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2
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38k
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Prove that in a full binary tree with n vertices, the number of pendant vertices is (n+1)/2.
discrete mathematics updated 2.8 years ago by sagarkolekar ★ 11k
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20k
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Functions f, g, h are defined on a set, X= {1,2,3} as f= {(1,2) (2,3) (3,1)} g = {(1,2} (2,1) {3,3)) h = {(1, 1 ) (2,2) (3,1)} (i) Find fog, g o f are they equal ? (ii) Find fogoh and fohog.
discrete mathematics updated 2.8 years ago by pedsangini276 • 4.8k
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1.6k
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Write short note on growth of functions.
discrete mathematics updated 2.5 years ago by Krishna_Agrawal • 2.7k
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22k
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Find the generating function for the following sequence 1,2,3,4,5,6.........
discrete mathematics updated 2.8 years ago by pedsangini276 • 4.8k
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558
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Find the normals to the ellipse $x^{2} / 9+y^{2} / 4=1$ which are farthest from its centre.
discrete mathematics updated 2.6 years ago by prajapatijaimin • 3.2k
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482
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If $\alpha=e^{2 \pi i / 7}$ and $f(x)=A_{0}+\sum_{k=1}^{20} A_{k} x^{k} \\$, then find the value of, $f(x)+f(\alpha x)+\ldots+f\left(\alpha^{6} x\right)$ independent of $\alpha .$
discrete mathematics updated 2.6 years ago by prajapatijaimin • 3.2k
2
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625
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If, $ f(x)=x, \quad 0<x<\frac{\pi}{2} $ $ =\pi-x, \quad \frac{\pi}{2}<x<\pi $ show that, (i) $f(x)=\frac{4}{\pi}\left[\sin x-\frac{\sin 3 x}{3^{2}}+\frac{\sin 5 x}{5^{2}}-\ldots \ldots\right]$
discrete mathematics updated 2.6 years ago by prajapatijaimin • 3.2k
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1.1k
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Determine the Eulerian and Hamiltonian path, if exists, in the following graphs:
discrete mathematics updated 2.8 years ago by pedsangini276 • 4.8k
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3.8k
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Define isometric graphs. Show that following graphs are isomorphic.
discrete mathematics updated 2.8 years ago by sagarkolekar ★ 11k
1
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21k
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How many vertices are necessary to construct a graph with exactly 6 edges in which each vertex is of degree 2.
discrete mathematics updated 2.8 years ago by sagarkolekar ★ 11k
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1.8k
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Let the function f, g and h defined as follows: $f: R- > R, f(x)=2x+3\\ g:R- > R, g(x)=3x+4\\ h:R- > R, h(x)=4x \\ \text{Find gof, fog, foh, hof, gofoh}$
discrete mathematics updated 2.8 years ago by sagarkolekar ★ 11k
0
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985
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Find the generating function for the following series
discrete mathematics updated 2.8 years ago by pedsangini276 • 4.8k
0
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1.2k
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Find the generating function for the following sequence
discrete mathematics updated 2.8 years ago by pedsangini276 • 4.8k
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3.9k
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Find the solution to the recurrence relation $a_n=6a_{n-1}+11a_{n-2}-6a_{n-3}$ given $a_0=20,a_1=5 \ \ and \ \ a_2=15$
discrete mathematics updated 2.8 years ago by pedsangini276 • 4.8k
2
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49k
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R be a relation on set of integers Z defined by R = {(x, y) | x-y is divisible by 3} Show that R is an equivalence relation and describe the equivalence classes.
discrete mathematics updated 2.1 years ago by sagarkolekar ★ 11k
0
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834
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Show that the following graphs are isometric
discrete mathematics updated 2.8 years ago by pedsangini276 • 4.8k
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1.6k
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Determine if following graphs g and G' are isomorphic or not.
discrete mathematics updated 2.8 years ago by pedsangini276 • 4.8k
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1.5k
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Determine Euler Cycle and path in graph shown below
discrete mathematics updated 2.8 years ago by pedsangini276 • 4.8k
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2.0k
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If f:A->B and if g:B->C are both one-one and onto, then $(g o f)^{-1} =f^{-1} o g ^{-1}$
discrete mathematics updated 2.8 years ago by pedsangini276 • 4.8k
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1.2k
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Define Eular path and Eular circuit, determine whether the given graph has Eular path and Eular circuit.
discrete mathematics updated 2.8 years ago by pedsangini276 • 4.8k
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3.6k
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Define isomorphic graphs. Show that the following two graphs are isomorphic.
discrete mathematics updated 2.8 years ago by pedsangini276 • 4.8k
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3.1k
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Let G be the set of rational numbers other than 1.
discrete mathematics updated 2.8 years ago by pedsangini276 • 4.8k
1
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19k
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Show that if every element in a group is its own inverse, then the group must be abelian.
discrete mathematics updated 2.8 years ago by pedsangini276 • 4.8k
0
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1.1k
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prove that by mathematical induction
discrete mathematics updated 2.8 years ago by pedsangini276 • 4.8k
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4.9k
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How many vertices are necessary to construct a graph with exactly 6 edges in which each vertex is of degree 2.
discrete mathematics updated 2.8 years ago by pedsangini276 • 4.8k
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