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Recent questions and answers in Engineering Mathematics

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Recent questions and answers in Engineering Mathematics

55 votes
7 answers
1
GATE2006-25
Let $S = \{1, 2, 3,\ldots, m\}, m >3.$ Let $X_1,\ldots,X_n$ be subsets of $S$ each of size $3.$ Define a function $f$ from $S$ to the set of natural numbers as, $f(i)$ is the number of sets $X_j$ that contain the element $i.$ That is $f(i)=\left | \left\{j \mid i\in X_j \right\} \right|$ then $ \sum_{i=1}^{m} f(i)$ is: $3m$ $3n$ $2m+1$ $2n+1$
Let $S = \{1, 2, 3,\ldots, m\}, m >3.$ Let $X_1,\ldots,X_n$ be subsets of $S$ each of size $3.$ Define a function $f$ from $S$ to the set of natural numbers as, $f(i)$ is the number of sets $X_j$ that contain the element $i.$ That is $f(i)=\left | \left\{j \mid i\in X_j \right\} \right|$ then $ \sum_{i=1}^{m} f(i)$ is: $3m$ $3n$ $2m+1$ $2n+1$
answered 23 hours ago in Set Theory & Algebra anurags228 4.5k views
0 votes
1 answer
2
UGCNET-Oct2020-II: 3
Which of the following pairs of propositions are not logically equivalent? $((p \rightarrow r) \wedge (q \rightarrow r))$ and $((p \vee q) \rightarrow r)$ $p \leftrightarrow q$ and $(\neg p \leftrightarrow \neg q)$ $((p \wedge q) \vee (\neg p \wedge \neg q))$ and $p \leftrightarrow q$ $((p \wedge q) \rightarrow r)$ and $((p \rightarrow r) \wedge (q \rightarrow r))$
Which of the following pairs of propositions are not logically equivalent? $((p \rightarrow r) \wedge (q \rightarrow r))$ and $((p \vee q) \rightarrow r)$ $p \leftrightarrow q$ and $(\neg p \leftrightarrow \neg q)$ $((p \wedge q) \vee (\neg p \wedge \neg q))$ and $p \leftrightarrow q$ $((p \wedge q) \rightarrow r)$ and $((p \rightarrow r) \wedge (q \rightarrow r))$
answered 4 days ago in Discrete Mathematics Sanjay Sharma 27 views
0 votes
1 answer
3
UGCNET-Oct2020-II: 2
How many ways are there to pack six copies of the same book into four identical boxes, where a box can contain as many as six books? $4$ $6$ $7$ $9$
How many ways are there to pack six copies of the same book into four identical boxes, where a box can contain as many as six books? $4$ $6$ $7$ $9$
answered 4 days ago in Combinatory Sanjay Sharma 37 views
0 votes
1 answer
4
UGCNET-Oct2020-II: 1
The number of positive integers not exceeding $100$ that are either odd or the square of an integer is _______ $63$ $59$ $55$ $50$
The number of positive integers not exceeding $100$ that are either odd or the square of an integer is _______ $63$ $59$ $55$ $50$
answered 5 days ago in Set Theory & Algebra Ashwani Kumar 2 71 views
37 votes
7 answers
5
GATE2016-2-26
A binary relation $R$ on $\mathbb{N} \times \mathbb{N}$ is defined as follows: $(a, b) R(c, d)$ if $a \leq c$ or $b \leq d$. Consider the following propositions: $P:$ $R$ is reflexive. $Q:$ $R$ is transitive. Which one of the following statements is TRUE? Both $P$ and $Q$ are true. $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are false.
