Recent questions tagged tifr2014 / GATE Overflow for GATE CSE

7 votes

3 answers

31

TIFR CSE 2014 | Part A | Question: 10
A person went out between $4$pm and $5$pm to chat with her friend and returned between $5$pm and $6$pm. On her return, she found that the hour-hand and the minute-hand of her (well-functioning) clock had just exchanged their positions with respect to ... $\dfrac{1}{3}$ minutes past $4$pm. Twenty eight minutes past $4$pm. None of the above.

A person went out between $4$pm and $5$pm to chat with her friend and returned between $5$pm and $6$pm. On her return, she found that the hour-hand and the minute-hand of...

makhdoom ghaya

1.3k views

makhdoom ghaya asked Nov 9, 2015

9 votes

6 answers

32

TIFR CSE 2014 | Part A | Question: 9
Solve min $x^{2}+y^{2}$ subject to $\begin {align*} x + y &\geq 10,\\ 2x + 3y &\geq 20,\\ x &\geq 4,\\ y &\geq 4. \end{align*}$ $32$ $50$ $52$ $100$ None of the above

Solve min $x^{2}+y^{2}$ subject to$$\begin {align*} x + y &\geq 10,\\2x + 3y &\geq 20,\\x &\geq 4,\\y &\geq 4.\end{align*}$$$32$$50$$52$$100$None of the above

makhdoom ghaya

1.8k views

makhdoom ghaya asked Nov 9, 2015

27 votes

5 answers

33

TIFR CSE 2014 | Part A | Question: 8
All that glitters is gold. No gold is silver. Claims: No silver glitters. Some gold glitters. Then, which of the following is TRUE? Only claim $1$ follows. Only claim $2$ follows. Either claim $1$ or claim $2$ follows but not both. Neither claim $1$ nor claim $2$ follows. Both claim $1$ and claim $2$ follow.

All that glitters is gold. No gold is silver.Claims:No silver glitters.Some gold glitters.Then, which of the following is TRUE?Only claim $1$ follows.Only claim $2$ follo...

makhdoom ghaya

3.5k views

makhdoom ghaya asked Nov 9, 2015

6 votes

1 answer

34

TIFR CSE 2014 | Part A | Question: 7
Consider a sequence of non-negative numbers ${x_{n} : n = 1, 2, . . .}$. Which of the following statements cannot be true? $\sum ^{\infty }_{n=1} x_{n}= \infty $ and $\sum ^{\infty }_{n=1} x_{n}^{2}= \infty$. $\sum ^{\infty }_{n=1} x_{n}= \infty $ ... $\sum ^{\infty }_{n=1} x_{n} < \infty $ and $\sum ^{\infty }_{n=1} x_{n}^{2}= \infty$.

Consider a sequence of non-negative numbers ${x_{n} : n = 1, 2, . . .}$. Which of the following statements cannot be true?$\sum ^{\infty }_{n=1} x_{n}= \infty $ and $\sum...

makhdoom ghaya

971 views

makhdoom ghaya asked Nov 9, 2015

24 votes

3 answers

35

TIFR CSE 2014 | Part A | Question: 5
The rules for the University of Bombay five-a-side cricket competition specify that the members of each team must have birthdays in the same month. What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students? $23$ $91$ $60$ $49$ None of the above

The rules for the University of Bombay five-a-side cricket competition specify that the members of each team must have birthdays in the same month. What is the minimum nu...

makhdoom ghaya

3.6k views

makhdoom ghaya asked Nov 9, 2015

4 votes

2 answers

36

TIFR CSE 2014 | Part A | Question: 4
Consider numbers greater than one that satisfy the following properties: They have no repeated prime factors; For all primes $p \geq 2$, $p$ divides the number if and only if $p − 1$ divides the number. The number of such numbers is $0$ $5$ $100$ Infinite None of the above

Consider numbers greater than one that satisfy the following properties:They have no repeated prime factors;For all primes $p \geq 2$, $p$ divides the number if and only ...

makhdoom ghaya

1.1k views

makhdoom ghaya asked Nov 9, 2015

17 votes

2 answers

37

TIFR CSE 2014 | Part A | Question: 3
The Fibonacci sequence is defined as follows: $F_{0} = 0, F_{1} = 1,$ and for all integers $n \geq 2, F_{n} = F_{n−1} + F_{n−2}$. Then which of the following statements is FALSE? $F_{n+2} = 1 + \sum ^{n}_{i=0} F_{i}$ ... $3$, for every integer $n \geq 0$. $F_{5n}$ is a multiple of $4$, for every integer $n \geq 0$.

The Fibonacci sequence is defined as follows: $F_{0} = 0, F_{1} = 1,$ and for all integers $n \geq 2, F_{n} = F_{n−1} + F_{n−2}$. Then which of the following statemen...

makhdoom ghaya

1.6k views

makhdoom ghaya asked Nov 9, 2015

6 votes

2 answers

38

TIFR CSE 2014 | Part A | Question: 2
A body at a temperature of $30$ Celsius is immersed into a heat bath at $0$ Celsius at time $t = 0$. The body starts cooling at a rate proportional to the temperature difference. Assuming that the heat bath does not change in temperature throughout the process, calculate the ... $\dfrac{\log 29}{\log 25}$ $\large e^{5}$ $1 + \log_{6} 5$ None of the above

A body at a temperature of $30$ Celsius is immersed into a heat bath at $0$ Celsius at time $t = 0$. The body starts cooling at a rate proportional to the temperature dif...

makhdoom ghaya

857 views

makhdoom ghaya asked Nov 9, 2015

3 votes

1 answer

39

TIFR CSE 2014 | Part A | Question: 1
Consider the reactions $X + 2Y \rightarrow 3Z$$2X + Z \rightarrow Y.$ Let $n_{X}$, $n_{Y}$, $n_{Z}$ denote the numbers of molecules of chemicals $X, Y, Z$ in the reaction chamber. Then which of the following is conserved by both reactions? $n_{X} + n_{Y} + n_{Z}$. ... $2n_{X} + 9n_{Y} − 3n_{Z}$. $3n_{X} − 3n_{Y} + 13n_{Z}$. None of the above.

Consider the reactions $$X + 2Y \rightarrow 3Z$$$$2X + Z \rightarrow Y.$$ Let $n_{X}$, $n_{Y}$, $n_{Z}$ denote the numbers of molecules of chemicals $X, Y, Z$ in the reac...

makhdoom ghaya

832 views

makhdoom ghaya asked Nov 9, 2015

32 votes

6 answers

40

TIFR CSE 2010 | Part A | Question: 19, TIFR CSE 2014 | Part A | Question: 6
Karan tells truth with probability $\dfrac{1}{3}$ and lies with probability $\dfrac{2}{3}.$ Independently, Arjun tells truth with probability $\dfrac{3}{4}$ and lies with probability $\dfrac{1}{4}.$ Both watch a cricket match. Arjun tells ... $\left(\dfrac{5}{6}\right)$ $\left(\dfrac{6}{7}\right)$

Karan tells truth with probability $\dfrac{1}{3}$ and lies with probability $\dfrac{2}{3}.$ Independently, Arjun tells truth with probability $\dfrac{3}{4}$ and lies with...

makhdoom ghaya

6.0k views

makhdoom ghaya asked Oct 4, 2015

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