Recent questions and answers in Mathematical Logic

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1 answer

1

Math Probability
Consider the random variable X such that it takes values +1,-1 and +2 with probability 0.1 each .Calculate values of the commulative frequencydistribution function F(x) at x=-1 and x=1 and x=2 are ?

Consider the random variable X such that it takes values +1,-1 and +2 with probability 0.1 each .Calculate values of the commulative frequencydistribution function F(x) at x=-1 and x=1 and x=2 are ?

answered 2 days ago in Mathematical Logic arun yadav 77 views

18 votes

3 answers

2

TIFR2016-B-4
In the following, $A$ stands for a set of apples, and $S(x, y)$ stands for "$x$ is sweeter than $y$. Let $\Psi \equiv \exists x : x \in A$ $\Phi \equiv \forall x \in A : \exists y \in A : S(x, y).$ Which of the following statements implies that there are infinitely many apples ( ...

In the following, $A$ stands for a set of apples, and $S(x, y)$ stands for "$x$ is sweeter than $y$. Let $\Psi \equiv \exists x : x \in A$ $\Phi \equiv \forall x \in A : \exists y \in A : S(x, y).$ ...

answered 3 days ago in Mathematical Logic Deepakk Poonia (Dee) 1.2k views

0 votes

1 answer

3

probability
Let X and Y be two exponentially distributed and independent random variables with mean α and β, respectively. If Z = max (X, Y), then the mean of Z is…. please explain in detail… https://gateoverflow.in/3676/gate2004-it-33 for min(X, Y) solution is already given as question asked in gate 2004. what about max(X, Y).

Let X and Y be two exponentially distributed and independent random variables with mean α and β, respectively. If Z = max (X, Y), then the mean of Z is…. please explain in detail… https://gateoverflow.in/3676/gate2004-it-33 for min(X, Y) solution is already given as question asked in gate 2004. what about max(X, Y).

answered 4 days ago in Mathematical Logic arun yadav 44 views

23 votes

10 answers

4

GATE2019-35
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z \mid x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z \mid w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ ... Set of all positive integers $S3:$ Set of all integers Which of the above sets satisfy $\varphi$? S1 and S2 S1 and S3 S2 and S3 S1, S2 and S3

Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z \mid x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z \mid w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ ... $S3:$ Set of all integers Which of the above sets satisfy $\varphi$? S1 and S2 S1 and S3 S2 and S3 S1, S2 and S3

answered 6 days ago in Mathematical Logic S.R. 7.7k views

4 votes

2 answers

5

CMI2010-A-04
Let $m$ and $n$ range over natural numbers and let $\text{Prime}(n)$ be true if $n$ is a prime number. Which of the following formulas expresses the fact that the set of prime numbers is infinite? $(\forall m) (\exists n) (n > m) \text{ implies Prime}(n)$ ... $(\exists n) (\forall m) (n > m) \wedge \text{Prime}(n)$

Let $m$ and $n$ range over natural numbers and let $\text{Prime}(n)$ be true if $n$ is a prime number. Which of the following formulas expresses the fact that the set of prime numbers is infinite? $(\forall m) (\exists n) (n > m) \text{ implies Prime}(n)$ ... $(\exists n) (\forall m) (n > m) \wedge \text{Prime}(n)$

answered Sep 12 in Mathematical Logic indranil21 230 views

23 votes

2 answers

6

GATE1995-2.19
If the proposition $\lnot p \to q$ is true, then the truth value of the proposition $\lnot p \lor \left ( p \to q \right )$, where $\lnot$ is negation, $\lor$ is inclusive OR and $\to$ is implication, is True Multiple Values False Cannot be determined

If the proposition $\lnot p \to q$ is true, then the truth value of the proposition $\lnot p \lor \left ( p \to q \right )$, where $\lnot$ is negation, $\lor$ is inclusive OR and $\to$ is implication, is True Multiple Values False Cannot be determined

answered Sep 11 in Mathematical Logic Mitali gupta 3.2k views

8 votes

5 answers

7

GATE 2020 CSE | Question: 39
Which one of the following predicate formulae is NOT logically valid? Note that $W$ is a predicate formula without any free occurrence of $x$. $\forall x (p(x) \vee W) \equiv \forall x \: ( px) \vee W$ ... $\exists x(p(x) \rightarrow W) \equiv \forall x \: p(x) \rightarrow W$

