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3 votes
3 answers
8744
Find out the recurrence relation for the given problem
If $a_n$ is number of ternary sequences of length $n$ with even number of $0$'s, then the recurrence relation for $a_n$ is? Also find the value of $a_8$.
If $a_n$ is number of ternary sequences of length $n$ with even number of $0$'s, then the recurrence relation for $a_n$ is?Also find the value of $a_8$.
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1 votes
2 answers
8745
Use generating function to solve question
Use generating function to determine the number of different ways 10 identical balloons can be given to 4 children if each children receives at least 2 balloons.
Use generating function to determine the number of different ways 10 identical balloons can be given to 4 children if each children receives at least 2 balloons.
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2 votes
1 answer
8747
What is the number of linearly independent solutions of a set of vectors taken from identity matrix?
If I have 3 sets of vectors X=(1,0,0) , Y= (0,1,0) and Z=(0,0,1) then these all form a linearly independent set of vectors ,so K(X)+P(Y)+Q(Z) =0 , so we get K=P=Q=0 , but...
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2 votes
1 answer
8748
If rank of a matrix is n-1 then how is it that adjoint of matrix is not equal to zero ?
Clearly |A|=0 ,so A*adj A=0 now since A is not null therefore Adj A can be anything , is may or may not be null so how can we say directly that adj A is not equal to 0        
Clearly |A|=0 ,so A*adj A=0 now since A is not null therefore Adj A can be anything , is may or may not be null so how can we say directly that adj A is not equal to 0 �...
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25 votes
7 answers
8750
TIFR CSE 2011 | Part A | Question: 19
Three dice are rolled independently. What is the probability that the highest and the lowest value differ by $4$? $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{6}\right)$ $\left(\dfrac{1}{9}\right)$ $\left(\dfrac{5}{18}\right)$ $\left(\dfrac{2}{9}\right)$
Three dice are rolled independently. What is the probability that the highest and the lowest value differ by $4$? $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{6}\righ...
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6 votes
1 answer
8751
TIFR CSE 2011 | Part A | Question: 17
What is $\lim_{x \to 0} \frac{2^x-1}{x}$ $0$ $\log_2(e)$ $\log_e(2)$ $1$ None of the above
What is $$\lim_{x \to 0} \frac{2^x-1}{x}$$$0$$\log_2(e)$$\log_e(2)$$1$None of the above
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3 votes
1 answer
8752
symmetric matrix
Let $A =\begin{bmatrix} P & Q\\ R & Q\ \end{bmatrix}$. If $P,Q,R$ and $S$ are symmetric , What can you say about $A$?
Let $A =\begin{bmatrix} P & Q\\ R & Q\ \end{bmatrix}$. If $P,Q,R$ and $S$ are symmetric , What can you say about $A$?
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12 votes
4 answers
8753
TIFR CSE 2011 | Part A | Question: 14
The limit $\lim_{x \to 0} \frac{d}{dx}\,\frac{\sin^2 x}{x}$ is $0$ $2$ $1$ $\frac{1}{2}$ None of the above
The limit $$\lim_{x \to 0} \frac{d}{dx}\,\frac{\sin^2 x}{x}$$ is$0$$2$$1$$\frac{1}{2}$None of the above
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10 votes
3 answers
8755
TIFR CSE 2011 | Part A | Question: 11
$\int_{0}^{1} \log_e(x) dx=$ $1$ $-1$ $\infty $ $-\infty $ None of the above
$$\int_{0}^{1} \log_e(x) dx=$$$1$$-1$$\infty $$-\infty $None of the above
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1 votes
0 answers
8756
Graph
Find Maximum and Minimum no of edges in a graph G with n vertices if G has 3 component with 2 non acyclic and 1 acyclic component?
Find Maximum and Minimum no of edges in a graph G with n vertices if G has 3 component with 2 non acyclic and 1 acyclic component?
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21 votes
3 answers
8757
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
8759
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
8760
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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