Recent activity by ankitgupta.1729

6 answers

1

GATE2014-1-GA-5
The roots of $ax^{2}+bx+c = 0$ are real and positive. $a, b$ and $c$ are real. Then $ax^{2}+b\mid x \mid + c =0$ has no roots $2$ real roots $3$ real roots $4$ real roots

commented 1 day ago in Numerical Ability | 3.2k views

3 answers

2

GATE2014-1-8
The base (or radix) of the number system such that the following equation holds is____________. $\frac{312}{20} = 13.1$

commented 1 day ago in Digital Logic | 2.5k views

2 answers

3

Boolean algebra theorem(Lattices)
THEOREM:- The Poset $[D_{n};/] $ is a boolean algebra iff 'n' is a square-free number. If the Poset $[D_{n};/] $ is a boolean algebra then compliment of $x = \dfrac{n}{x}\: \forall x\in D_{n}$ Please explain this theorem?? and following question Q)Which of the following is not a ... $ A) [ D_{110};/ ] $ $ B) [ D_{91};/ ] $ $ C) [ D_{45};/ ]$ $ D) [ D_{64};/ ]$

commented 2 days ago in Set Theory & Algebra | 497 views

4 answers

4

GATE2019-44
Consider the following matrix: $R = \begin{bmatrix} 1 & 2 & 4 & 8 \\ 1 & 3 & 9 & 27 \\ 1 & 4 & 16 & 64 \\ 1 & 5 & 25 & 125 \end{bmatrix}$ The absolute value of the product of Eigen values of $R$ is _______

commented Jan 5 in Linear Algebra | 3.4k views

2 answers

5

ISRO2018-57
Given a binary-max heap. The elements are stored in an arrays as $25, 14, 16, 13, 10, 8, 12$. What is the content of the array after two delete operations? $14,13,8,12,10$ $14,12,13,10,8$ $14,13,12,8,10$ $14,13,12,10,8$

commented Jan 5 in Others | 1.1k views

2 answers

6

$\textbf{NTA NET dec 2019 ( Recurrence relation)}$
$\text{Give asymptotic upper and lower bound for $\mathbf{T(n)}$ given below.}\;\text{Assume $\mathrm {T(n)}$ is constant for $\mathrm {n\le 2}.$}$ $\large{\mathrm{T(n) = 4T\left (\sqrt n \right ) + \lg^2 n}}$ ... $4)\;\;\mathrm{T(n) = \theta (\lg (\lg n)\lg n)}$

answered Jan 2 in Algorithms | 133 views

1 answer

7

ISI 2004 MIII
Let $X$ be a nonempty set and let $\mathcal{P}(X)$ denote the collection of all subsets of $X.$ Define $\textit{f}:\textit{X$\times$ $\mathcal{P}$(X)}\rightarrow \mathbb{R}$ by $f(x,A) = \begin{cases} 1 \text{ if } x \in A & \\ 0 \text{ if } x \notin A & \end{cases}$ ... $f(x,A)+f(x,B) - f(x,A) \cdot f(x,B)$ $f(x,A)+ \mid f(x,A) - f(x,B) \mid$

answered Dec 31, 2019 in Set Theory & Algebra | 151 views

1 answer

8

GATE1987-9f
Give the composition tables (Cayley Tables) of the two non isomorphic groups of order 4 with elements $e, a, b, c$ where $c$ is the identity element. Use the order $e, a, b, c$ for the rows and columns.

commented Dec 30, 2019 in Set Theory & Algebra | 216 views

4 answers

9

GATE2018-18
The chromatic number of the following graph is _____

commented Dec 24, 2019 in Graph Theory | 2.8k views

1 answer

10

GATE1997-4.6
Let $T(n)$ be the function defined by $T(1) =1, \: T(n) = 2T (\lfloor \frac{n}{2} \rfloor ) + \sqrt{n}$ for $n \geq 2$. Which of the following statements is true? $T(n) = O \sqrt{n}$ $T(n)=O(n)$ $T(n) = O (\log n)$ None of the above

