Answers by pratekag / GATE Overflow for GATE CSE

1 votes

1

Self Doubt about ME Test Series
Are comparison charts of Made easy genuine? And say now if my rank is 3 in a test and after sometime if someone scores more than me will my rank get shifted to 4?

Are comparison charts of Made easy genuine?And say now if my rank is 3 in a test and after sometime if someone scores more than me will my rank get shifted to 4?

645 views

answered May 26, 2019

2 votes

2

ISI2019-MMA-21
A function $f:\mathbb{R^2} \rightarrow \mathbb{R}$ is called degenerate on $x_i$, if $f(x_1,x_2)$ remains constant when $x_i$ varies $(i=1,2)$. Define $f(x_1,x_2) = \mid 2^{\pi _i/x_1} \mid ^{x_2} \text{ for } x_1 \neq 0$, where $i = \sqrt {-1}$. ... $x_1$ but not on $x_2$ $f$ is degenerate on $x_2$ but not on $x_1$ $f$ is neither degenerate on $x_1$ nor on $x_2$

A function $f:\mathbb{R^2} \rightarrow \mathbb{R}$ is called degenerate on $x_i$, if $f(x_1,x_2)$ remains constant when $x_i$ varies $(i=1,2)$. Define$$f(x_1,x_2) = \mid ...

1.4k views

answered May 13, 2019

0 votes

3

ISI2019-MMA-12
Given a positive integer $m$, we define $f(m)$ as the highest power of $2$ that divides $m$. If $n$ is a prime number greater than $3$, then $f(n^3-1) = f(n-1)$ $f(n^3-1) = f(n-1) +1$ $f(n^3-1) = 2f(n-1)$ None of the above is necessarily true

Given a positive integer $m$, we define $f(m)$ as the highest power of $2$ that divides $m$. If $n$ is a prime number greater than $3$, then$f(n^3-1) = f(n-1)$$f(n^3-1) =...

1.9k views

answered May 10, 2019

1 votes

4

ISI2019-MMA-13
Let $V$ be the vector space of all $4 \times 4$ matrices such that the sum of the elements in any row or any column is the same. Then the dimension of $V$ is $8$ $10$ $12$ $14$

Let $V$ be the vector space of all $4 \times 4$ matrices such that the sum of the elements in any row or any column is the same. Then the dimension of $V$ is$8$$10$$12$$1...

2.4k views

answered May 9, 2019

3 votes

5

ISI2019-MMA-8
For $0 \leq x < 2 \pi$, the number of solutions of the equation $\sin^2x + 2 \cos^2x + 3\sin x \cos x = 0$ is $1$ $2$ $3$ $4$

For $0 \leq x < 2 \pi$, the number of solutions of the equation$$\sin^2x + 2 \cos^2x + 3\sin x \cos x = 0$$is$1$$2$$3$$4$

1.3k views

answered May 7, 2019

1 votes

6

ISI2019-MMA-20
Suppose that the number plate of a vehicle contains two vowels followed by four digits. However, to avoid confusion, the letter $‘O’$ and the digit $‘0’$ are not used in the same number plate. How many such number plates can be formed? $164025$ $190951$ $194976$ $219049$

Suppose that the number plate of a vehicle contains two vowels followed by four digits. However, to avoid confusion, the letter $‘O’$ and the digit $‘0’$ are not ...

2.5k views

answered May 7, 2019

1 votes

7

ISI2019-MMA-24
Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a continuous function such that $\lim _{n\rightarrow \infty} f^n(x)$ exists for every $x \in \mathbb{R}$, where $f^n(x) = f \circ f^{n-1}(x)$ for $n \geq 2$ ... $S \subset T$ $T \subset S$ $S = T$ None of the above

Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a continuous function such that $\lim _{n\rightarrow \infty} f^n(x)$ exists for every $x \in \mathbb{R}$, where $f^n(x) = f ...

1.6k views

answered May 7, 2019

1 votes

8

ISI2019-MMA-26
If $t = \begin{pmatrix} 200 \\ 100 \end{pmatrix}/4^{100} $, then $t < \frac{1}{3}$ $\frac{1}{3} < t < \frac{1}{2}$ $\frac{1}{2} < t < \frac{2}{3}$ $\frac{2}{3} < t < 1$

If $t = \begin{pmatrix} 200 \\ 100 \end{pmatrix}/4^{100} $, then$t < \frac{1}{3}$$\frac{1}{3} < t < \frac{1}{2}$$\frac{1}{2} < t < \frac{2}{3}$$\frac{2}{3} < t < 1$

1.6k views

answered May 7, 2019

7 votes

9

ISI2019-MMA-30
Consider the function $h$ defined on $\{0,1,…….10\}$ with $h(0)=0, \: h(10)=10 $ and $2[h(i)-h(i-1)] = h(i+1) – h(i) \: \text{ for } i = 1,2, \dots ,9.$ Then the value of $h(1)$ is $\frac{1}{2^9-1}\\$ $\frac{10}{2^9+1}\\$ $\frac{10}{2^{10}-1}\\$ $\frac{1}{2^{10}+1}$

Consider the function $h$ defined on $\{0,1,…….10\}$ with $h(0)=0, \: h(10)=10 $ and$$2[h(i)-h(i-1)] = h(i+1) – h(i) \: \text{ for } i = 1,2, \dots ,9.$$Then t...

