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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?
If the eigenvalues of a 3x3 matrix A are 1,2 and 3 then inverse of A is?
theakatsuki4
4.7k
views
theakatsuki4
asked
Sep 16, 2021
Linear Algebra
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 $P(A\mid B) = \dfrac{P(A)}{P(B)} P(B\mid A)$ $P(A\mid B) = P(A) P(B) P(B\mid A)$ $P(A\mid B) = \dfrac{P(A)}{P(B)}$ $P(A\mid B) = P(A)+P(B)$
If $A$ and $B$ are two related events, and $P(A \mid B)$ represents the conditional probability, Bayes’ theorem states that $P(A\mid B) = \dfrac{P(A)}{P(B)} P(B\mid A)$...
admin
762
views
admin
asked
Apr 2, 2020
Probability
nielit2016mar-scientistc
engineering-mathematics
probability
+
–
1
votes
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 $\text{5 and -5}$ $\text{5 and -1}$ $\text{1 and -5}$ $\text{2 and 3}$
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}$$\text{2 and 3}$
admin
612
views
admin
asked
Apr 2, 2020
Linear Algebra
nielit2016mar-scientistc
engineering-mathematics
linear-algebra
eigen-value
+
–
0
votes
1
answer
94
NIELIT 2016 MAR Scientist C - Section B: 9
Consider three vectors $x=\begin{bmatrix}1\\2 \end{bmatrix}, y=\begin{bmatrix}4\\8 \end{bmatrix},z=\begin{bmatrix}3\\1 \end{bmatrix}$. Which of the folowing statements is true $x$ and $y$ are linearly independent $x$ and $y$ are linearly dependent $x$ and $z$ are linearly dependent $y$ and $z$ are linearly dependent
Consider three vectors $x=\begin{bmatrix}1\\2 \end{bmatrix}, y=\begin{bmatrix}4\\8 \end{bmatrix},z=\begin{bmatrix}3\\1 \end{bmatrix}$. Which of the folowing statements is...
admin
539
views
admin
asked
Apr 2, 2020
Linear Algebra
nielit2016mar-scientistc
engineering-mathematics
linear-algebra
eigen-vector
+
–
2
votes
1
answer
95
NIELIT 2016 MAR Scientist C - Section B: 10
$\underset{x \rightarrow 0}{\lim} \dfrac{x^{3}+x^{2}-5x-2}{2x^{3}-7x^{2}+4x+4}=?$ $-0.5$ $(0.5)$ $\infty$ None of the above
$\underset{x \rightarrow 0}{\lim} \dfrac{x^{3}+x^{2}-5x-2}{2x^{3}-7x^{2}+4x+4}=?$ $-0.5$$(0.5)$$\infty$None of the above
admin
432
views
admin
asked
Apr 2, 2020
Calculus
nielit2016mar-scientistc
engineering-mathematics
calculus
limits
+
–
1
votes
1
answer
96
NIELIT 2016 MAR Scientist C - Section B: 11
$\displaystyle \int_{0}^{\dfrac{\pi}{2}} \sin^{7}\theta \cos ^{4} \theta d\theta=?$ $16/1155$ $16/385$ $16\pi/385$ $8\pi/385$
$\displaystyle \int_{0}^{\dfrac{\pi}{2}} \sin^{7}\theta \cos ^{4} \theta d\theta=?$$16/1155$$16/385$$16\pi/385$$8\pi/385$
admin
342
views
admin
asked
Apr 2, 2020
Calculus
nielit2016mar-scientistc
engineering-mathematics
calculus
definite-integral
+
–
1
votes
0
answers
97
NIELIT 2016 MAR Scientist C - Section B: 12
$\displaystyle \lim_{x \rightarrow a}\frac{1}{x^{2}-a^{2}} \displaystyle \int_{a}^{x}\sin (t^{2})dt=$? $2a \sin (a^{2})$ $2a$ $\sin (a^{2})$ None of the above
$\displaystyle \lim_{x \rightarrow a}\frac{1}{x^{2}-a^{2}} \displaystyle \int_{a}^{x}\sin (t^{2})dt=$?$2a \sin (a^{2})$$2a$$\sin (a^{2})$None of the above
admin
313
views
admin
asked
Apr 2, 2020
Calculus
nielit2016mar-scientistc
engineering-mathematics
calculus
+
–
1
votes
1
answer
98
NIELIT 2016 MAR Scientist C - Section B: 17
A ladder $13$ feet long rests against the side of a house. The bottom of the ladder slides away from the house at a rate of $0.5$ ft/s. How fast is the top of the ladder sliding down the wall when the bottom of the ladder is $5$ ... $-\dfrac{5}{24} \text {ft/s} \\$ $-\dfrac{5}{12} \text{ ft/s}$
A ladder $13$ feet long rests against the side of a house. The bottom of the ladder slides away from the house at a rate of $0.5$ ft/s. How fast is the top of the ladder ...
