2
Let $f$ be a real-valued function of a real variable defined as $f(x) = x^{2}$ for $x\geq0$ and $f(x) = -x^{2}$ for $x < 0$.Which one of the following statements is true? $f(x) \text{is discontinuous at x = 0}$ ... $f(x) \text{is differentiable but its first derivative is not differentiable at x = 0}$
3
Functions $F(a, b)$ and $G(a, b)$ are defined as follows: $F(a, b) = (a − b)^2$ and $G(a, b) = \mid a − b\mid$, where $\mid x \mid$ represents the absolute value of $x$. What would be the value of $G(F(1, 3), G(1, 3))$? $2$ $4$ $6$ $36$
4
Consider a long-lived $TCP$ session with an end-to-end bandwidth of $1$ $\text{Gbps}$ (-$10^9$ bits-per-second). The session starts with a sequence number of $1234$. The minimum time (in seconds, rounded to the closet integer) before this sequence number can be used again is ____
5
A nationalized bank has found that the daily balance available in its saving bank accounts follows a normal distribution with a mean of Rs. 500 and a standard deviation of Rs. 50. The percentage of savings account holders who maintain an average daily balance more than Rs. 500 is _______________. Explain the calculation of the probability of Z score. Do GATE provide Z score table?
1 vote
6
7
Find Value of alpha?
8
The number of elements in the power set of $\{\{1,2\},\{2,1,1\},\{2,1,1,2\}\}$ is $3$ $8$ $4$ $2$
9
L = { <M> | M is a TM and |L(M)| <= 3 }. Is it Recursively Enumerable or not ?
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11
$R= 10 +(0 +11)0^{*}1.$ The minimum number of states in any DFA accepting this regular expression.
12
Which of the following is true: (a) differentiable and continous (d) none of these (c) not differentiable but continous (b) neither differentiable nor continous
13
The innermost loop will execute when j is multiple of i, and that will happen exactly i times. Please help me to find the time complexity of the below program:
14
S = { < M> | M is a DFA that accepts some string containing an equal number of 0s and 1s}. Then what will be S - a) Recursive enumerable b) undecidable c) decidable d) Turing co-recognizable
15
Construct a minimal dfa over {0,1} which neither accept 00 as a substring nor 11 as a substring.
1 vote
16
A synchronous transmission T has transfer rate of 100 char/ sec. If T uses some synchronous characters followed by some 8 bit info characters, what is the total number of synchronous bits required where bit rate is 1000 bits/ sec?
17
Let language defined is { Number of a's =2 and length of string is atleast 3} over alphabet {a,b}.What are number of states in minimal DFA?
18
Whether the following statement is true or false?? "The OS maintains scheduling and accounting information for each thread"
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1 vote
20
Consider a hypothetical processor which supports the 64Kb physical memory. Processor uses the memory mapped IO configuration in which the 3 MSB bits of the address is 1, then assign them to IO ports. How many IO address and how many memory address are possible in the processor.
21
#include<stdio.h> int main() { char c = 125; c = c+10; printf("%d", c); return 0; } in this we know -121 is printed also know the logic but what will be in int main() { char c = 125; c = c+10; printf("%u", c); return 0; } plz explain with logic
22
This matrix is singular with rank one. Find three $λ$’s and three eigenvectors. $\begin{bmatrix}1\\2 \\1 \end{bmatrix}$ $\begin{bmatrix}2&1 &2 \end{bmatrix}$ = $\begin{bmatrix}2 & 1 &2\\4 & 2 & 4\\2 & 1 &2\end{bmatrix}$
23
If f : R ---->R defined by f(x) = x2 + 1, then values of f -1 (17) and f -1(-3) are A. {Ø}, (4, - 4) B. {3,-3},{Ø} C. {Ø},{3,-3} D. {4,-4},Ø Answer is "D". But i dint understand how
1 vote
24
identify the class of language {a^(m)b^(n)} for following a) m + n = 10 b) m + n <=10 c)m+n>10 d) m+n<10 e) m + n>=10 f) m/n = 10 g) m - n = 10
25
<code>#include <stdio.h> int main() { unsigned int b = 20; b = ~b; printf("%d\n", b); }</code>