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Recent questions tagged tifr2011

21 votes
3 answers
31
TIFR CSE 2011 | Part A | Question: 10
Let $m$, $n$ denote two integers from the set $\{1, 2,\dots,10\}$. The number of ordered pairs $\left ( m, n \right )$ such that $2^{m}+2^{n}$ is divisible by $5$ is. $10$ $14$ $24$ $8$ None of the above
Let $m$, $n$ denote two integers from the set $\{1, 2,\dots,10\}$. The number of ordered pairs $\left ( m, n \right )$ such that $2^{m}+2^{n}$ is divisible by $5$ is.$10$...
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14 votes
1 answer
34
TIFR CSE 2011 | Part A | Question: 7
Let $X$ and $Y$ be two independent and identically distributed random variables. Then $P\left ( X> Y \right )$ is. $\frac{1}{2}$ 1 0 $\frac{1}{3}$ Information is insufficient.
Let $X$ and $Y$ be two independent and identically distributed random variables. Then $P\left ( X Y \right )$ is.$\frac{1}{2}$10$\frac{1}{3}$Information is insufficient.
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19 votes
4 answers
35
TIFR CSE 2011 | Part A | Question: 6
Assume that you are flipping a fair coin, i.e. probability of heads or tails is equal. Then the expected number of coin flips required to obtain two consecutive heads for the first time is. $4$ $3$ $6$ $10$ $5$
Assume that you are flipping a fair coin, i.e. probability of heads or tails is equal. Then the expected number of coin flips required to obtain two consecutive heads for...
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10 votes
2 answers
37
TIFR CSE 2011 | Part A | Question: 4
Consider the problem of maximizing $x^{2}-2x+5$ such that $0< x< 2$. The value of $x$ at which the maximum is achieved is: $0.5$ $1$ $1.5$ $1.75$ None of the above
Consider the problem of maximizing $x^{2}-2x+5$ such that $0< x< 2$. The value of $x$ at which the maximum is achieved is:$0.5$$1$$1.5$$1.75$None of the above
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14 votes
4 answers
38
TIFR CSE 2011 | Part A | Question: 3
The probability of three consecutive heads in four tosses of a fair coin is $\left(\dfrac{1}{4}\right)$ $\left(\dfrac{1}{8}\right)$ $\left(\dfrac{1}{16}\right)$ $\left(\dfrac{3}{16}\right)$ None of the above
The probability of three consecutive heads in four tosses of a fair coin is$\left(\dfrac{1}{4}\right)$$\left(\dfrac{1}{8}\right)$$\left(\dfrac{1}{16}\right)$$\left(\dfrac...
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13 votes
2 answers
39
TIFR CSE 2011 | Part A | Question: 2
In how many ways can the letters of the word $\text{ABACUS}$ be rearranged such that the vowels always appear together? $\dfrac{(6+3)!}{2!}$ $\dfrac{6!}{2!}$ $\dfrac{3!3!}{2!}$ $\dfrac{4!3!}{2!}$ None of the above
In how many ways can the letters of the word $\text{ABACUS}$ be rearranged such that the vowels always appear together?$\dfrac{(6+3)!}{2!}$ $\dfrac{6!}{2!}$ $\dfrac{3!3!}...
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