admin
402
views
admin
asked
Apr 2, 2020
Calculus
nielit2016mar-scientistc
engineering-mathematics
calculus
+
–
1
votes
2
answers
99
NIELIT 2017 OCT Scientific Assistant A (CS) - Section C: 9
$M$ is a square matrix of order $’n’$ and its determinant value is $5.$ If all the elements of $M$ are multiple by $2,$ its determinant value becomes $40.$ The value of $’n’$ is $2$ $3$ $5$ $4$
$M$ is a square matrix of order $’n’$ and its determinant value is $5.$ If all the elements of $M$ are multiple by $2,$ its determinant value becomes $40.$ The value ...
admin
1.4k
views
admin
asked
Apr 1, 2020
Linear Algebra
nielit2017oct-assistanta-cs
engineering-mathematics
linear-algebra
matrix
determinant
+
–
1
votes
2
answers
100
NIELIT 2017 OCT Scientific Assistant A (CS) - Section B: 16
If $P$ is risk probability, $L$ is loss, then Risk Exposure $(RE)$ is computed as. $RE = P/L$ $RE = P + L$ $RE = P \ast L$ $RE = 2 \ast P \ast L$
If $P$ is risk probability, $L$ is loss, then Risk Exposure $(RE)$ is computed as.$RE = P/L$ $RE = P + L$$RE = P \ast L$$RE = 2 \ast P \ast L$
admin
1.6k
views
admin
asked
Apr 1, 2020
Probability
nielit2017oct-assistanta-cs
engineering-mathematics
probability
+
–
2
votes
1
answer
101
NIELIT 2017 OCT Scientific Assistant A (CS) - Section B: 18
What is the maximum value of the function $f(x) = 2x^{2} – 2x + 6$ in the interval $[0,2]?$ $6$ $10$ $12$ $5,5$
What is the maximum value of the function $f(x) = 2x^{2} – 2x + 6$ in the interval $[0,2]?$$6$$10$$12$$5,5$
admin
627
views
admin
asked
Apr 1, 2020
Calculus
nielit2017oct-assistanta-cs
engineering-mathematics
calculus
maxima-minima
+
–
0
votes
1
answer
102
NIELIT 2017 OCT Scientific Assistant A (CS) - Section B: 19
The value of the Integral $I = \displaystyle{}\int_{0}^{\pi/2} x^{2}\sin x dx$ is $(x+2)/2$ $2/(\pi-2)$ $\pi – 2$ $\pi + 2$
The value of the Integral $I = \displaystyle{}\int_{0}^{\pi/2} x^{2}\sin x dx$ is$(x+2)/2$$2/(\pi-2)$$\pi – 2$$\pi + 2$
admin
465
views
admin
asked
Apr 1, 2020
Calculus
nielit2017oct-assistanta-cs
engineering-mathematics
calculus
definite-integral
+
–
1
votes
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
The function $f\left ( x \right )=\dfrac{x^{2}-1}{x-1}$ at $x=1$ is :Continuous and differentiableContinuous but not differentiableDifferentiable but not continuousNeith...