commented Dec 24, 2019 in Algorithms | 1k views

4 answers

11

GATE1988-2xii
Consider the following program skeleton and below figure which shows activation records of procedures involved in the calling sequence. $p \rightarrow s \rightarrow q \rightarrow r \rightarrow q.$Write the access links of the activation records to enable correct access and variables in the ... q; procedure r; begin q end r; begin r end q; procedure s; begin q end s; begin s end p;

commented Dec 12, 2019 in Compiler Design | 1.3k views

6 answers

12

TIFR2010-B-32
Consider the following solution (expressed in Dijkstra's guarded command notation) to the mutual exclusion problem. process P1 is begin loop Non_critical_section; while not (Turn=1) do skip od; Critical_section_1; Turn:=2; end loop end ∥ process P2 is begin loop Non_critical_section; ... (3), but does not satisfies the requirement (2). Satisfies all the requirement (1), (2), and (3).

commented Dec 12, 2019 in Operating System | 1.1k views

8 answers

13

GATE2019-35
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z \mid x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z \mid w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ ... Set of all positive integers $S3:$ Set of all integers Which of the above sets satisfy $\varphi$? S1 and S2 S1 and S3 S2 and S3 S1, S2 and S3

commented Dec 11, 2019 in Mathematical Logic | 5.9k views

3 answers

14

Integration
$\int \left ( \sin\theta \right )^{\frac{1}{2}}d\theta$

commented Dec 11, 2019 in Calculus | 145 views

3 answers

15

GATE2008-7
The most efficient algorithm for finding the number of connected components in an undirected graph on $n$ vertices and $m$ edges has time complexity $\Theta(n)$ $\Theta(m)$ $\Theta(m+n)$ $\Theta(mn)$

comment edited Dec 9, 2019 in Algorithms | 2.9k views

4 answers

16

GATE2007-21
How many different non-isomorphic Abelian groups of order $4$ are there? $2$ $3$ $4$ $5$

comment edited Dec 7, 2019 in Set Theory & Algebra | 6k views

3 answers

17

TIFR2016-A-13
Let $n \geq 2$ be any integer. Which of the following statements is not necessarily true? $\begin{pmatrix} n \\ i \end{pmatrix} = \begin{pmatrix} n-1 \\ i \end{pmatrix} + \begin{pmatrix} n-1 \\ i-1 \end{pmatrix}, \text{ where } 1 \leq i \leq n-1$ $n!$ divides the product of any ... $ i \in \{1, 2, \dots , n-1\}$ If $n$ is an odd prime, then $n$ divides $2^{n-1} -1$

commented Dec 4, 2019 in Others | 171 views

1 answer

18

TIFR2013-A-8
Find the sum of the infinite series $\dfrac{1}{1\times 3 \times 5} + \dfrac{1}{3\times 5\times 7} + \dfrac{1}{5\times 7 \times 9} + \dfrac{1}{7\times 9 \times 11} + ......$ $\;\;\infty $ $\left(\dfrac{1}{2}\right)$ $\left(\dfrac{1}{6}\right)$ $\left(\dfrac{1}{12}\right)$ $\left(\dfrac{1}{14}\right)$

commented Dec 4, 2019 in Numerical Ability | 336 views

2 answers

19

TIFR2015-A-3
Let $|z| < 1$. Define $M_{n}(z)= \sum_{i=1}^{10} z^{10^{n}(i - 1)}?$ what is $\prod_{i=0}^{\infty} M_{i}(z)= M_{0}(z)\times M_{1}(z) \times M_{2}(z) \times ...?$ Can't be determined. $1/ (1 - z)$ $1/ (1 + z)$ $1 - z^{9}$ None of the above.