1.8k views

answered May 7, 2019

4 votes

10

ISI2019-MMA-28
Consider the functions $f,g:[0,1] \rightarrow [0,1]$ given by $f(x)=\frac{1}{2}x(x+1) \text{ and } g(x)=\frac{1}{2}x^2(x+1).$ Then the area enclosed between the graphs of $f^{-1}$ and $g^{-1}$ is $1/4$ $1/6$ $1/8$ $1/24$

Consider the functions $f,g:[0,1] \rightarrow [0,1]$ given by$$f(x)=\frac{1}{2}x(x+1) \text{ and } g(x)=\frac{1}{2}x^2(x+1).$$Then the area enclosed between the graphs of...

2.1k views

answered May 7, 2019

4 votes

11

ISI2019-MMA-29
Let $\psi : \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function with $\psi(y) =0$ for all $y \notin [0,1]$ and $\int_{0}^{1} \psi(y) dy=1$. Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a twice differentiable function. Then the value of $\lim _{n\rightarrow \infty}n \int_{0}^{100} f(x)\psi(nx)dx$ is $f(0)$ $f’(0)$ $f’’(0)$ $f(100)$

Let $\psi : \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function with $\psi(y) =0$ for all $y \notin [0,1]$ and $\int_{0}^{1} \psi(y) dy=1$. Let $f:\mathbb{R} \rig...

2.0k views

answered May 7, 2019

2 votes

12

ISI2019-MMA-23
Let $A$ be $2 \times 2$ matrix with real entries. Now consider the function $f_A(x)$ = $Ax$ . If the image of every circle under $f_A$ is a circle of the same radius, then A must be an orthogonal matrix A must be a symmetric matrix A must be a skew-symmetric matrix None of the above must necessarily hold

Let $A$ be $2 \times 2$ matrix with real entries. Now consider the function $f_A(x)$ = $Ax$ . If the image of every circle under $f_A$ is a circle of the same radius, the...

1.8k views

answered May 7, 2019

11 votes

13

ISI2019-MMA-11
How many triplets of real numbers $(x,y,z)$ are simultaneous solutions of the equations $x+y=2$ and $xy-z^2=1$? $0$ $1$ $2$ infinitely many

How many triplets of real numbers $(x,y,z)$ are simultaneous solutions of the equations $x+y=2$ and $xy-z^2=1$?$0$$1$$2$infinitely many

1.8k views

answered May 7, 2019

2 votes

14

ISI2019-MMA-25
Let $a,b,c$ be non-zero real numbers such that $\int_{0}^{1} (1 + \cos^8x)(ax^2 + bx +c)dx = \int_{0}^{2}(1+ \cos^8x)(ax^2 + bx + c) dx =0$ Then the quadratic equation $ax^2 + bx +c=0$ has no roots in $(0,2)$ one root in $(0,2)$ and one root outside this interval one repeated root in $(0,2)$ two distinct real roots in $(0,2)$

Let $a,b,c$ be non-zero real numbers such that $\int_{0}^{1} (1 + \cos^8x)(ax^2 + bx +c)dx = \int_{0}^{2}(1+ \cos^8x)(ax^2 + bx + c) dx =0$Then the quadratic equation $ax...

1.2k views

answered May 7, 2019

13 votes

15

ISI2019-MMA-27
A general election is to be scheduled on $5$ days in May such that it is not scheduled on two consecutive days. In how many ways can the $5$ days be chosen to hold the election? $\begin{pmatrix} 26 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 27 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 30 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 31 \\ 5 \end{pmatrix}$

A general election is to be scheduled on $5$ days in May such that it is not scheduled on two consecutive days. In how many ways can the $5$ days be chosen to hold the el...

5.0k views

answered May 7, 2019

3 votes

16

ISI2019-MMA-22
A coin with probability $p (0 < p < 1)$ of getting head, is tossed until a head appears for the first time. If the probability that the number of tosses required is even is $2/5$, then the value of $p$ is $2/7$ $1/3$ $5/7$ $2/3$

A coin with probability $p (0 < p < 1)$ of getting head, is tossed until a head appears for the first time. If the probability that the number of tosses required is even ...

912 views

answered May 7, 2019

0 votes

17

ISI2019-MMA-13
Let $V$ be the vector space of all $4 \times 4$ matrices such that the sum of the elements in any row or any column is the same. Then the dimension of $V$ is $8$ $10$ $12$ $14$

Let $V$ be the vector space of all $4 \times 4$ matrices such that the sum of the elements in any row or any column is the same. Then the dimension of $V$ is$8$$10$$12$$1...