admin
1.1k
views
admin
asked
Mar 31, 2020
Calculus
nielit2017dec-assistanta
engineering-mathematics
calculus
continuity
+
–
1
votes
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
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
1.1k
views
admin
asked
Mar 31, 2020
Probability
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 $P\left(Y \right)$ = ___________ . $0.54$ $0.66$ $0.33$ $0.44$
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 $P\left(Z \right)$ = ...
admin
1.9k
views
admin
asked
Mar 31, 2020
Probability
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 $1$ $2$ $3$ $4$
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$$4$
admin
774
views
admin
asked
Mar 31, 2020
Set Theory & Algebra
nielit2016mar-scientistb
engineering-mathematics
functions
polynomials
+
–
2
votes
1
answer
107
NIELIT 2016 MAR Scientist B - Section B: 4
What is the determinant of the matrix $\begin{bmatrix}5&3&2\\1&2&6\\3&5&10\end{bmatrix}$ $-76$ $-28$ $+28$ $+72$
What is the determinant of the matrix $\begin{bmatrix}5&3&2\\1&2&6\\3&5&10\end{bmatrix}$$-76$$-28$$+28$$+72$
admin
688
views
admin
asked
Mar 31, 2020
Linear Algebra
nielit2016mar-scientistb
engineering-mathematics
linear-algebra
determinant
+
–
3
votes
2
answers
108
NIELIT 2016 MAR Scientist B - Section B: 5
The greatest and the least value of $f(x)=x^4-8x^3+22x^2-24x+1$ in $[0,2]$ are $0,8$ $0,-8$ $1,8$ $1,-8$
The greatest and the least value of $f(x)=x^4-8x^3+22x^2-24x+1$ in $[0,2]$ are$0,8$$0,-8$$1,8$$1,-8$
admin
646
views
admin
asked
Mar 31, 2020
Calculus
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.
The system of simultaneous equations$x+2y+z=6\\2x+y+2z=6\\x+y+z=5$hasunique solution.infinite number of solutions.no solution.exactly two solutions.
admin
706
views
admin
asked
Mar 31, 2020
Linear Algebra
nielit2016mar-scientistb
engineering-mathematics
linear-algebra
system-of-equations
+
–
1
votes
1
answer
110
NIELIT 2016 MAR Scientist B - Section B: 9
The value of improper integral $\displaystyle\int_{0}^{1} x\ln x =?$ $1/4$ $0$ $-1/4$ $1$
The value of improper integral $\displaystyle\int_{0}^{1} x\ln x =?$$1/4$$0$$-1/4$$1$
admin
712
views
admin
asked
Mar 31, 2020
Calculus
nielit2016mar-scientistb
engineering-mathematics
calculus
integration
definite-integral
+
–
1
votes
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 $x=4$
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$$x=3$ and $x=4$
admin
547
views
admin
asked
Mar 31, 2020
Calculus
nielit2016mar-scientistb
engineering-mathematics
calculus
maxima-minima
+
–
1
votes
2
answers
112
NIELIT 2016 MAR Scientist B - Section B: 11
What is the derivative w.r.t $x$ of the function given by $\large \Phi(x)= \displaystyle \int_{0}^{x^2}\sqrt t\:dt$, $2x^2$ $\sqrt x$ $0$ $1$
What is the derivative w.r.t $x$ of the function given by$\large \Phi(x)= \displaystyle \int_{0}^{x^2}\sqrt t\:dt$,$2x^2$$\sqrt x$$0$$1$
admin
532
views
admin
asked
Mar 31, 2020
Calculus
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? $\det(AB)=\det(A) \det(B)$ $\det(kA)=k^n \det(A)$ $\det(A+B)=\det(A)+\det(B)$ $\det(A^T)=1/\det(A^{-1})$
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...