Which one of the following predicate formulae is NOT logically valid? Note that $W$ is a predicate formula without any free occurrence of $x$. $\forall x (p(x) \vee W) \equiv \forall x \: ( px) \vee W$ $\exists x(p(x) \wedge W) \equiv \exists x \: p(x) \wedge W$ ... $\exists x(p(x) \rightarrow W) \equiv \forall x \: p(x) \rightarrow W$

answered Sep 7 in Mathematical Logic Musa 3k views

0 votes

2 answers

8

ISI-2014-SAMPLE-1
Let $\{f_n(x)\}$ be a sequence of polynomials defined inductively as $f_1(x) = (x-2)^2$ $f_{n+1}(x) = (f_n(x)-2)^2, \qquad n\geq 1.$ Let $a_n$ and $b_n$ respectively denote the constant term and the coefficient of $x$ in $f_n(x).$ Then $a_n = 4, b_n = -4^n$ $a_n = 4, b_n = -4n^2$ $a_n = 4^{(n-1)!}, b_n = -4^n$ $a_n = 4^{(n-1)!}, b_n = -4n^2$

Let $\{f_n(x)\}$ be a sequence of polynomials defined inductively as $f_1(x) = (x-2)^2$ $f_{n+1}(x) = (f_n(x)-2)^2, \qquad n\geq 1.$ Let $a_n$ and $b_n$ respectively denote the constant term and the coefficient of $x$ in $f_n(x).$ Then $a_n = 4, b_n = -4^n$ $a_n = 4, b_n = -4n^2$ $a_n = 4^{(n-1)!}, b_n = -4^n$ $a_n = 4^{(n-1)!}, b_n = -4n^2$

answered Sep 4 in Mathematical Logic `JEET 86 views

29 votes

10 answers

9

GATE2014-1-53
Which one of the following propositional logic formulas is TRUE when exactly two of $p,q$ and $r$ are TRUE? $(( p \leftrightarrow q) \wedge r) \vee (p \wedge q \wedge \sim r)$ $( \sim (p \leftrightarrow q) \wedge r)\vee (p \wedge q \wedge \sim r)$ $( (p \to q) \wedge r) \vee (p \wedge q \wedge \sim r)$ $(\sim (p \leftrightarrow q) \wedge r) \wedge (p \wedge q \wedge \sim r) $

Which one of the following propositional logic formulas is TRUE when exactly two of $p,q$ and $r$ are TRUE? $(( p \leftrightarrow q) \wedge r) \vee (p \wedge q \wedge \sim r)$ $( \sim (p \leftrightarrow q) \wedge r)\vee (p \wedge q \wedge \sim r)$ $( (p \to q) \wedge r) \vee (p \wedge q \wedge \sim r)$ $(\sim (p \leftrightarrow q) \wedge r) \wedge (p \wedge q \wedge \sim r) $

answered Sep 4 in Mathematical Logic Musa 4.5k views

25 votes

6 answers

10

GATE2009-23
Which one of the following is the most appropriate logical formula to represent the statement? "Gold and silver ornaments are precious". The following notations are used: $G(x): x$ is a gold ornament $S(x): x$ is a silver ornament $P(x): x$ ... $\exists x((G(x) \wedge S(x)) \implies P(x))$ $\forall x((G(x) \vee S(x)) \implies P(x))$

Which one of the following is the most appropriate logical formula to represent the statement? "Gold and silver ornaments are precious". The following notations are used: $G(x): x$ is a gold ornament $S(x): x$ is a silver ornament $P(x): x$ is precious $\forall x(P(x) \implies (G(x) \wedge S(x)))$ ... $\exists x((G(x) \wedge S(x)) \implies P(x))$ $\forall x((G(x) \vee S(x)) \implies P(x))$

answered Sep 4 in Mathematical Logic Musa 2.7k views

42 votes

4 answers

11

GATE2010-30
Suppose the predicate $F(x, y, t)$ is used to represent the statement that person $x$ can fool person $y$ at time $t$. Which one of the statements below expresses best the meaning of the formula, $\qquad∀x∃y∃t(¬F(x,y,t))$ Everyone can fool some person at some time No one can fool everyone all the time Everyone cannot fool some person all the time No one can fool some person at some time