A binary relation $R$ on $\mathbb{N} \times \mathbb{N}$ is defined as follows: $(a, b) R(c, d)$ if $a \leq c$ or $b \leq d$. Consider the following propositions: $P:$ $R$ is reflexive. $Q:$ $R$ is transitive. Which one of the following statements is TRUE? Both $P$ and $Q$ are true. $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are false.
answered Nov 18 in Set Theory & Algebra Lasani Hussain 6.6k views
28 votes
10 answers
6
GATE2007-24
Suppose we uniformly and randomly select a permutation from the $20 !$ permutations of $1, 2, 3\ldots ,20.$ What is the probability that $2$ appears at an earlier position than any other even number in the selected permutation? $\left(\dfrac{1}{2} \right)$ $\left(\dfrac{1}{10}\right)$ $\left(\dfrac{9!}{20!}\right)$ None of these
Suppose we uniformly and randomly select a permutation from the $20 !$ permutations of $1, 2, 3\ldots ,20.$ What is the probability that $2$ appears at an earlier position than any other even number in the selected permutation? $\left(\dfrac{1}{2} \right)$ $\left(\dfrac{1}{10}\right)$ $\left(\dfrac{9!}{20!}\right)$ None of these
answered Nov 15 in Probability Dheeraj Varma 6.5k views
37 votes
7 answers
7
GATE2009-21
An unbalanced dice (with $6$ faces, numbered from $1$ to $6$) is thrown. The probability that the face value is odd is $90\%$ of the probability that the face value is even. The probability of getting any even numbered face is the same. If the probability that the ... of the following options is closest to the probability that the face value exceeds $3$? $0.453$ $0.468$ $0.485$ $0.492$
An unbalanced dice (with $6$ faces, numbered from $1$ to $6$) is thrown. The probability that the face value is odd is $90\%$ of the probability that the face value is even. The probability of getting any even numbered face is the same. If the probability that the face is ... one of the following options is closest to the probability that the face value exceeds $3$? $0.453$ $0.468$ $0.485$ $0.492$
answered Nov 14 in Probability Dheeraj Varma 6k views
0 votes
1 answer
8
ISI2014-DCG-53
The value of the integral $\displaystyle{}\int_{-1}^1 \dfrac{x^2}{1+x^2} \sin x \sin 3x \sin 5x dx$ is $0$ $\frac{1}{2}$ $ – \frac{1}{2}$ $1$
The value of the integral $\displaystyle{}\int_{-1}^1 \dfrac{x^2}{1+x^2} \sin x \sin 3x \sin 5x dx$ is $0$ $\frac{1}{2}$ $ – \frac{1}{2}$ $1$
answered Nov 14 in Calculus raja11sep 183 views
16 votes
3 answers
10
GATE2005-12, ISRO2009-64
Let $f(x)$ be the continuous probability density function of a random variable $x$, the probability that $a < x \leq b$, is : $f(b-a)$ $f(b) - f(a)$ $\int\limits_a^b f(x) dx$ $\int\limits_a^b xf (x)dx$
Let $f(x)$ be the continuous probability density function of a random variable $x$, the probability that $a < x \leq b$, is : $f(b-a)$ $f(b) - f(a)$ $\int\limits_a^b f(x) dx$ $\int\limits_a^b xf (x)dx$
answered Nov 13 in Probability varunrajarathnam 3.7k views
27 votes
6 answers
11
GATE2001-2.1
How many $4$-digit even numbers have all $4$ digits distinct $2240$ $2296$ $2620$ $4536$
How many $4$-digit even numbers have all $4$ digits distinct $2240$ $2296$ $2620$ $4536$
answered Nov 11 in Combinatory Chandrabhan Vishwa 1 5.5k views
0 votes
3 answers
12
NIELIT 2017 July Scientist B (IT) - Section B: 14
There are four bus lines between $A$ and $B$; and three bus lines between $B$ and $C$. The number of way a person roundtrip by bus from $A$ to $C$ by way of $B$ will be $12$ $7$ $144$ $264$
