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Recent questions tagged engineering-mathematics
2
votes
1
answer
91
Linear Algebra Eigenvalues
If the eigenvalues of a 3x3 matrix A are 1,2 and 3 then inverse of A is?
theakatsuki4
asked
in
Linear Algebra
Sep 16, 2021
by
theakatsuki4
4.7k
views
linear-algebra
engineering-mathematics
eigen-value
matrix
3
votes
1
answer
92
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 $P(A\mid B) = \dfrac{P(A)}{P(B)} P(B\mid A)$ $P(A\mid B) = P(A) P(B) P(B\mid A)$ $P(A\mid B) = \dfrac{P(A)}{P(B)}$ $P(A\mid B) = P(A)+P(B)$
admin
asked
in
Probability
Apr 2, 2020
by
admin
770
views
nielit2016mar-scientistc
engineering-mathematics
probability
1
vote
2
answers
93
NIELIT 2016 MAR Scientist C - Section B: 8
The eigenvalues of the matrix $\begin{bmatrix}1 & 2\\ 4 & 3 \end{bmatrix}$ are $\text{5 and -5}$ $\text{5 and -1}$ $\text{1 and -5}$ $\text{2 and 3}$
admin
asked
in
Linear Algebra
Apr 2, 2020
by
admin
621
views
nielit2016mar-scientistc
engineering-mathematics
linear-algebra
eigen-value
0
votes
1
answer
94
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
admin
asked
in
Linear Algebra
Apr 2, 2020
by
admin
546
views
nielit2016mar-scientistc
engineering-mathematics
linear-algebra
eigen-vector
2
votes
1
answer
95
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
admin
asked
in
Calculus
Apr 2, 2020
by
admin
437
views
nielit2016mar-scientistc
engineering-mathematics
calculus
limits
1
vote
1
answer
96
NIELIT 2016 MAR Scientist C - Section B: 11
$\displaystyle \int_{0}^{\dfrac{\pi}{2}} \sin^{7}\theta \cos ^{4} \theta d\theta=?$ $16/1155$ $16/385$ $16\pi/385$ $8\pi/385$
admin
asked
in
Calculus
Apr 2, 2020
by
admin
350
views
nielit2016mar-scientistc
engineering-mathematics
calculus
definite-integral
1
vote
0
answers
97
NIELIT 2016 MAR Scientist C - Section B: 12
$\displaystyle \lim_{x \rightarrow a}\frac{1}{x^{2}-a^{2}} \displaystyle \int_{a}^{x}\sin (t^{2})dt=$? $2a \sin (a^{2})$ $2a$ $\sin (a^{2})$ None of the above
admin
asked
in
Calculus
Apr 2, 2020
by
admin
315
views
nielit2016mar-scientistc
engineering-mathematics
calculus
1
vote
1
answer
98
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 $5$ ... $-\dfrac{5}{24} \text {ft/s} \\$ $-\dfrac{5}{12} \text{ ft/s}$
admin
asked
in
Calculus
Apr 2, 2020
by
admin
407
views
nielit2016mar-scientistc
engineering-mathematics
calculus
1
vote
2
answers
99
NIELIT 2017 OCT Scientific Assistant A (CS) - Section C: 9
$M$ is a square matrix of order $’n’$ and its determinant value is $5.$ If all the elements of $M$ are multiple by $2,$ its determinant value becomes $40.$ The value of $’n’$ is $2$ $3$ $5$ $4$
admin
asked
in
Linear Algebra
Apr 1, 2020
by
admin
1.4k
views
nielit2017oct-assistanta-cs
engineering-mathematics
linear-algebra
matrix
determinant
1
vote
2
answers
100
NIELIT 2017 OCT Scientific Assistant A (CS) - Section B: 16
If $P$ is risk probability, $L$ is loss, then Risk Exposure $(RE)$ is computed as. $RE = P/L$ $RE = P + L$ $RE = P \ast L$ $RE = 2 \ast P \ast L$
admin
asked
in
Probability
Apr 1, 2020
by
admin
1.6k
views
nielit2017oct-assistanta-cs