Suppose the predicate $F(x, y, t)$ is used to represent the statement that person $x$ can fool person $y$ at time $t$. Which one of the statements below expresses best the meaning of the formula, $\qquad∀x∃y∃t(¬F(x,y,t))$ Everyone can fool some person at some time No one can fool everyone all the time Everyone cannot fool some person all the time No one can fool some person at some time

answered Sep 3 in Mathematical Logic Musa 6k views

33 votes

7 answers

12

GATE2013-27
What is the logical translation of the following statement? "None of my friends are perfect." $∃x(F (x)∧ ¬P(x))$ $∃ x(¬ F (x)∧ P(x))$ $ ∃x(¬F (x)∧¬P(x))$ $ ¬∃ x(F (x)∧ P(x))$

What is the logical translation of the following statement? "None of my friends are perfect." $∃x(F (x)∧ ¬P(x))$ $∃ x(¬ F (x)∧ P(x))$ $ ∃x(¬F (x)∧¬P(x))$ $ ¬∃ x(F (x)∧ P(x))$

answered Sep 3 in Mathematical Logic Musa 4.8k views

21 votes

6 answers

13

GATE2017-1-01
The statement $\left ( ¬p \right ) \Rightarrow \left ( ¬q \right )$ is logically equivalent to which of the statements below? $p \Rightarrow q$ $q \Rightarrow p$ $\left ( ¬q \right ) \vee p$ $\left ( ¬p \right ) \vee q$ I only I and IV only II only II and III only

The statement $\left ( ¬p \right ) \Rightarrow \left ( ¬q \right )$ is logically equivalent to which of the statements below? $p \Rightarrow q$ $q \Rightarrow p$ $\left ( ¬q \right ) \vee p$ $\left ( ¬p \right ) \vee q$ I only I and IV only II only II and III only

answered Sep 3 in Mathematical Logic Supriyo21 3.6k views

0 votes

1 answer

14

Kenneth Rosen Edition 7th Exercise 1.4 Question 21 (Page No. 54)
For each fo these statements find a domain for which the statements is true and a domain for which the statement is false. Everyone is studying discrete mathematics. Everyone is older than 21 years. Everyone two people have the same mother. No two different people have the same grandmother.

For each fo these statements find a domain for which the statements is true and a domain for which the statement is false. Everyone is studying discrete mathematics. Everyone is older than 21 years. Everyone two people have the same mother. No two different people have the same grandmother.

answered Sep 2 in Mathematical Logic Pawan Sharnagate 31 views

0 votes

1 answer

15

Kenneth Rosen Edition 7th Exercise 1.7 Question 17 (Page No. 91)
Show that if $n$ is an integer and $n^3+5$ is odd, then $n$ is even using. a proof by contraposition. a proof by contradiction.

Show that if $n$ is an integer and $n^3+5$ is odd, then $n$ is even using. a proof by contraposition. a proof by contradiction.

answered Aug 29 in Mathematical Logic nocturnal123 25 views

0 votes

1 answer

16

Kenneth Rosen Edition 7th Exercise 1.7 Question 16 (Page No. 91)
Prove that if $m$ and $n$ are integers and $mn$ is even, then $m$ is even or $n$ is even.

Prove that if $m$ and $n$ are integers and $mn$ is even, then $m$ is even or $n$ is even.

answered Aug 29 in Mathematical Logic nocturnal123 22 views

8 votes

3 answers

17

GATE1999-14
Show that the formula $\left[(\sim p \vee q) \Rightarrow (q \Rightarrow p)\right]$ is not a tautology. Let $A$ be a tautology and $B$ any other formula. Prove that $(A \vee B)$ is a tautology.

