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In equilibrium, A and B are in a horizontal line. If $ \angle B A C=\alpha \text { and } \angle A B C=\beta \text {, What is the ratio of } \tan \alpha: \tan \beta ? $
data structures and graph theory updated 20 hours ago by prajapatijaimin • 2.3k
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If the line of action of the resultant of two forces P and Q divides the angle between them in the ratio 1 : 2, What is magnitude of the resultant?
data structures and graph theory updated 21 hours ago by prajapatijaimin • 2.3k
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Find all spanning trees for the graph G pictured below.
data structures and graph theory updated 2 days ago by prajapatijaimin • 2.3k
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Solve the following recurrence relation : (i) $a_{r}-7 a_{r-1}+10 a_{r-2}=0$ given that $a_{0}=0$, $a_{1}=3$ (ii) $a_{r}-4 a_{r-1}+4 a_{r}-2=0$ given that $a_{0}=1$ and $a_{1}=6$
data structures and graph theory updated 2 days ago by prajapatijaimin • 2.3k
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If $A=\{1,2,3,4,5\}$ and $R=\{(1,2),(3,4),(4,5),(4,1),(1,1)\}$ find its transitive closure.
data structures and graph theory updated 2 days ago by prajapatijaimin • 2.3k
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Obtain disjunctive normal form of, i) $(p \rightarrow q) \wedge(\sim p \wedge q)$ ii) $(p \wedge(p \rightarrow q)) \rightarrow q$
data structures and graph theory updated 8 days ago by prajapatijaimin • 2.3k
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Find the shortest path between each pair of vertices for a simple graph using Warshall's algorithm.
data structures and graph theory updated 10 days ago by prajapatijaimin • 2.3k
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Find a root of $x^{4}-x^{3}+10 x+7=0$ correct up to three decimal places between $-2$ and $-1$ by Newten Raphson method.
data structures and graph theory updated 10 days ago by prajapatijaimin • 2.3k
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Find a root of the equation $x^{3}+x-1=0$ correct to three decimal places, by the method of False Position.
data structures and graph theory updated 10 days ago by prajapatijaimin • 2.3k
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Find a root of $x^{3}-x-1=0$ using Bisection methed correct to three decimal places.
data structures and graph theory updated 10 days ago by prajapatijaimin • 2.3k
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$ \text { If } C(n, 3)+C(n+2,3)=P(n, 3) \text {, find } n \text {. } $
data structures and graph theory updated 11 days ago by prajapatijaimin • 2.3k
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How many automobile license plates can be made if each plate contains taw different letters followed by three different digits. Solve the problem if the first digit can't be 0.
data structures and graph theory updated 11 days ago by prajapatijaimin • 2.3k
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a) Find the number of students staying in all three subjects. b) Find the number of students studying exactly one of the three subjects.
data structures and graph theory updated 11 days ago by prajapatijaimin • 2.3k
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How many integers between 1 to 2000 are divisible by 2, 3, 5 or 7?
data structures and graph theory updated 11 days ago by prajapatijaimin • 2.3k
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Define a binary operation *on the set $\{0,1,2,3,4,5\}$ as,
data structures and graph theory updated 14 days ago by prajapatijaimin • 2.3k
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Show that function $f: \mathbf{R} \rightarrow\{x \in \mathbf{R}:-1<x<1\}$ defined by $f(x)=\frac{x}{1+|x|}, x \in \mathbf{R}$ is one-one and onto function.
data structures and graph theory updated 14 days ago by prajapatijaimin • 2.3k
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Let $f: \mathrm{W} \rightarrow \mathrm{W}$ be defined as $f(n)=n-1$, if is odd and $f(n)=n+1$, if $n$ is even. Show that $f$ is invertible. Find the inverse of $f$. Here, $W$ is the set of all whole n
data structures and graph theory updated 14 days ago by prajapatijaimin • 2.3k
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Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be defined as $f(x)=10 x+7$. Find the function $g: \mathbf{R} \rightarrow \mathbf{R}$ such that $g$ o $f=f$ $\circ g=1_{\mathbf{R}}$.
data structures and graph theory updated 16 days ago by prajapatijaimin • 2.3k
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Consider $f:\{1,2,3\} \rightarrow\{a, b, c\}$ given by $f(1)=a, f(2)=b$ and $f(3)=c$. Find $f^{-1}$ and show that $\left(f^{-1}\right)^{-1}=f$.
data structures and graph theory updated 16 days ago by prajapatijaimin • 2.3k
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Consider $f: \mathbf{R}_{+} \rightarrow[-5, \infty)$ given by $f(x)=9 x^{2}+6 x-5 .$ Show that $f$ is invertible with $ f^{-1}(y)=\left(\frac{(\sqrt{y+6})-1}{3}\right) $
data structures and graph theory updated 16 days ago by prajapatijaimin • 2.3k
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Show that $f$ is invertible with the inverse $f^{-1}$ of given $f$ by $f^{-1}(y)=\sqrt{y-4}$ where $\mathbf{R}_{+}$is the set of all non-negative real numbers.
data structures and graph theory updated 17 days ago by prajapatijaimin • 2.3k
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Show that $f:[-1,1] \rightarrow \mathbf{R}$, given by $f(x)=\frac{x}{(x+2)}$ is one-one. Find the inverse of the function $f:[-1,1] \rightarrow$ Range $f$.
data structures and graph theory updated 17 days ago by prajapatijaimin • 2.3k
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Let f, g and h be functions from R to R. Show that,
data structures and graph theory updated 18 days ago by prajapatijaimin • 2.3k
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In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.
data structures and graph theory updated 18 days ago by prajapatijaimin • 2.3k
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What is the set of all elements in A related to the right angle triangle T with sides 3, 4 and 5?
data structures and graph theory updated 19 days ago by prajapatijaimin • 2.3k
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