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Hot questions in Engineering Mathematics
0
votes
0
answers
1
GATE201512
If a continuous function $f(x)$ does not have a root in the interval $[a, b]$, then which one of the following statements is TRUE? $f(a) . f(b)=0$ $f(a) . f(b) < 0$ $f(a) . f(b) > 0$ $f(a) / f(b) \leq 0$
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.3k
points)
gate2015ee1
continuousfunction
roots
interval
0
votes
0
answers
2
GATE2014228
The minimum value of the function $f(x)=x^33x^224x+100$ in the interval $[3,3]$ is $20$ $28$ $16$ $32$
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.3k
points)
gate2014ee2
linearfunctions
0
votes
0
answers
3
GATE20142GA8
If x is real and $x^2 − 2x + 3$ = $11$, then possible values of $ x^3 + x^2 − x$ include $2,4$ $2,14$ $4,52$ $14,52$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2014ee2
algebra
matrix
0
votes
0
answers
4
GATE2015228
A differential equation $\frac{di}{dt}0.2i=0$ is applicable over $−10 < t < 10$. If $i(4) = 10$, then $i(−5)$ is _________.
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.3k
points)
gate2015ee2
nonlinearequation
eulersequation
numericalanswers
0
votes
0
answers
5
GATE2014218
The state transition matrix for the system $\begin{bmatrix} \dot{x_1}\\ \dot{x_2} \end{bmatrix}=\begin{bmatrix} 1 & 0\\ 1 & 1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}+\begin{bmatrix} 1\\ 1 \end{bmatrix}u$ ... $\begin{bmatrix} e^t &te^t \\ 0&e^t \end{bmatrix}$
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.3k
points)
gate2014ee2
state
transition
matrix
0
votes
0
answers
6
GATE201521
Given $f(z) = g(z) + h(z)$, where $f, g, h$ are complex valued functions of a complex variable $z$. Which one of the following statements is TRUE? If $f(z)$ is differentiable at $z_{0}$, then $g(z)$ and $h(z)$ are also differentiable at $z_{0}$ ... at $z_{0}$, then it is differentiable at $z_{0}$. If $f(z)$ is differentiable at $z_{0}$, then so are its real and imaginary parts
asked
Feb 12, 2017
in
Complex Variables
by
makhdoom ghaya
(
9.3k
points)
gate2015ee2
complexvaluedfunctions
complexvariable
0
votes
0
answers
7
GATE20152GA5
Consider a function $f(x) = 1  x$ on $1 \leq x \leq 1$. The value of $x$ at which the function attains a maximum, and the minimum value of the function are: $0, 1$ $1, 0$ $0, 1$ $1, 2$
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.3k
points)
gate2015ee2
maxima
minima
0
votes
0
answers
8
GATE201325
The equation$\begin{bmatrix} 2&2 \\ 1& 1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}=\begin{bmatrix} 0\\0 \end{bmatrix}$ has no solution only one solution $\begin{bmatrix} x1\\x2 \end{bmatrix}=\begin{bmatrix} 0\\0 \end{bmatrix}$ nonzero unique solution multiple solutions
asked
Feb 12, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2013ee
linearalgebra
matrix
systemoflinearequations
0
votes
0
answers
9
GATE2014326
Integration of the complex function $f(z)=\frac{z^2}{z^21}$ , in the counterclockwise direction, around $\mid z1 \mid$ = $1$, is $\pi i$ $0$ $\pi i$ $2 \pi i$
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.3k
points)
gate2014ee3
complexfunctions
integration
0
votes
0
answers
10
GATE2014226
To evaluate the double integral $\int_{0}^{8}(\int_{(y/2)}^{y/2+1}(\frac{2xy}{2})dx)dy$ , we make the substitution $u=(\frac{2xy}{2})$ and $v=\frac{y}{2}$ The integral will reduce $\int_{0}^{4}(\int_{0}^{2}2udu) dv$ $\int_{0}^{4}(\int_{0}^{1}2udu) dv$ $\int_{0}^{4}(\int_{0}^{1}udu) dv$ $\int_{0}^{4}(\int_{0}^{2}udu) dv$
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.3k
points)
gate2014ee2
integral
upperlimit
lowerlimit
0
votes
0
answers
11
GATE20151GA5
Given set $A=\left\{ 2, 3, 4, 5\right\}$ and set $B=\left\{ 11, 12, 13, 14, 15\right\}$, two numbers are randomly selected, one from each set. What is the probability that the sum of two numbers equal $16$? $0.20$ $0.25$ $0.30$ $0.33$
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.3k
points)
gate2015ee1
samplespace
events
0
votes
0
answers
12
GATE20151GA9
The probabilities that a student passes in Mathematics, Physics, and Chemistry are $m, p,$ and $c$ respectively. Of these subjects, the student has $75$% chance of passing in at least one, a $50$% chance of passing in at least two and a $40$% chance of passing in ... $I$ is true. Only relation $II$ is true. Relations $II$ and $III$ are true. Relations $I$ and $III$ are true.