Show that the formula $\left[(\sim p \vee q) \Rightarrow (q \Rightarrow p)\right]$ is not a tautology. Let $A$ be a tautology and $B$ any other formula. Prove that $(A \vee B)$ is a tautology.

answered Aug 26 in Mathematical Logic subbus 691 views

36 votes

9 answers

18

GATE2002-1.8
"If $X$ then $Y$ unless $Z$" is represented by which of the following formulas in prepositional logic? ("$\neg$" is negation, "$\land$" is conjunction, and "$\rightarrow$" is implication) $(X\land \neg Z) \rightarrow Y$ $(X \land Y) \rightarrow \neg Z$ $X \rightarrow(Y\land \neg Z)$ $(X \rightarrow Y)\land \neg Z$

"If $X$ then $Y$ unless $Z$" is represented by which of the following formulas in prepositional logic? ("$\neg$" is negation, "$\land$" is conjunction, and "$\rightarrow$" is implication) $(X\land \neg Z) \rightarrow Y$ $(X \land Y) \rightarrow \neg Z$ $X \rightarrow(Y\land \neg Z)$ $(X \rightarrow Y)\land \neg Z$

answered Aug 25 in Mathematical Logic subbus 6.1k views

19 votes

6 answers

19

GATE2009-24
The binary operation $\Box$ ... of the following is equivalent to $P \vee Q$? $\neg Q \Box \neg P$ $P\Box \neg Q$ $\neg P\Box Q$ $\neg P\Box \neg Q$

The binary operation $\Box$ ... $P \vee Q$? $\neg Q \Box \neg P$ $P\Box \neg Q$ $\neg P\Box Q$ $\neg P\Box \neg Q$

answered Aug 24 in Mathematical Logic subbus 2.9k views

31 votes

5 answers

20

GATE2017-1-29
Let $p$, $q$ and $r$ be propositions and the expression $\left ( p\rightarrow q \right )\rightarrow r$ be a contradiction. Then, the expression $\left ( r\rightarrow p \right )\rightarrow q$ is a tautology a contradiction always TRUE when $p$ is FALSE always TRUE when $q$ is TRUE

Let $p$, $q$ and $r$ be propositions and the expression $\left ( p\rightarrow q \right )\rightarrow r$ be a contradiction. Then, the expression $\left ( r\rightarrow p \right )\rightarrow q$ is a tautology a contradiction always TRUE when $p$ is FALSE always TRUE when $q$ is TRUE

answered Aug 24 in Mathematical Logic subbus 4.2k views

1 vote

2 answers

21

NIELIT 2017 July Scientist B (IT) - Section B: 13
Which of the following statements is false? $(P\land Q)\lor(\sim P\land Q)\lor(P \land \sim Q)$ is equal to $\sim Q\land \sim P$ $(P\land Q)\lor(\sim P\land Q)\lor(P \wedge \sim Q)$ is equal to $Q\lor P$ ... $(P\land Q)\lor(\sim P\land Q)\lor (P \land \sim Q)$ is equal to $P\lor (Q\land \sim P)$

Which of the following statements is false? $(P\land Q)\lor(\sim P\land Q)\lor(P \land \sim Q)$ is equal to $\sim Q\land \sim P$ $(P\land Q)\lor(\sim P\land Q)\lor(P \wedge \sim Q)$ is equal to $Q\lor P$ $(P\wedge Q)\lor (\sim P\land Q)\lor(P \wedge \sim Q)$ is equal to $Q\lor (P\wedge \sim Q)$ $(P\land Q)\lor(\sim P\land Q)\lor (P \land \sim Q)$ is equal to $P\lor (Q\land \sim P)$

answered Aug 22 in Mathematical Logic Lakshman Patel RJIT 49 views

0 votes

1 answer

22

NIELIT 2016 MAR Scientist C - Section B: 9
Consider three vectors $x=\begin{bmatrix}1\\2 \end{bmatrix}, y=\begin{bmatrix}4\\8 \end{bmatrix},z=\begin{bmatrix}3\\1 \end{bmatrix}$. Which of the folowing statements is true $x$ and $y$ are linearly independent $x$ and $y$ are linearly dependent $x$ and $z$ are linearly dependent $y$ and $z$ are linearly dependent