admin
6.5k
views
admin
asked
Mar 31, 2020
Linear Algebra
nielit2016mar-scientistb
engineering-mathematics
linear-algebra
determinant
+
–
1
votes
2
answers
114
NIELIT 2016 MAR Scientist B - Section B: 13
$\underset{x\to 0}{\lim} \dfrac{(1-\cos x)}{2}$ is equal to $0$ $1$ $1/3$ $1/2$
$\underset{x\to 0}{\lim} \dfrac{(1-\cos x)}{2}$ is equal to$0$$1$$1/3$$1/2$
admin
595
views
admin
asked
Mar 31, 2020
Calculus
nielit2016mar-scientistb
engineering-mathematics
calculus
limits
+
–
0
votes
1
answer
115
NIELIT 2016 MAR Scientist B - Section B: 14
The minimum value of $\mid x^2-5x+2\mid$ is $-5$ $0$ $-1$ $-2$
The minimum value of $\mid x^2-5x+2\mid$ is$-5$$0$$-1$$-2$
admin
557
views
admin
asked
Mar 31, 2020
Calculus
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.
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\...
admin
1.1k
views
admin
asked
Mar 31, 2020
Probability
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 ________. $0$ $1$ $15$ $-1$
Two eigenvalues of a $3\times3$ real matrix $P$ are $(2+ \sqrt-1)$ and $3$. The determinant of $P$ is ________.$0$$1$$15$$-1$
admin
929
views
admin
asked
Mar 31, 2020
Linear Algebra
nielit2016dec-scientistb-it
engineering-mathematics
linear-algebra
determinant
eigen-value
+
–
2
votes
2
answers
118
NIELIT 2016 DEC Scientist B (CS) - Section B: 21
Let $A,B,C,D$ be $n\times n$ matrices, each with non-zero determinant. If $ABCD=1$, then $B^{-1}$ is: $D^{-1}C^{-1}A^{-1}$ $CDA$ $ADC$ Does not necessarily exist.
Let $A,B,C,D$ be $n\times n$ matrices, each with non-zero determinant. If $ABCD=1$, then $B^{-1}$ is:$D^{-1}C^{-1}A^{-1}$$CDA$$ADC$Does not necessarily exist.
admin
762
views
admin
asked
Mar 31, 2020
Linear Algebra
nielit2016dec-scientistb-cs
engineering-mathematics
linear-algebra
matrix
determinant
+
–
1
votes
1
answer
119
NIELIT 2016 DEC Scientist B (CS) - Section B: 26
Consider the function $f(x)=\sin(x)$ in the interval $\bigg [\dfrac{ \pi}{4},\dfrac{7\pi}{4}\bigg ]$. The number and location(s) of the minima of this function are: One, at $\dfrac{\pi}{2} \\$ One, at $\dfrac{3\pi}{2} \\$ Two, at $\dfrac{\pi}{2}$ and $\dfrac{3\pi}{2} \\$ Two, at $\dfrac{\pi}{4}$ and $\dfrac{3\pi}{2}$
Consider the function $f(x)=\sin(x)$ in the interval $\bigg [\dfrac{ \pi}{4},\dfrac{7\pi}{4}\bigg ]$. The number and location(s) of the minima of this function are:One...
admin
575
views
admin
asked
Mar 31, 2020
Calculus
nielit2016dec-scientistb-cs
engineering-mathematics
calculus
maxima-minima
+
–
1
votes
1
answer
120
NIELIT 2017 July Scientist B (IT) - Section B: 23
The probability that top and bottom cards of a randomly shuffled deck are both aces is: $4/52\times 4/52$ $4/52\times 3/52$ $4/52\times 3/51$ $4/52\times 4/51$
The probability that top and bottom cards of a randomly shuffled deck are both aces is:$4/52\times 4/52$$4/52\times 3/52$$4/52\times 3/51$$4/52\times 4/51$
admin
566
views
admin
asked
Mar 30, 2020
Probability
nielit2017july-scientistb-it
engineering-mathematics
probability
+
–
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