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GATE CSE 2014 Set 1 | Question: 47
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 exists a $y$ in the interval $(0,1)$ such that $f(y) = f(y+1)$ For every $y$ ... the function in the interval $(0,2)$ is $1$ There exists a $y$ in the interval $(0,1)$ such that $f(y)$ = $-f(2-y)$

answered in Calculus Jan 28, 2015

16.1k views

8 answers

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GATE CSE 2007 | Question: 84
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move to either $(i + 1, j)$ or $(i,j + 1)$. How many distinct paths are there for the ... $(10,10)$ starting from the initial position $(0,0)$? $^{20}\mathrm{C}_{10}$ $2^{20}$ $2^{10}$ None of the above

commented in Combinatory Jan 25, 2015

9.6k views

4 answers

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GATE CSE 2000 | Question: 2.4
A polynomial $p(x)$ satisfies the following: $p(1) = p(3) = p(5) = 1$ $p(2) = p(4) = -1$ The minimum degree of such a polynomial is $1$ $2$ $3$ $4$

answered in Set Theory & Algebra Jan 24, 2015

5.6k views

8 answers

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GATE CSE 2014 Set 2 | Question: GA-10
At what time between $6$ a. m. and $7$ a. m. will the minute hand and hour hand of a clock make an angle closest to $60^{\circ}$? $6: 22$ a.m. $6: 27$ a.m. $6: 38$ a.m. $6: 45$ a.m.

answered in Quantitative Aptitude Jan 23, 2015

8.2k views

5 answers

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GATE CSE 2014 Set 3 | Question: 6
If $\int \limits_0^{2 \pi} |x \: \sin x| dx=k\pi$, then the value of $k$ is equal to ______.

answered in Calculus Jan 22, 2015

8.5k views

4 answers

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GATE CSE 2014 Set 2 | Question: 25
In the diagram shown below, $L1$ is an Ethernet LAN and $L2$ is a Token-Ring LAN. An $IP$ packet originates from sender $S$ and traverses to $R$, as shown. The links within each $\text{ISP}$ and across the two $\text{ISP}$s, are all ... $\text{TTL}$ field is $32$. The maximum possible value of the $\text{TTL}$ field when $R$ receives the datagram is _______.

commented in Computer Networks Jan 20, 2015

14.4k views

6 answers

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GATE IT 2004 | Question: 5
What is the maximum number of edges in an acyclic undirected graph with $n$ vertices? $n-1$ $n$ $n+1$ $2n-1$

answered in Graph Theory Jan 20, 2015

5.5k views

4 answers

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GATE CSE 2014 Set 1 | Question: 6
Let the function ... $\theta \in (\frac{\pi}{6},\frac{\pi}{3})$ such that $f'(\theta)\neq 0$ I only II only Both I and II Neither I nor II

answered in Calculus Jan 19, 2015

10.2k views

12 answers

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GATE CSE 2014 Set 1 | Question: 42
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 * 3 Half of the product of the $3$ consecutive integers. One-third of the product of the $3$ consecutive integers. One-sixth of the product of the $3$ consecutive integers. None of the above.

commented in Algorithms Jan 19, 2015

26.8k views

4 answers

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GATE CSE 2013 | Question: 7
Which one of the following is the tightest upper bound that represents the time complexity of inserting an object into a binary search tree of $n$ nodes? $O(1)$ $O(\log n)$ $O(n)$ $O(n \log n)$

answered in DS Jan 18, 2015

9.3k views

7 answers

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GATE CSE 2011 | Question: 34
A deck of $5$ cards (each carrying a distinct number from $1$ to $5$) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number ... $\left(\dfrac{4}{25}\right)$ $\left(\dfrac{1}{4}\right)$ $\left(\dfrac{2}{5}\right)$

answered in Probability Jan 18, 2015

14.0k views

4 answers

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GATE CSE 1998 | Question: 2.2
Consider the following determinant $\Delta = \begin{vmatrix} 1 & a & bc \\ 1 & b & ca \\ 1 & c & ab \end{vmatrix}$ Which of the following is a factor of $\Delta$? $a+b$ $a-b$ $a+b+c$ $abc$

answered in Linear Algebra Jan 18, 2015

5.4k views

7 answers

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GATE IT 2008 | Question: 44
When $n = 2^{2k}$ for some $k \geqslant 0$, the recurrence relation $T(n) = √(2) T(n/2) + √n$, $T(1) = 1$ evaluates to : $√(n) (\log n + 1)$ $√(n) \log n$ $√(n) \log √(n)$ $n \log √n$

answered in Algorithms Jan 7, 2015

13.1k views

4 answers

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GATE CSE 2006 | Question: 85
The grammar $S\rightarrow AC\mid CB$ $C\rightarrow aCb\mid \epsilon$ $A\rightarrow aA\mid a$ $B\rightarrow Bb\mid b$ generates the language $ L=\left \{ a^{i}b^{j}\mid i\neq j \right \}$. In this grammar what is the length of the derivation (number of steps starting from $S$) to generate ... $l\neq m$ $\max (l,m) + 2$ $l + m + 2$ $l + m + 3$ $\max (l,m) + 3$

answered in Compiler Design Jan 7, 2015

5.4k views

4 answers

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GATE CSE 2006 | Question: 84
Which one of the following grammars generates the language $ L=\left \{ a^{i}b^{j}\mid i\neq j \right \}$? $S\rightarrow AC\mid CB$ $C\rightarrow aCb\mid a\mid b$ $A\rightarrow aA\mid \varepsilon$ $B\rightarrow Bb\mid \varepsilon$ ... $S\rightarrow AC\mid CB$ $C\rightarrow aCb\mid \varepsilon$ $A\rightarrow aA\mid a$ $B\rightarrow Bb\mid b$

answered in Compiler Design Jan 7, 2015

10.1k views

4 answers

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GATE IT 2008 | Question: 45
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 Spanning Tree? $\text{(a, b), (d, f), (f, c), (g, i), (d, a), (g, h), (c, e), (f, h)}$ ... $\text{(h, g), (g, i), (h, f), (f, c), (f, d), (d, a), (a, b), (c, e)}$

commented in Algorithms Jan 7, 2015

10.4k views

4 answers

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GATE IT 2008 | Question: 71
A Binary Search Tree (BST) stores values in the range $37$ to $573$. Consider the following sequence of keys. $81, 537, 102, 439, 285, 376, 305$ $52, 97, 121, 195, 242, 381, 472$ $142, 248, 520, 386, 345, 270, 307$ ... list nodes in the order in which we could have encountered them in the search? II and III only I and III only III and IV only III only

answered in DS Jan 7, 2015

11.3k views

5 answers

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GATE IT 2008 | Question: 16
A paging scheme uses a Translation Look-aside Buffer (TLB). A TLB-access takes $10$ ns and the main memory access takes $50$ ns. What is the effective access time(in ns) if the TLB hit ratio is $\text{90%}$ and there is no page-fault? $54$ $60$ $65$ $75$

answered in Operating System Dec 11, 2014

11.4k views