Consider three vectors $x=\begin{bmatrix}1\\2 \end{bmatrix}, y=\begin{bmatrix}4\\8 \end{bmatrix},z=\begin{bmatrix}3\\1 \end{bmatrix}$. Which of the folowing statements is true $x$ and $y$ are linearly independent $x$ and $y$ are linearly dependent $x$ and $z$ are linearly dependent $y$ and $z$ are linearly dependent

answered Aug 21 in Mathematical Logic nocturnal123 25 views

0 votes

1 answer

23

NIELIT 2016 MAR Scientist C - Section B: 17
A ladder $13$ feet long rests against the side of a house. The bottom of the ladder slides away from the house at a rate of $0.5$ ft/s. How fast is the top of the ladder sliding down the wall when the bottom of the ladder is $5$ ... $-\dfrac{5}{24} \text {ft/s} \\$ $-\dfrac{5}{12} \text{ ft/s}$

A ladder $13$ feet long rests against the side of a house. The bottom of the ladder slides away from the house at a rate of $0.5$ ft/s. How fast is the top of the ladder sliding down the wall when the bottom of the ladder is $5$ feet from the house? $\dfrac{5}{24} \text{ ft/s} \\$ $\dfrac{5}{12} \text{ ft/s} \\$ $-\dfrac{5}{24} \text {ft/s} \\$ $-\dfrac{5}{12} \text{ ft/s}$

answered Aug 20 in Mathematical Logic nocturnal123 27 views

1 vote

2 answers

24

Probability # Distribution
A traffic office imposes on an average 5 number of penalities daily on traffic violators.Assume that the number of the penalties on different days is independent and follows a Poisson distribution.The probability that there will be less than 4 penalties in a day is _______________ ?

A traffic office imposes on an average 5 number of penalities daily on traffic violators.Assume that the number of the penalties on different days is independent and follows a Poisson distribution.The probability that there will be less than 4 penalties in a day is _______________ ?

answered Aug 19 in Mathematical Logic Gyanu 159 views

42 votes

5 answers

25

GATE2006-IT-21
Consider the following first order logic formula in which $R$ is a binary relation symbol. $∀x∀y (R(x, y) \implies R(y, x))$ The formula is satisfiable and valid satisfiable and so is its negation unsatisfiable but its negation is valid satisfiable but its negation is unsatisfiable

Consider the following first order logic formula in which $R$ is a binary relation symbol. $∀x∀y (R(x, y) \implies R(y, x))$ The formula is satisfiable and valid satisfiable and so is its negation unsatisfiable but its negation is valid satisfiable but its negation is unsatisfiable

answered Aug 19 in Mathematical Logic Jhaiyam 5.5k views

1 vote

1 answer

26

relations and functions

answered Aug 16 in Mathematical Logic Jhaiyam 84 views

1 vote

2 answers

27

relations and functions
A binary relation R on Z × Z is defined as follows: (a, b) R (c, d) iff a = c or b = d Consider the following propositions: 1. R is reflexive. 2. R is symmetric. 3. R is antisymmetric. Which one of the above statements is True?

A binary relation R on Z × Z is defined as follows: (a, b) R (c, d) iff a = c or b = d Consider the following propositions: 1. R is reflexive. 2. R is symmetric. 3. R is antisymmetric. Which one of the above statements is True?

answered Aug 16 in Mathematical Logic Jhaiyam 231 views

50 votes

3 answers

28

GATE2015-2-55
Which one of the following well-formed formulae is a tautology? $\forall x \, \exists y \, R(x,y) \, \leftrightarrow \, \exists y \, \forall x \, R(x, y)$ ... $\forall x \, \forall y \, P(x,y) \, \rightarrow \, \forall x \, \forall y \, P(y, x)$

Which one of the following well-formed formulae is a tautology? $\forall x \, \exists y \, R(x,y) \, \leftrightarrow \, \exists y \, \forall x \, R(x, y)$ $( \forall x \, [\exists y \, R(x,y) \, \rightarrow \, S(x, y)]) \, \rightarrow \, \forall x \, \exists y \, S(x, y)$ ... $\forall x \, \forall y \, P(x,y) \, \rightarrow \, \forall x \, \forall y \, P(y, x)$

answered Aug 15 in Mathematical Logic Madhab 7.8k views

16 votes

4 answers

29

GATE1989-14a
Symbolize the expression "Every mother loves her children" in predicate logic.

