1

$\lim_{x\rightarrow 0}\frac{ \sin x^{\circ}}{x}$

2

A context free grammar G is said to be ambiguous ,if there exists some w belongs to L(G) that has at least 2 distinct derivation trees. If every grammar that generate L is ambiguous then language is called inherently ambiguous ...eg for inherently grammar is L= {a^nb^nc^m}∪{a^nb^mc^m} http://infolab.stanford.edu/~ullman/ialc/slides/slides7.pdf

3

so , answer should be (a) , (b) and (c) are TRUE .

6

$T(n) = 2T\left(n^{\frac{1}{2}}\right)+1$ $ = 2\left(2T\left(n^{\frac{1}{2^2}}\right) + 1\right) + 1 $ $ = 4\times T\left(n^{\frac{1}{2^2}}\right) + 5 $ $ = 8\times T\left(n^{\frac{1}{2^3}}\right) + 13 \\ \cdots$ ... $T(n) = \Theta(\log n)$

7

Its a monoid. Closure, associativity, Identity are defined for Real numbers.But inverse is not defined as R can be zero also. So (R,*) is neither Group nor Abelian(commutative), but Monoid.

8

It is given that head has appeared so we have only two options either the coin is HH one or HT one, so chances of coming tail would be 1/4, I am just guessing.

9

Hello all, I wish you all the very best for GATE 2019. Tomorrow will be your day. Don’t change your strategy of solving the paper just by listening to anyone today, keep it yours :) All the top ranks are waiting for you all ;) Enjoy the paper as well, it will be surely a great experience!!!

**ALL THE BEST...**

10

Let us define a new function $g:$ $g(y) = f(y) -f(y+1)$ Since, function $f$ is continuous in $[0,2],$ $g$ would be continuous in $[0,1]$. $g(0) = -2, g(1) = 2$ Since, $g$ is continuous and goes from negative to positive value in $[0,1],$ at some point $g$ would be $0$ in $(0,1).$ $g=0 \implies f(y) = f(y+1)$ for some $y \in (0,1).$ Therefore, correct answer would be $(A).$

11

For Next two days i am not in the mood of working on any electronic device …..as lately i am spending more time on youtube after every one or two hour study ,there is 1 hour youtube :) so i think its good time to leave gadgets ….so best of luck from my side to everyone , hopefully everyone who worked hard will get their results ….

“SIMPLY BEST OF LUCK FROM MY SIDE TO EVERYONE : )”

“SIMPLY BEST OF LUCK FROM MY SIDE TO EVERYONE : )”

12

Hello All… I hope everyone is **doing great **with the GATE ‘19 preparations :)

Some of you might already know me. Well I got some calls and messages in my inbox for some motivation, I thought I should post something for you all.

Well It’s **more or less 20** days remaining for GATE 2019. Hot time in this cool season huh!!! Some of you are getting great scores in all the mocks, some of you are struggling with it and maybe some of you still not started giving mocks yet. Don’t worry still you have 20*24 = 480 hrs in your hand, out of which each day 7-7.30 hrs of sleep is must so, **480...**

13

But sir why would (*a)++ give error? Wouldn't it simply increment the value pointed by a?

14

Acc. to me it should be (C) because: according to condition, out of all, one philosopher will get both the forks. So, deadlock should not be there.

15

Number of equivalence relations possible on a set is actually not Catalan number- it is Bell number. I'll have to do some thinking to do this explanation as it is not a single formula but a recurrence relation. Shall update when done.

17

A. that Who and whom are people, not dogs. Regarding that and which... Restrictive Clause-That A restrictive clause is just part of a sentence that you can't get rid of because it specifically restricts some other part of the sentence. Here's an ... You can think of a nonrestrictive clause as simply additional information. Here's an example: Diamonds, which are expensive, often elicit forgiveness.

18

Consider the finite automaton in the following figure: What is the set of reachable states for the input string $0011$? $\{q_0,q_1,q_2\}$ $\{q_0,q_1\}$ $\{q_0,q_1,q_2,q_3\}$ $\{q_3\}$

19

i think with select operator we can calculate sum and sum is not a relation operator Where can i find the keys of all gate paper ?

20

No adversity justifies giving up hope.. it is the most closest one