commented Dec 4, 2019 in Numerical Ability | 256 views

2 answers

20

TIFR2018-B-11
Consider the language $L\subseteq \left \{ a,b,c \right \}^{*}$ defined as $L = \left \{ a^{p}b^{q}c^{r} : p=q\quad or\quad q=r \quad or\quad r=p \right \}.$ Which of the following answer is TRUE about the complexity of this language? $L$ is regular ... $L,$ defined as $\overline{L} = \left \{ a,b,c \right \}^{*}\backslash L,$ is regular. $L$ is regular, context-free and decidable

edited Dec 4, 2019 in Theory of Computation | 530 views

6 answers

21

GATE2019-13
Compute $\displaystyle \lim_{x \rightarrow 3} \frac{x^4-81}{2x^2-5x-3}$ $1$ $53/12$ $108/7$ Limit does not exist

commented Dec 3, 2019 in Calculus | 2k views

4 answers

22

GATE2007-27
Consider the set of (column) vectors defined by$X = \left \{x \in R^3 \mid x_1 + x_2 + x_3 = 0, \text{ where } x^T = \left[x_1,x_2,x_3\right]^T\right \}$ ... a linearly independent set, but it does not span $X$ and therefore is not a basis of $X$. $X$ is not a subspace of $R^3$. None of the above

commented Dec 2, 2019 in Linear Algebra | 3.7k views

1 answer

23

ISI2018-DCG-30
Let $0.01^x+0.25^x=0.7$ . Then $x\geq1$ $0\lt x\lt1$ $x\leq0$ no such real number $x$ is possible.

commented Dec 1, 2019 in Numerical Ability | 50 views

3 answers

24

GATE2004-71
How many solutions does the following system of linear equations have? $-x + 5y = -1$ $x - y = 2$ $x + 3y = 3$ infinitely many two distinct solutions unique none

commented Nov 30, 2019 in Linear Algebra | 1.9k views

2 answers

25

ISI 2014 PCB A2
Let $m$ and $n$ be two integers such that $m \geq n \geq 1.$ Count the number of functions $f : \{1, 2, \ldots , n\} \to \{1, 2, \ldots , m\}$ of the following two types: strictly increasing; i.e., whenever $x < y, f(x) < f(y),$ and non-decreasing; i.e., whenever $x < y, f(x) ≤ f(y).$

commented Nov 25, 2019 in Set Theory & Algebra | 297 views

1 answer

26

GATE2017 EC-1: GA-5
Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusion can be deduced from the preceding sentences? At least one bench is a table At least one shelf is a bench At least one chair is a table All benches are chairs Only i Only ii Only ii and iii Only iv

commented Nov 24, 2019 in Verbal Ability | 158 views

1 answer

27

TIFR2014-A-13
Let $L$ be a line on the two dimensional plane. $L'$s intercepts with the $X$ and $Y$ axes are respectively $a$ and $b$. After rotating the co-ordinate system (and leaving $L$ untouched), the new intercepts are $a'$ and $b'$ ... $\frac{b}{a}+\frac{a}{b}=\frac{b'}{a'}+\frac{a'}{b'}$. None of the above.

commented Nov 22, 2019 in Numerical Ability | 271 views

3 answers

28

GATE1990-11b
The following program computes values of a mathematical function $f(x)$. Determine the form of $f(x)$. main () { int m, n; float x, y, t; scanf ("%f%d", &x, &n); t = 1; y = 0; m = 1; do { t *= (-x/m); y += t; } while (m++ < n); printf ("The value of y is %f", y); }

commented Nov 11, 2019 in Algorithms | 418 views

2 answers

29

GATE1997-4.2
Let $A=(a_{ij})$ be an $n$-rowed square matrix and $I_{12}$ be the matrix obtained by interchanging the first and second rows of the $n$-rowed Identify matrix. Then $AI_{12}$ is such that its first Row is the same as its second row Row is the same as the second row of $A$ Column is the same as the second column of $A$ Row is all zero

commented Oct 25, 2019 in Linear Algebra | 1.1k views

2 answers

30

GATE1988-16i
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lower-triangular with all diagonal elements equal to 1, $U$ is upper-triangular, and $P$ is a permutation matrix. For $A = \begin{bmatrix} 2 & 5 & 9 \\ 4 & 6 & 5 \\ 8 & 2 & 3 \end{bmatrix}$ Compute $L, U,$ and $P$ using Gaussian elimination with partial pivoting.