Symbolize the expression "Every mother loves her children" in predicate logic.

answered Aug 13 in Mathematical Logic Prashant08 1.5k views

22 votes

2 answers

30

GATE2004-70
The following propositional statement is $\left(P \implies \left(Q \vee R\right)\right) \implies \left(\left(P \wedge Q \right)\implies R\right)$ satisfiable but not valid valid a contradiction None of the above

The following propositional statement is $\left(P \implies \left(Q \vee R\right)\right) \implies \left(\left(P \wedge Q \right)\implies R\right)$ satisfiable but not valid valid a contradiction None of the above

answered Aug 8 in Mathematical Logic taran97 2.6k views

48 votes

6 answers

31

GATE2016-2-27
Which one of the following well-formed formulae in predicate calculus is NOT valid ? $(\forall _{x} p(x) \implies \forall _{x} q(x)) \implies (\exists _{x} \neg p(x) \vee \forall _{x} q(x))$ $(\exists x p(x) \vee \exists x q (x)) \implies \exists x (p(x) \vee q (x))$ ... $\forall x (p(x) \vee q(x)) \implies (\forall x p(x) \vee \forall x q(x))$

Which one of the following well-formed formulae in predicate calculus is NOT valid ? $(\forall _{x} p(x) \implies \forall _{x} q(x)) \implies (\exists _{x} \neg p(x) \vee \forall _{x} q(x))$ $(\exists x p(x) \vee \exists x q (x)) \implies \exists x (p(x) \vee q (x))$ ... $\forall x (p(x) \vee q(x)) \implies (\forall x p(x) \vee \forall x q(x))$

answered Aug 3 in Mathematical Logic Yogesh88 7.5k views

27 votes

4 answers

32

GATE1991-15,b
Consider the following first order formula: ... Does it have finite models? Is it satisfiable? If so, give a countable model for it.

Consider the following first order formula: ... Does it have finite models? Is it satisfiable? If so, give a countable model for it.

answered Jul 3 in Mathematical Logic Deepakk Poonia (Dee) 2.4k views

2 votes

1 answer

33

J.P TREMBLAY EXCERCISE 1-4.1 4 TH QUESTION

answered Jul 1 in Mathematical Logic ubibhatt 251 views

1 vote

0 answers

34

NIELIT 2016 MAR Scientist C - Section B: 1
Choose the most appropriate option. The Newton-Raphson iteration $x_{n+1}=\dfrac{x_{n}}{2}+\dfrac{3}{2x_{n}}$ can be used to solve the equation $x^{2}=3$ $x^{3}=3$ $x^{2}=2$ $x^{3}=2$

Choose the most appropriate option. The Newton-Raphson iteration $x_{n+1}=\dfrac{x_{n}}{2}+\dfrac{3}{2x_{n}}$ can be used to solve the equation $x^{2}=3$ $x^{3}=3$ $x^{2}=2$ $x^{3}=2$

asked Apr 2 in Mathematical Logic Lakshman Patel RJIT 67 views

0 votes

1 answer

35

NIELIT 2016 MAR Scientist C - Section B: 4
If $A$ and $B$ are two related events, and $P(A \mid B)$ represents the conditional probability, Bayes’ theorem states that $P(A\mid B) = \dfrac{P(A)}{P(B)} P(B\mid A)$ $P(A\mid B) = P(A) P(B) P(B\mid A)$ $P(A\mid B) = \dfrac{P(A)}{P(B)}$ $P(A\mid B) = P(A)+P(B)$

