Recent questions tagged tifr2013 / GATE Overflow for GATE CSE

9 votes

3 answers

31

TIFR CSE 2013 | Part A | Question: 10
Three men and three rakhsasas arrive together at a ferry crossing to find a boat with an oar, but no boatman. The boat can carry one or at the most two persons, for example, one man and one rakhsasas, and each man or rakhsasas can row. But if at any ... any mishap, what is the minimum number of times that the boat must cross the river? $7$ $9$ $11$ $13$ $15$

Three men and three rakhsasas arrive together at a ferry crossing to find a boat with an oar, but no boatman. The boat can carry one or at the most two persons, for examp...

makhdoom ghaya

1.6k views

makhdoom ghaya asked Nov 4, 2015

22 votes

5 answers

32

TIFR CSE 2013 | Part A | Question: 9
There are $n$ kingdoms and $2n$ champions. Each kingdom gets $2$ champions. The number of ways in which this can be done is: $\frac{\left ( 2n \right )!}{2^{n}}$ $\frac{\left ( 2n \right )!}{n!}$ $\frac{\left ( 2n \right )!}{2^{n} . n!}$ $\frac{n!}{2}$ None of the above

There are $n$ kingdoms and $2n$ champions. Each kingdom gets $2$ champions. The number of ways in which this can be done is:$\frac{\left ( 2n \right )!}{2^{n}}$$\frac{\le...

makhdoom ghaya

3.3k views

makhdoom ghaya asked Nov 4, 2015

10 votes

1 answer

33

TIFR CSE 2013 | Part A | Question: 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 $ $\left(\dfrac{1}{2}\right)$ $\left(\dfrac{1}{6}\right)$ $\left(\dfrac{1}{12}\right)$ $\left(\dfrac{1}{14}\right)$

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} + .......

makhdoom ghaya

1.3k views

makhdoom ghaya asked Nov 4, 2015

2 votes

1 answer

34

TIFR CSE 2013 | Part A | Question: 7
For any complex number $z$, $arg$ $z$ defines its phase, chosen to be in the interval $0\leq arg z < 360^{∘}$. If $z_{1}, z_{2}$ and $z_{3}$ ... $\frac{1}{3}$ 1 3 $\frac{1}{2}$

For any complex number $z$, $arg$ $z$ defines its phase, chosen to be in the interval $0\leq arg z < 360^{∘}$. If $z_{1}, z_{2}$ and $z_{3}$ are three complex numbers w...

makhdoom ghaya

629 views

makhdoom ghaya asked Nov 4, 2015

19 votes

7 answers

35

TIFR CSE 2013 | Part A | Question: 6
You are lost in the National park of Kabrastan. The park population consists of tourists and Kabrastanis. Tourists comprise two-thirds of the population the park and give a correct answer to requests for directions with probability $\dfrac{3}{4}$. The air of Kabrastan has an ... $\left(\dfrac{1}{2}\right)$ $\left(\dfrac{2}{3}\right)$ $\left(\dfrac{3}{4}\right)$

You are lost in the National park of Kabrastan. The park population consists of tourists and Kabrastanis. Tourists comprise two-thirds of the population the park and give...

makhdoom ghaya

3.3k views

makhdoom ghaya asked Nov 4, 2015

5 votes

3 answers

36

TIFR CSE 2013 | Part A | Question: 5
The late painter Maqbool Fida Husain once coloured the surface of a huge hollow steel sphere, of radius $1$ metre, using just two colours, Red and Blue. As was his style however, both the red and blue areas were a bunch of highly irregular disconnected ... $11 sq. metres$; None of the above.

The late painter Maqbool Fida Husain once coloured the surface of a huge hollow steel sphere, of radius $1$ metre, using just two colours, Red and Blue. As was his style ...

makhdoom ghaya

2.8k views

makhdoom ghaya asked Nov 4, 2015

11 votes

1 answer

37

TIFR CSE 2013 | Part A | Question: 4
A biased coin is tossed repeatedly. Assume that the outcomes of different tosses are independent and probability of heads is $\dfrac{2}{3}$ in each toss. What is the probability of obtaining an even number of heads in $5$ tosses, zero being treated as an even ... $\left(\dfrac{124}{243}\right)$ $\left(\dfrac{125}{243}\right)$ $\left(\dfrac{128}{243}\right)$

A biased coin is tossed repeatedly. Assume that the outcomes of different tosses are independent and probability of heads is $\dfrac{2}{3}$ in each toss. What is the prob...

makhdoom ghaya

1.6k views

makhdoom ghaya asked Nov 4, 2015

18 votes

3 answers

38

TIFR CSE 2013 | Part A | Question: 3
Three candidates, Amar, Birendra and Chanchal stand for the local election. Opinion polls are conducted and show that fraction $a$ of the voters prefer Amar to Birendra, fraction $b$ prefer Birendra to Chanchal and fraction $c$ ... $(a, b, c) = (0.49, 0.49, 0.49);$ None of the above.

Three candidates, Amar, Birendra and Chanchal stand for the local election. Opinion polls are conducted and show that fraction $a$ of the voters prefer Amar to Birendra, ...

makhdoom ghaya

2.5k views

makhdoom ghaya asked Nov 4, 2015

6 votes

1 answer

39

TIFR CSE 2013 | Part A | Question: 2
Consider the following two types of elections to determine which of two parties $A$ and $B$ forms the next government in the 2014 Indian elections. Assume for simplicity an Indian population of size $545545 (=545 * 1001)$ ... by election TYPE P, then it will also form the govt. by election TYPE C. All of the above None of the above

Consider the following two types of elections to determine which of two parties $A$ and $B$ forms the next government in the 2014 Indian elections. Assume for simplicity ...

makhdoom ghaya

734 views

makhdoom ghaya asked Nov 4, 2015

7 votes

3 answers

40

TIFR CSE 2013 | Part A | Question: 1
An infinite two-dimensional pattern is indicated below. The smallest closed figure made by the lines is called a unit triangle. Within every unit triangle, there is a mouse. At every vertex there is a laddoo. What is the average number of laddoos per mouse? $\quad 3$ $\quad 2$ $\quad 1$ $\left(\dfrac{1}{2}\right)$ $\left(\dfrac{1}{3}\right)$

An infinite two-dimensional pattern is indicated below.The smallest closed figure made by the lines is called a unit triangle. Within every unit triangle, there is a mous...

makhdoom ghaya

1.6k views

makhdoom ghaya asked Nov 4, 2015

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