There are four bus lines between $A$ and $B$; and three bus lines between $B$ and $C$. The number of way a person roundtrip by bus from $A$ to $C$ by way of $B$ will be $12$ $7$ $144$ $264$
answered Nov 10 in Combinatory Ashwani Kumar 2 106 views
17 votes
6 answers
13
GATE2004-78
Two $n$ bit binary strings, $S_1$ and $S_2$ are chosen randomly with uniform probability. The probability that the Hamming distance between these strings (the number of bit positions where the two strings differ) is equal to $d$ is $\dfrac{^{n}C_{d}}{2^{n}}$ $\dfrac{^{n}C_{d}}{2^{d}}$ $\dfrac{d}{2^{n}}$ $\dfrac{1}{2^{d}}$
Two $n$ bit binary strings, $S_1$ and $S_2$ are chosen randomly with uniform probability. The probability that the Hamming distance between these strings (the number of bit positions where the two strings differ) is equal to $d$ is $\dfrac{^{n}C_{d}}{2^{n}}$ $\dfrac{^{n}C_{d}}{2^{d}}$ $\dfrac{d}{2^{n}}$ $\dfrac{1}{2^{d}}$
answered Nov 7 in Probability varunrajarathnam 3.1k views
45 votes
8 answers
15
GATE2004-75
Mala has the colouring book in which each English letter is drawn two times. She wants to paint each of these $52$ prints with one of $k$ colours, such that the colour pairs used to colour any two letters are different. Both prints of a letter can also be coloured with the same colour. What is the minimum value of $k$ that satisfies this requirement? $9$ $8$ $7$ $6$
Mala has the colouring book in which each English letter is drawn two times. She wants to paint each of these $52$ prints with one of $k$ colours, such that the colour pairs used to colour any two letters are different. Both prints of a letter can also be coloured with the same colour. What is the minimum value of $k$ that satisfies this requirement? $9$ $8$ $7$ $6$
answered Nov 6 in Combinatory Dheeraj Varma 6k views
1 vote
1 answer
16
NIELIT 2018-21
The value of $p$ such that the vector $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ is an eigen vector of the matrix $\begin{bmatrix} 4 & 1 & 2 \\ p & 2 & 1 \\ 14 & -4 & 10 \end{bmatrix}$ is $15$ $16$ $17$ $18$
The value of $p$ such that the vector $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ is an eigen vector of the matrix $\begin{bmatrix} 4 & 1 & 2 \\ p & 2 & 1 \\ 14 & -4 & 10 \end{bmatrix}$ is $15$ $16$ $17$ $18$
answered Nov 2 in Linear Algebra Debapriya Sarkar 222 views
45 votes
10 answers
17
GATE1994-1.6, ISRO2008-29
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$
answered Oct 31 in Graph Theory rupesh17 15.5k views
5 votes
2 answers
18
TIFR-2015-Maths-A-1
Let $A$ be an invertible $10 \times 10$ matrix with real entries such that the sum of each row is $1$. Then The sum of the entries of each row of the inverse of $A$ is $1$ The sum of the entries of each column of the inverse of $A$ is $1$ The trace of the inverse of $A$ is non-zero None of the above
Let $A$ be an invertible $10 \times 10$ matrix with real entries such that the sum of each row is $1$. Then The sum of the entries of each row of the inverse of $A$ is $1$ The sum of the entries of each column of the inverse of $A$ is $1$ The trace of the inverse of $A$ is non-zero None of the above
answered Oct 29 in Linear Algebra Mohnish 423 views
22 votes
5 answers
19
GATE2015-1-54
Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.
Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.