If $A$ and $B$ are two related events, and $P(A \mid B)$ represents the conditional probability, Bayes’ theorem states that $P(A\mid B) = \dfrac{P(A)}{P(B)} P(B\mid A)$ $P(A\mid B) = P(A) P(B) P(B\mid A)$ $P(A\mid B) = \dfrac{P(A)}{P(B)}$ $P(A\mid B) = P(A)+P(B)$

asked Apr 2 in Mathematical Logic Lakshman Patel RJIT 42 views

1 vote

0 answers

36

NIELIT 2016 MAR Scientist C - Section B: 6
If $y=f(x)$, in the interval $[a,b]$ is rotated about the $x$-axis, the Volume of the solid of revolution is $(f’(x)=dy/dx)$ $\int_{a}^{b} \pi [f(x)]^{2} dx \\$ $\int_{a}^{b}[f(x)]^{3} dx \\$ $\int_{a}^{b} \pi [{f}'(x)]^{2} dx \\$ $\int_{a}^{b} \pi^{2} f(x)dx \\$

If $y=f(x)$, in the interval $[a,b]$ is rotated about the $x$-axis, the Volume of the solid of revolution is $(f’(x)=dy/dx)$ $\int_{a}^{b} \pi [f(x)]^{2} dx \\$ $\int_{a}^{b}[f(x)]^{3} dx \\$ $\int_{a}^{b} \pi [{f}'(x)]^{2} dx \\$ $\int_{a}^{b} \pi^{2} f(x)dx \\$

asked Apr 2 in Mathematical Logic Lakshman Patel RJIT 19 views

0 votes

0 answers

37

NIELIT 2016 MAR Scientist C - Section B: 7
The area under the curve $y(x)=3e^{-5x}$ from $x=0 \text{ to } x=\infty$ is $\dfrac{3}{5}$ $\dfrac{-3}{5}$ ${5}$ $\dfrac{5}{3}$

The area under the curve $y(x)=3e^{-5x}$ from $x=0 \text{ to } x=\infty$ is $\dfrac{3}{5}$ $\dfrac{-3}{5}$ ${5}$ $\dfrac{5}{3}$

asked Apr 2 in Mathematical Logic Lakshman Patel RJIT 22 views

0 votes

1 answer

38

NIELIT 2016 MAR Scientist C - Section B: 8
The eigenvalues of the matrix $\begin{bmatrix}1 & 2\\ 4 & 3 \end{bmatrix}$ are $\text{5 and -5}$ $\text{5 and -1}$ $\text{1 and -5}$ $\text{2 and 3}$

The eigenvalues of the matrix $\begin{bmatrix}1 & 2\\ 4 & 3 \end{bmatrix}$ are $\text{5 and -5}$ $\text{5 and -1}$ $\text{1 and -5}$ $\text{2 and 3}$

asked Apr 2 in Mathematical Logic Lakshman Patel RJIT 34 views

0 votes

1 answer

39

NIELIT 2016 MAR Scientist C - Section B: 10
$\underset{x \rightarrow 0}{\lim} \dfrac{x^{3}+x^{2}-5x-2}{2x^{3}-7x^{2}+4x+4}=?$ $-0.5$ $(0.5)$ $\infty$ None of the above

$\underset{x \rightarrow 0}{\lim} \dfrac{x^{3}+x^{2}-5x-2}{2x^{3}-7x^{2}+4x+4}=?$ $-0.5$ $(0.5)$ $\infty$ None of the above

asked Apr 2 in Mathematical Logic Lakshman Patel RJIT 21 views

0 votes

1 answer

40

NIELIT 2016 MAR Scientist C - Section B: 11
$\displaystyle \int_{0}^{\dfrac{\pi}{2}} \sin^{7}\theta \cos ^{4} \theta d\theta=?$ $16/1155$ $16/385$ $16\pi/385$ $8\pi/385$

$\displaystyle \int_{0}^{\dfrac{\pi}{2}} \sin^{7}\theta \cos ^{4} \theta d\theta=?$ $16/1155$ $16/385$ $16\pi/385$ $8\pi/385$

asked Apr 2 in Mathematical Logic Lakshman Patel RJIT 26 views

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