commented Oct 24, 2019 in Linear Algebra | 371 views

2 answers

31

ISI2018-DCG-1
The digit in the unit place of the number $7^{78}$ is $1$ $3$ $7$ $9$

answer edited Oct 22, 2019 in Numerical Ability | 73 views

1 answer

32

ISI2016-DCG-63
If $\sin^{-1}\frac{1}{\sqrt{5}}$ and $\cos^{-1}\frac{3}{\sqrt{10}}$ lie in $\left[0,\frac{\pi}{2}\right],$ their sum is equal to $\frac{\pi}{6}$ $\frac{\pi}{3}$ $\sin^{-1}\frac{1}{\sqrt{50}}$ $\frac{\pi}{4}$

comment edited Oct 19, 2019 in Geometry | 34 views

1 answer

33

GATE2017 ME-1: GA-8
Let $S_1$ be the plane figure consisting of the points $(x, y)$ given by the inequalities $\mid x - 1 \mid \leq 2$ and $\mid y+2 \mid \leq 3$. Let $S_2$ be the plane figure given by the inequalities $x-y \geq -2, \: y \geq 1$, and $x \leq 3$. Let $S$ be the union of $S_1$ and $S_2$. The area of $S$ is. $26$ $28$ $32$ $34$

answer edited Oct 13, 2019 in Numerical Ability | 145 views

2 answers

34

ISI2014-DCG-4
$\underset{n \to \infty}{\lim} \dfrac{1}{n} \bigg( \dfrac{n}{n+1} + \dfrac{n}{n+2} + \cdots + \dfrac{n}{2n} \bigg)$ is equal to $\infty$ $0$ $\log_e 2$ $1$

comment edited Oct 11, 2019 in Calculus | 119 views

4 answers

35

GATE2012-11
Let A be the $ 2 × 2 $ matrix with elements $a_{11} = a_{12} = a_{21} = +1 $ and $ a_{22} = −1 $ . Then the eigenvalues of the matrix $A^{19}$ are $1024$ and $−1024$ $1024\sqrt{2}$ and $−1024 \sqrt{2}$ $4 \sqrt{2}$ and $−4 \sqrt{2}$ $512 \sqrt{2}$ and $−512 \sqrt{2}$

answer edited Oct 5, 2019 in Linear Algebra | 2.9k views

11 answers

36

GATE2016-1-26
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.

comment edited Oct 4, 2019 in Combinatory | 9.7k views

0 answers

37

ISI2015-DCG-40
The equations $x=a \cos \theta + b \sin \theta$ and $y=a \sin \theta + b \cos \theta$, $( 0 \leq \theta \leq 2 \pi$ and $a,b$ are arbitrary constants) represent a circle a parabola an ellipse a hyperbola

comment edited Oct 2, 2019 in Numerical Ability | 46 views

1 answer

38

ISI2019-MMA-14
If the system of equations $\begin{array} \\ax +y+z= 0 \\ x+by +z = 0 \\ x+y + cz = 0 \end{array}$ with $a,b,c \neq 1$ has a non trivial solutions, the value of $\frac{1}{1-a} + \frac{1}{1-b} + \frac{1}{1-c}$ is $1$ $-1$ $3$ $-3$

edited Sep 23, 2019 in Linear Algebra | 157 views

1 answer

39

ISI2015-DCG-32
The set of vectors constituting an orthogonal basis in $\mathbb{R} ^3$ is $\begin{Bmatrix} \begin{pmatrix} 1 \\ -1 \\ 0 \end{pmatrix}, & \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix}, & \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \end{Bmatrix}$ ... None of these

comment edited Sep 23, 2019 in Linear Algebra | 56 views

3 answers

40

GATE2007-IT-17
Exponentiation is a heavily used operation in public key cryptography. Which of the following options is the tightest upper bound on the number of multiplications required to compute $b^n \bmod{m}, 0 \leq b, n \leq m$ ? $O(\log n)$ $O(\sqrt n)$ $O\Biggl (\frac{n}{\log n} \Biggr )$ $O(n)$

comment edited Sep 22, 2019 in Algorithms | 3.1k views