engineering-mathematics
probability
2
votes
1
answer
101
NIELIT 2017 OCT Scientific Assistant A (CS) - Section B: 18
What is the maximum value of the function $f(x) = 2x^{2} – 2x + 6$ in the interval $[0,2]?$ $6$ $10$ $12$ $5,5$
admin
asked
in
Calculus
Apr 1, 2020
by
admin
640
views
nielit2017oct-assistanta-cs
engineering-mathematics
calculus
maxima-minima
0
votes
1
answer
102
NIELIT 2017 OCT Scientific Assistant A (CS) - Section B: 19
The value of the Integral $I = \displaystyle{}\int_{0}^{\pi/2} x^{2}\sin x dx$ is $(x+2)/2$ $2/(\pi-2)$ $\pi – 2$ $\pi + 2$
admin
asked
in
Calculus
Apr 1, 2020
by
admin
470
views
nielit2017oct-assistanta-cs
engineering-mathematics
calculus
definite-integral
1
vote
3
answers
103
NIELIT 2017 DEC Scientific Assistant A - Section B: 10
The function $f\left ( x \right )=\dfrac{x^{2}-1}{x-1}$ at $x=1$ is : Continuous and differentiable Continuous but not differentiable Differentiable but not continuous Neither continuous nor differentiable
admin
asked
in
Calculus
Mar 31, 2020
by
admin
1.1k
views
nielit2017dec-assistanta
engineering-mathematics
calculus
continuity
1
vote
2
answers
104
NIELIT 2017 DEC Scientific Assistant A - Section B: 41
If a random coin is tossed $11$ times, then what is the probability that for $7$th toss head appears exactly $4$ times? $5/32$ $15/128$ $35/128$ None of the options
admin
asked
in
Probability
Mar 31, 2020
by
admin
1.1k
views
nielit2017dec-assistanta
engineering-mathematics
probability
2
votes
2
answers
105
NIELIT 2017 DEC Scientific Assistant A - Section B: 44
If $X, Y$ and $Z$ are three exhaustive and mutually exclusive events related with any experiment and the $P\left(X \right)=0.5P\left(Y \right)$ and $P\left(Z \right)$ = $0.3P\left(Y \right)$. Then $P\left(Y \right)$ = ___________ . $0.54$ $0.66$ $0.33$ $0.44$
admin
asked
in
Probability
Mar 31, 2020
by
admin
2.0k
views
nielit2017dec-assistanta
engineering-mathematics
probability
3
votes
1
answer
106
NIELIT 2016 MAR Scientist B - Section C: 21
A polynomial $p(x)$ is such that $p(0)=5, \: p(1)=4, \: p(2)=9$ and $p(3)=20$. The minimum degree it can have is $1$ $2$ $3$ $4$
admin
asked
in
Set Theory & Algebra
Mar 31, 2020
by
admin
778
views
nielit2016mar-scientistb
engineering-mathematics
functions
polynomials
2
votes
1
answer
107
NIELIT 2016 MAR Scientist B - Section B: 4
What is the determinant of the matrix $\begin{bmatrix}5&3&2\\1&2&6\\3&5&10\end{bmatrix}$ $-76$ $-28$ $+28$ $+72$
admin
asked
in
Linear Algebra
Mar 31, 2020
by
admin
700
views
nielit2016mar-scientistb
engineering-mathematics
linear-algebra
determinant
3
votes
2
answers
108
NIELIT 2016 MAR Scientist B - Section B: 5
The greatest and the least value of $f(x)=x^4-8x^3+22x^2-24x+1$ in $[0,2]$ are $0,8$ $0,-8$ $1,8$ $1,-8$
admin
asked
in
Calculus
Mar 31, 2020
by
admin
654
views
nielit2016mar-scientistb
engineering-mathematics
calculus
maxima-minima
4
votes
1
answer
109
NIELIT 2016 MAR Scientist B - Section B: 6
The system of simultaneous equations $x+2y+z=6\\2x+y+2z=6\\x+y+z=5$ has unique solution. infinite number of solutions. no solution. exactly two solutions.