2.4k views

answered May 7, 2019

0 votes

18

MadeEasy Test Series: Programming & DS - Stack
My doubt : What should we consider ^ operator as Bitwise XOR ? or Exponentiation

My doubt : What should we consider ^ operator as Bitwise XOR ? or Exponentiation

1.3k views

answered May 6, 2019

4 votes

19

ISI2019-MMA-5
If $f(a)=2, \: f’(a) = 1, \: g(a) =-1$ and $g’(a) =2$, then the value of $\lim _{x\rightarrow a}\frac{g(x) f(a) – f(x) g(a)}{x-a}$ is $-5$ $-3$ $3$ $5$

If $f(a)=2, \: f’(a) = 1, \: g(a) =-1$ and $g’(a) =2$, then the value of $$\lim _{x\rightarrow a}\frac{g(x) f(a) – f(x) g(a)}{x-...

783 views

answered May 6, 2019

6 votes

20

ISI2019-MMA-2
The number of $6$ digit positive integers whose sum of the digits is at least $52$ is $21$ $22$ $27$ $28$

The number of $6$ digit positive integers whose sum of the digits is at least $52$ is$21$$22$$27$$28$

3.5k views

answered May 6, 2019

4 votes

21

ISI2019-MMA-4
Suppose that $6$-digit numbers are formed using each of the digits $1, 2, 3, 7, 8, 9$ exactly once. The number of such $6$-digit numbers that are divisible by $6$ but not divisible by $9$ is equal to $120$ $180$ $240$ $360$

Suppose that $6$-digit numbers are formed using each of the digits $1, 2, 3, 7, 8, 9$ exactly once. The number of such $6$-digit numbers that are divisible by $6$ but not...

2.1k views

answered May 6, 2019

5 votes

22

ISI2019-MMA-1
The highest power of $7$ that divides $100!$ is : $14$ $15$ $16$ $18$

The highest power of $7$ that divides $100!$ is : $14$$15$$16$$18$

3.6k views

answered May 6, 2019

4 votes

23

ISI2019-MMA-3
The sum of all $3$ digit numbers that leave a remainder of $2$ when divided by $3$ is: $189700$ $164850$ $164750$ $149700$

The sum of all $3$ digit numbers that leave a remainder of $2$ when divided by $3$ is:$189700$$164850$$164750$$149700$

964 views

answered May 6, 2019

1 votes

24

IIIT PGEE 2019
Which of the following gives O(1) complexity if we want to check whether an edge exists between two given nodes in a graph? Adjacency List Adjacency Matrix Incidence Matrix None of these

Which of the following gives O(1) complexity if we want to check whether an edge exists between two given nodes in a graph?Adjacency ListAdjacency MatrixIncidence MatrixN...

1.4k views

answered Apr 29, 2019

0 votes

25

Admission Query GATE 2019
For ~77 marks (GO Estimated AIR 53-55, Score ~882) in GATE 2019, is there a chance of getting direct admission into IISc or IIT Bombay/Delhi? The rank has been dropping steadily in the last few days. I'm very confused as I would like to ... admissions seem improbable. GO has taken me this far but I'll need a little more help :D Any insights would be really appreciated!

For ~77 marks (GO Estimated AIR 53-55, Score ~882) in GATE 2019, is there a chance of getting direct admission into IISc or IIT Bombay/Delhi? The rank has been dropping s...

1.9k views

answered Apr 27, 2019

0 votes

26

IIT Bombay MTech Admission form
What to fill in qualifying degree and duration of course if one is a Dual (BTech+ MTech) student and wants to pursue postgraduate from IIT again?

What to fill in qualifying degree and duration of course if one is a Dual (BTech+ MTech) student and wants to pursue postgraduate from IIT again?

764 views

answered Apr 27, 2019

11 votes

27

GATE CSE 2019 | Question: 46
Let $T$ be a full binary tree with $8$ leaves. (A full binary tree has every level full.) Suppose two leaves $a$ and $b$ of $T$ are chosen uniformly and independently at random. The expected value of the distance between $a$ and $b$ in $T$ (ie., the number of edges in the unique path between $a$ and $b$) is (rounded off to $2$ decimal places) _________.

Let $T$ be a full binary tree with $8$ leaves. (A full binary tree has every level full.) Suppose two leaves $a$ and $b$ of $T$ are chosen uniformly and independently at ...

30.9k views

answered Feb 19, 2019

4 votes

28

Gate 2019
When will the official key be released?Are there any wrong answers given in GO rank predictor?

When will the official key be released?Are there any wrong answers given in GO rank predictor?

1.5k views

answered Feb 12, 2019

0 votes

29

GATE CSE 2019 | Question: 26
Consider the following C function. void convert (int n ) { if (n<0) printf{ %d , n); else { convert(n/2); printf( %d , n%2); } } Which one of the following will happen when the function convert is called with any positive ... order and terminate It will print the binary representation of $n$ but will not terminate It will not print anything and will not terminate

Consider the following C function.void convert (int n ) { if (n<0) printf{“%d”, n); else { convert(n/2); printf(“%d”, n%2); } }Which one of the following will hap...

16.8k views

answered Feb 11, 2019

0 votes

30

gate 2019
what about time ordering protocol?

what about time ordering protocol?

431 views

answered Feb 6, 2019

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