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Recent questions tagged engineering-mathematics

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self doubt
Can anybody please tell what is the subjects fall under discrete and engineering mathematics for gate cse
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Applied Test Series
A final exam is a discrete mathematics course consisting of 20 true-false questions, each worth 3 points and 10 multiple choice questions, each worth 4 points. Suppose th...
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Applied Test Series
Consider the system of equations x+y+z=3x+2y+3z=4x+4y+kz=6 The above system of equations will not have a unique solution for k equals to___
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Applied Test Series
What is the correct procedure to solve this limit ?The value of $\lim _{x \rightarrow 0}\left[\frac{2}{x^{3}}\left(\sin ^{-1} x-\tan ^{-1} x\right)\right]^{\frac{2}{x^{2}...
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Applied Test Series
A large bowl contains 15 balls that are identical except for their colors 6 are colored red, 5 are colored blue and 4 are colored green. What is the probability that two ...
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Linear Algebra Eigenvalues
If the eigenvalues of a 3x3 matrix A are 1,2 and 3 then inverse of A is?
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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)$$P...
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NIELIT 2016 MAR Scientist C - Section B: 8
The eigenvalues of the matrix $\begin{bmatrix}1 & 2\\ 4 & 3 \end{bmatrix}$ are$\text{5 and -5}$$\text{5 and -1}$$\text{1 and -5}$$\text{2 and 3}$
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2 2 answers
985
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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...
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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
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1 1 vote
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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$
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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
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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 ...
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3 3 votes
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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 $...
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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$
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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$
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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$$\pi + 2$
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NIELIT 2017 DEC Scientific Assistant A - Section B: 10
The function $f\left ( x \right )=\dfrac{x^{2}-1}{x-1}$ at $x=1$ is :Continuous and differentiableContinuous but not differentiableDifferentiable but not continuousNeith...
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NIELIT 2017 DEC Scientific Assistant A - Section B: 41
If a random coin is tossed $11$ times, then what is the probability that for $7$th toss head appears exactly $4$ times?$5/32$$15/128$$35/128$None of the options
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NIELIT 2017 DEC Scientific Assistant A - Section B: 44
If $X, Y$ and $Z$ are three exhaustive and mutually exclusive events related with any experiment and the $P\left(X \right)=0.5P\left(Y \right)$ and $P\left(Z \right)$ = ...
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NIELIT 2016 MAR Scientist B - Section C: 21
A polynomial $p(x)$ is such that $p(0)=5, \: p(1)=4, \: p(2)=9$ and $p(3)=20$. The minimum degree it can have is$1$$2$$3$$4$
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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$
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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$$1,-8$
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4 4 votes
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NIELIT 2016 MAR Scientist B - Section B: 6
The system of simultaneous equations$x+2y+z=6\\2x+y+2z=6\\x+y+z=5$hasunique solution.infinite number of solutions.no solution.exactly two solutions.
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1 1 vote
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NIELIT 2016 MAR Scientist B - Section B: 9
The value of improper integral $\displaystyle\int_{0}^{1} x\ln x =?$$1/4$$0$$-1/4$$1$
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1 1 vote
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890
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NIELIT 2016 MAR Scientist B - Section B: 10
Maxima and minimum of the function $f(x)=2x^3-15x^2+36x+10$ occur; respectively at $x=3$ and $x=2$$x=1$ and $x=3$$x=2$ and $x=3$$x=3$ and $x=4$
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1 1 vote
2 2 answers
994
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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$$1$
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4 4 votes
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NIELIT 2016 MAR Scientist B - Section B: 12
If $A$ and $B$ are square matrices of size $n\times n$, then which of the following statements is not true?$\det(AB)=\det(A) \det(B)$$\det(kA)=k^n \det(A)$$\det(A+B)=\det...
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938
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NIELIT 2016 MAR Scientist B - Section B: 13
$\underset{x\to 0}{\lim} \dfrac{(1-\cos x)}{2}$ is equal to$0$$1$$1/3$$1/2$
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835
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NIELIT 2016 MAR Scientist B - Section B: 14
The minimum value of $\mid x^2-5x+2\mid$ is$-5$$0$$-1$$-2$
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