admin
asked
in
Linear Algebra
Mar 31, 2020
by
admin
712
views
nielit2016mar-scientistb
engineering-mathematics
linear-algebra
system-of-equations
1
vote
1
answer
110
NIELIT 2016 MAR Scientist B - Section B: 9
The value of improper integral $\displaystyle\int_{0}^{1} x\ln x =?$ $1/4$ $0$ $-1/4$ $1$
admin
asked
in
Calculus
Mar 31, 2020
by
admin
718
views
nielit2016mar-scientistb
engineering-mathematics
calculus
integration
definite-integral
1
vote
1
answer
111
NIELIT 2016 MAR Scientist B - Section B: 10
Maxima and minimum of the function $f(x)=2x^3-15x^2+36x+10$ occur; respectively at $x=3$ and $x=2$ $x=1$ and $x=3$ $x=2$ and $x=3$ $x=3$ and $x=4$
admin
asked
in
Calculus
Mar 31, 2020
by
admin
555
views
nielit2016mar-scientistb
engineering-mathematics
calculus
maxima-minima
1
vote
2
answers
112
NIELIT 2016 MAR Scientist B - Section B: 11
What is the derivative w.r.t $x$ of the function given by $\large \Phi(x)= \displaystyle \int_{0}^{x^2}\sqrt t\:dt$, $2x^2$ $\sqrt x$ $0$ $1$
admin
asked
in
Calculus
Mar 31, 2020
by
admin
546
views
nielit2016mar-scientistb
engineering-mathematics
calculus
integration
definite-integral
3
votes
2
answers
113
NIELIT 2016 MAR Scientist B - Section B: 12
If $A$ and $B$ are square matrices of size $n\times n$, then which of the following statements is not true? $\det(AB)=\det(A) \det(B)$ $\det(kA)=k^n \det(A)$ $\det(A+B)=\det(A)+\det(B)$ $\det(A^T)=1/\det(A^{-1})$
admin
asked
in
Linear Algebra
Mar 31, 2020
by
admin
6.5k
views
nielit2016mar-scientistb
engineering-mathematics
linear-algebra
determinant
1
vote
2
answers
114
NIELIT 2016 MAR Scientist B - Section B: 13
$\underset{x\to 0}{\lim} \dfrac{(1-\cos x)}{2}$ is equal to $0$ $1$ $1/3$ $1/2$
admin
asked
in
Calculus
Mar 31, 2020
by
admin
602
views
nielit2016mar-scientistb
engineering-mathematics
calculus
limits
0
votes
1
answer
115
NIELIT 2016 MAR Scientist B - Section B: 14
The minimum value of $\mid x^2-5x+2\mid$ is $-5$ $0$ $-1$ $-2$
admin
asked
in
Calculus
Mar 31, 2020
by
admin
562
views
nielit2016mar-scientistb
engineering-mathematics
calculus
maxima-minima
2
votes
3
answers
116
NIELIT 2016 MAR Scientist B - Section B: 16
A box contains $10$ screws, $3$ of which are defective. Two screws are drawn at random with replacement. The probability that none of two screws is defective will be $100\%$ $50\%$ $49\%$ None of these.
admin
asked
in
Probability
Mar 31, 2020
by
admin
1.1k
views
nielit2016mar-scientistb
engineering-mathematics
probability
3
votes
3
answers
117
NIELIT 2016 DEC Scientist B (IT) - Section B: 26
Two eigenvalues of a $3\times3$ real matrix $P$ are $(2+ \sqrt-1)$ and $3$. The determinant of $P$ is ________. $0$ $1$ $15$ $-1$
admin
asked
in
Linear Algebra
Mar 31, 2020
by
admin
939
views
nielit2016dec-scientistb-it
engineering-mathematics
linear-algebra
determinant
eigen-value
2
votes
2
answers
118
NIELIT 2016 DEC Scientist B (CS) - Section B: 21
Let $A,B,C,D$ be $n\times n$ matrices, each with non-zero determinant. If $ABCD=1$, then $B^{-1}$ is: $D^{-1}C^{-1}A^{-1}$ $CDA$ $ADC$ Does not necessarily exist.
admin
asked
in
Linear Algebra
Mar 31, 2020
by
admin
773
views
nielit2016dec-scientistb-cs
engineering-mathematics
linear-algebra
matrix
determinant
1
vote
1
answer
119
NIELIT 2016 DEC Scientist B (CS) - Section B: 26
Consider the function $f(x)=\sin(x)$ in the interval $\bigg [\dfrac{ \pi}{4},\dfrac{7\pi}{4}\bigg ]$. The number and location(s) of the minima of this function are: One, at $\dfrac{\pi}{2} \\$ One, at $\dfrac{3\pi}{2} \\$ Two, at $\dfrac{\pi}{2}$ and $\dfrac{3\pi}{2} \\$ Two, at $\dfrac{\pi}{4}$ and $\dfrac{3\pi}{2}$
admin
asked
in
Calculus
Mar 31, 2020
by
admin
576
views
nielit2016dec-scientistb-cs
engineering-mathematics
calculus
maxima-minima
1
vote
1
answer
120
NIELIT 2017 July Scientist B (IT) - Section B: 23
The probability that top and bottom cards of a randomly shuffled deck are both aces is: $4/52\times 4/52$ $4/52\times 3/52$ $4/52\times 3/51$ $4/52\times 4/51$
admin
asked
in
Probability
Mar 30, 2020
by
admin
568
views
nielit2017july-scientistb-it
engineering-mathematics
probability
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