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Recent questions tagged iitb-practice-set

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4
IITB Practice Set: 4
Kamala tosses $11$ fair coins and Rajani tosses $10$ fair coins. The probability that the number of heads obtained by Kamala is more than the number of tails obtained by Rajani is _____.
Kamala tosses $11$ fair coins and Rajani tosses $10$ fair coins. The probability that the number of heads obtained by Kamala is more than the number of tails obtained by ...
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9
IITB Practice Set: 9
Consider expression trees made up of variables and the operator $+$ ... $4$ registers to evaluate is _______.
Consider expression trees made up of variables and the operator $+$. Let the size of a tree be defined as the number of nodes in the tree, counting both internal and leaf...
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11
IITB Practice Set: 11
Let $F$ be a propositional formula. Let $G(x)$ be a propositional formula containing propositional variable $x.$ For some propositional formula $H,$ let $G(H)$ be the formula obtained by replacing all occurrences of $x$ by $H$ ... $F \Rightarrow G(F) \equiv F \Rightarrow G\text{(False)}$
Let $F$ be a propositional formula. Let $G(x)$ be a propositional formula containing propositional variable $x.$For some propositional formula $H,$ let $G(H)$ be the form...
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12
IITB Practice Set: 12
Which of the following identities are true for arbitrary regular languages $R$ and $S$. Choose ALL correct answers. $(R^\ast S^\ast)^{\ast}= (R+S)^{\ast}$ $(RS)^{\ast}R = R(SR)^{\ast}$ $(R+RS)^{\ast} = \left(R^{\ast} +RS^{\ast}\right)^{\ast}$ $(R+S)^{\ast} S = (R^{\ast} S)^{\ast}$
Which of the following identities are true for arbitrary regular languages $R$ and $S$. Choose ALL correct answers.$(R^\ast S^\ast)^{\ast}= (R+S)^{\ast}$$(RS)^{\ast}R = R...
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14
IITB Practice Set: 14
Suppose the ground is the $(x, y)$ plane and the sun is located at infinity in the direction of the vector $(1,2,1)$. When a flying bird is at the point $(1,1,1)$, its shadow on the ground will fall on the coordinates $(x, y)=$ ______.
Suppose the ground is the $(x, y)$ plane and the sun is located at infinity in the direction of the vector $(1,2,1)$.When a flying bird is at the point $(1,1,1)$, its sha...
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16
IITB Practice Set: 16
A $\textit{proper edge coloring}$ of a graph is an assignment of colors to the edges so that any two edges sharing a common vertex should get different colors. Let $G$ be a graph with $20$ vertices that has a proper edge coloring with $6$ colors. The maximum number of edges in $G$ can be ______.
A $\textit{proper edge coloring}$ of a graph is an assignment of colors to the edges so that any two edges sharing a common vertex should get different colors. Let $G$ be...
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28
IITB Practice Set: 28
Consider the following algorithm. What does the above algorithm compute?
Consider the following algorithm.What does the above algorithm compute?
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29
IITB Practice Set: 29
The input is an array $A$ of size $n\geq 5$. As output we require indices $i < j < k$ such that either $A[i] \leq A[ j] \leq A[k]\text{ or }A[i] \geq A[ j] \geq A[k]$. The worst case complexity of the best algorithm for this problem is $\theta$ ______ .
The input is an array $A$ of size $n\geq 5$. As output we require indices $i < j < k$ such that either $A[i] \leq A[ j] \leq A[k]\text{ or }A[i] \geq A[ j] \geq A[k]$. Th...
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30
IITB Practice Set: 30
How many ordered pairs of positive integers $(a,b)$ are there such that $\text{lcm}(a,b) = n \text{ and gcd}(a,b) = 1?$ Express your answer in terms of the prime factorization of $n$, given as $n = p_1^{d_1} \dots p_t^{d_t}.$
How many ordered pairs of positive integers $(a,b)$ are there such that $\text{lcm}(a,b) = n \text{ and gcd}(a,b) = 1?$Express your answer in terms of the prime factoriza...
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