DMGT Exam Prep
Full explanation, worked examples & memory tricks in the app
🎯 Exam Preparation Kit
DMGT Exam Prep
English 13 leveled MCQs Free
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What you'll study, topic by topic
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Sample questions with model answers
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7 marks Long answer
Find the co-efficient of $x^3 y^3 z^2$ in $(2x-y+z)^8$ multinomial.
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The coefficient is 6720.
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7 marks Long answer
Solve the recurrence relation $a_n - 4a_{n-1} + 3a_{n-2} = 2^n$, $n \ge 2$ with initial conditions $a_0=1, a_1=1$, using characteristic roots.
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The solution is $a_n = C_1 \cdot 3^n + C_2 \cdot 1^n + 2^n$.
The full exam-length answer is in the app.
5 marks Long answer
Solve the recurrence relation $a_n = 3a_{n-1} + 2^n$ where $a_0 = 1$ by generating function.
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The solution is $a_n = 2^n + 1$.
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5 marks Long answer
Prove that a tree with $n$ vertices has $n-1$ edges.
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By induction, a tree with $n$ vertices has $n-1$ edges.
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5 marks Long answer
Solve $a_n = a_{n-1} + f(n)$ for $n \ge 1$ by using substitution method.
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Use substitution to express $a_n$ in terms of $f(n)$.
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4 marks Medium answer
How many four digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, if repetition of digits is allowed?
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There are 5,000 four-digit numbers.
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4 marks Medium answer
Find the no. of arrangements of the letters in the word ENGINEERING.
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The number of arrangements is 1,260.
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4 marks Medium answer
Find how many solutions are there for $x_1+x_2+x_3=17$, subject to the constraints $x_1 \ge 1, x_2 \ge 2, x_3 \ge 3$.
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There are 105 solutions.
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4 marks Medium answer
Define (1) Directed graph (2) Complete graph (3) Hamiltonian graph (4) Eulerian graph.
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1. Directed graph: edges have directions. 2. Complete graph: every pair of vertices is connected. 3. Hamiltonian graph: contains a Hamiltonian cycle. 4. Eulerian graph: contains an Eulerian circuit.
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2 marks Short answer
Write Binomial theorem.
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The Binomial theorem states $(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k$.
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2 marks Short answer
Define Euler's formula & problems.
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Euler's formula states $e^{ix} = \cos(x) + i\sin(x)$.
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2 marks Short answer
State sum of degree theorem (or) handshaking theorem & problems.
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The sum of the degrees of a graph is twice the number of edges.
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2 marks Short answer
Define minimal spanning tree.
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A minimal spanning tree is a subset of edges connecting all vertices with the minimum total edge weight.
The full exam-length answer is in the app.
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