answered Oct 27 in Graph Theory prajjwalsingh_11 7.8k views
1 vote
1 answer
20
NIELIT 2018-24
If $f(x)=k$ exp, $\{ -(9x^2-12x+13)\}$, is a $p, d, f$ of a normal distribution ($k$, being a constant), the mean and standard deviation of the distribution: $\mu = \frac{2}{3}, \sigma = \frac{1}{3 \sqrt{2}}$ $\mu = 2, \sigma = \frac{1}{\sqrt{2}}$ $\mu = \frac{1}{3}, \sigma = \frac{1}{3 \sqrt{2}}$ $\mu = \frac{2}{3}, \sigma = \frac{1}{ \sqrt{3}}$
If $f(x)=k$ exp, $\{ -(9x^2-12x+13)\}$, is a $p, d, f$ of a normal distribution ($k$, being a constant), the mean and standard deviation of the distribution: $\mu = \frac{2}{3}, \sigma = \frac{1}{3 \sqrt{2}}$ $\mu = 2, \sigma = \frac{1}{\sqrt{2}}$ $\mu = \frac{1}{3}, \sigma = \frac{1}{3 \sqrt{2}}$ $\mu = \frac{2}{3}, \sigma = \frac{1}{ \sqrt{3}}$
answered Oct 27 in Probability Kumar1712 316 views
0 votes
0 answers
21
TIFR-2019-Maths-A: 6
The limit $\underset{n\rightarrow \infty }{\lim}\:n^{2}\int_{0}^{1}\:\frac{1}{\left ( 1+x^{2} \right )^{n}}\:dx$ is equal to $1$ $0$ $+\infty$ $1/2$
The limit $\underset{n\rightarrow \infty }{\lim}\:n^{2}\int_{0}^{1}\:\frac{1}{\left ( 1+x^{2} \right )^{n}}\:dx$ is equal to $1$ $0$ $+\infty$ $1/2$
asked Aug 30 in Calculus soujanyareddy13 122 views
0 votes
0 answers
22
NIELIT 2017 OCT Scientific Assistant A (IT) - Section D: 6
A solution for the differential equation $x’(t) + 2x(t) = \delta(t)$ with initial condition $x(\overline{0}) = 0$ $e^{-2t}u(t)$ $e^{2t}u(t)$ $e^{-t}u(t)$ $e^{t}u(t)$
A solution for the differential equation $x’(t) + 2x(t) = \delta(t)$ with initial condition $x(\overline{0}) = 0$ $e^{-2t}u(t)$ $e^{2t}u(t)$ $e^{-t}u(t)$ $e^{t}u(t)$
asked Aug 28 in Calculus Lakshman Patel RJIT 45 views
2 votes
1 answer
23
K H Rosen Ex
15. a) How many cards must be chosen from a standard deck of 52 cards to guarantee that at least two of the four aces are chosen? b) How many cards must be chosen from a standard deck of 52 cards to guarantee that at least two of the four aces and ... cards must be chosen from a standard deck of 52 cards to guarantee that there are at least two cards of each of two different kinds?
15. a) How many cards must be chosen from a standard deck of 52 cards to guarantee that at least two of the four aces are chosen? b) How many cards must be chosen from a standard deck of 52 cards to guarantee that at least two of the four aces and at least ... many cards must be chosen from a standard deck of 52 cards to guarantee that there are at least two cards of each of two different kinds?
asked Jul 4 in Combinatory Sanjay Sharma 300 views
4 votes
1 answer
24
Counting number of pairs whose sum is less than k
How many pairs $(x,y)$ such that $x+y <= k$, where x y and k are integers and $x,y>=0, k > 0$. Solve by summation rules. Solve by combinatorial argument.
How many pairs $(x,y)$ such that $x+y <= k$, where x y and k are integers and $x,y>=0, k > 0$. Solve by summation rules. Solve by combinatorial argument.
asked Jun 8 in Combinatory dd 378 views
0 votes
2 answers
27
Kenneth Rosen Edition 7th Exercise 8.3 Question 14 (Page No. 535)
Suppose that there are $n = 2^{k}$ teams in an elimination tournament, where there are $\frac{n}{2}$ games in the first round, with the $\frac{n}{2} = 2^{k-1}$ winners playing in the second round, and so on. Develop a recurrence relation for the number of rounds in the tournament.
Suppose that there are $n = 2^{k}$ teams in an elimination tournament, where there are $\frac{n}{2}$ games in the first round, with the $\frac{n}{2} = 2^{k-1}$ winners playing in the second round, and so on. Develop a recurrence relation for the number of rounds in the tournament.
asked May 10 in Combinatory Lakshman Patel RJIT 165 views
0 votes
0 answers
36
Kenneth Rosen Edition 7th Exercise 8.3 Question 5 (Page No. 535)
Determine a value for the constant C in Example $4$ and use it to estimate the number of bit operations needed to multiply two $64$-bit integers using the fast multiplication algorithm.
Determine a value for the constant C in Example $4$ and use it to estimate the number of bit operations needed to multiply two $64$-bit integers using the fast multiplication algorithm.
asked May 10 in Combinatory Lakshman Patel RJIT 50 views
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