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.3k
points)
gate2015ee1
events
samplespace
0
votes
0
answers
13
GATE2016126
Candidates were asked to come to an interview with $3$ pens each. Black, blue, green and red were the permitted pen colours that the candidate could bring. The probability that a candidate comes with all $3$ pens having the same colour is _________.
asked
Jan 30, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.3k
points)
gate2016ee1
randomvariable
event
mean
numericalanswers
0
votes
0
answers
14
GATE2016232
Let $P=\begin{bmatrix} 3&1 \\ 1 & 3 \end{bmatrix}$ Consider the set $S$ of all vectors $\begin{pmatrix} x\\ y \end{pmatrix}$ such that $a^{2}+b^{2}=1$ ... An ellipse with major axis along $\begin{pmatrix} 1\\ 1 \end{pmatrix}$ An ellipse with minor axis along $\begin{pmatrix} 1\\ 1 \end{pmatrix}$
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2016ee2
circleequations
vectors
0
votes
0
answers
15
GATE2016133
Given the following polynomial equation $s^{3}+5.5 s^{2}+8.5s+3=0$ the number of roots of the polynomial, which have real parts strictly less than $−1$, is ________.
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2016ee1
multiplicity
degreeofpolynomial
numericalanswers
0
votes
0
answers
16
GATE20162GA6
The following graph represents the installed capacity for cement production (in tonnes) and the actual production (in tonnes) of nine cement plants of a cement company. Capacity utilization of a plant is defined as ratio of actual production of cement to ... is called a small plant. The difference between total production of large plants and small plants, in tonnes is ____.
asked
Jan 30, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.3k
points)
gate2016ee2
collection
interpretation
standardizedtesting
numericalanswers
0
votes
0
answers
17
GATE201611
The maximum value attained by the function. $f(x) = x(x1) (x2)$ in the interval $[1, 2]$ is ___________.
asked
Jan 30, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.3k
points)
gate2016ee1
maxima
minima
criticalpoint
closedinterval
numericalanswers
0
votes
0
answers
18
GATE201612
Consider a $3 \times 3$ matrix with every element being equal to $1$. Its only nonzero eigenvalue is ________.
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2016ee1
characteristicequation
diagonalizingmatrices
invertiblematrix
numericalanswers
0
votes
0
answers
19
GATE2016249
Consider a linear time invariant system $\dot{x}=Ax$ with initial condition $x(0)$ at $t=0$. Suppose $\alpha$ and $\beta$ are eigenvectors of $(2 \times 2)$ matrix $A$ corresponding to distinct eigenvalues $\lambda_{1}$ and $\lambda_{2}$ respectively. Then the response $x(t)$ ... $e^{\lambda_{2}t}\beta$ $e^{\lambda_{2}t}\alpha$ $e^{\lambda_{1}t}\alpha+e^{\lambda_{2}t}\beta$
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2016ee2
lineartimeinvariantsystem
eigenvalues
0
votes
0
answers
20
GATE201629
The value of the line integral $\int_{c}^{} (2xy^{2}dx+2x^{2}y dy+dz)$ along a path joining the origin $(0, 0, 0)$ and the point $(1, 1, 1)$ is $0$ $2$ $4$ $6$
asked
Jan 30, 2017
in
Calculus
by
makhdoom ghaya
(
9.3k
points)
gate2016ee2
compositefunctions
additivity
space
riemannsum
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