Suresh said, “I did it yesterday.” Which one of the following options is the correct form of this sentence in indirect speech?
a.
Suresh said that I did it yesterday.
b.
Suresh says I did it yesterday.
c.
Suresh says that he did it the day before.
d.
Suresh said that he had done it the day before.
Correct Answer
No explanation saved for this question yet.
Q2mcq
To continue the sequence of tiles shown, the tile indicated by the question mark should be
a.
b.
c.
Correct Answer
d.
No explanation saved for this question yet.
Q3mcq
Consider an art gallery whose walkways are shown as lines in the diagram. A black dot represents a junction of two walkways. A guard may be placed at a junction to watch over the walkways that join at that junction. The minimum number of guards needed to watch all the walkways is ________.
a.
2
b.
3
Correct Answer
c.
4
d.
5
No explanation saved for this question yet.
Q4mcq
The 2 nd of June is a Thursday in a certain year. Which day of the week is the 3 rd of July in that year?
a.
Thursday
b.
Friday
c.
Saturday
d.
Sunday
Correct Answer
No explanation saved for this question yet.
Q5mcq
A coin with heads facing up is shown as and a coin with tails facing up is shown as. Six coins are placed in the Starting Arrangement, as shown in the figure below. A “step” is defined as interchanging a pair of adjacent coins without flipping them. The minimum number of steps needed to go from the Starting Arrangement to the Final Arrangement, as shown in the figure, is ________.
a.
3
b.
6
c.
9
Correct Answer
d.
12
No explanation saved for this question yet.
Q6mcq
Exacerbate: Mitigate:: ___________ Choose the option with the correct pair of words to fill the blank.
a.
Aggravate: Alleviate
Correct Answer
b.
Alleviate: Precipitate
c.
Aggravate: Precipitate
d.
Emancipate: Exonerate
No explanation saved for this question yet.
Q7mcq
A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct?
a.
Only (i) can correspond to the unfolded cube in Panel I.
b.
Only (ii) can correspond to the unfolded cube in Panel I.
Correct Answer
c.
Both (i) and (ii) can correspond to the unfolded cube in Panel I.
d.
Neither (i) nor (ii) can correspond to the unfolded cube in Panel I.
No explanation saved for this question yet.
Q8mcq
In a population, patients who have high cholesterol also have high blood-pressure (BP). Some patients with high BP also have diabetes. There are no patients who have both high cholesterol and diabetes. Furthermore, 1. the total number of patients with at least one of these conditions is 75, 2. the number of patients with high cholesterol is 10, 3. the number of patients with high BP is 45, and 4. the number of patients with only high BP and no other conditions is 20. Then the number of patients who have both diabetes and high BP is _______
a.
0
b.
15
Correct Answer
c.
20
d.
10
No explanation saved for this question yet.
Q9mcq
Four people P, Q, R, and S, of different ages, make the following observations. P – I am younger than S. Q – I am neither the youngest nor the oldest. R – P is older than me. Based on these observations, the youngest person is ______.
a.
P
b.
Q
c.
R
Correct Answer
d.
S
No explanation saved for this question yet.
Q10mcq
Circles $C$ 1, $C$ 2, and $C$ 3, with centers $O$ 1, $O$ 2, and $O$ 3, and radii $r$ 1, $r$ 2, and $r$ 3, respectively, touch each other as shown in the following figure. Given $r$ 1 = 2 cm, $r$ 2 = 1 cm and the angle $∠O$ 1 $O$ 3 $O$ 2 is 90°, $r$ 3 = _____ cm.
a.
1 (-3 + $\sqrt{17}$) 2
Correct Answer
b.
1 (3 + $\sqrt{17}$) 2
c.
1 (-2 + $\sqrt{17}$) 2
d.
1 (-3 + $2\sqrt{17}$) 2
No explanation saved for this question yet.
🎉 10 Free Sample Solutions Completed
Unlock All 65 Questions & Solutions
Sign up free in seconds to unlock step-by-step AI answers for the remaining 55 questions.
Let $M$ 3 (ℝ) be the vector space of all 3 $\times$ 3 real matrices over ℝ under usual matrix addition and scalar multiplication. Let $T$ 3 (ℝ) be the set of all 3 $\times$ 3 real upper triangular matrices. Which one of the following is TRUE?
a.
The quotient space 3 ⁄ $T$ (ℝ) is isomorphic to the vector space of all 3 $\times$ 3
$M$ (ℝ)
3 real skew symmetric matrices over ℝ under usual matrix addition and scalar multiplication.
b.
The quotient space 3 ⁄ $T$ (ℝ) is isomorphic to the vector space of all 3 $\times$ 3
$M$ (ℝ)
3 real symmetric matrices over ℝ under usual matrix addition and scalar multiplication.
c.
The quotient space 3 ⁄ $T$ (ℝ) is isomorphic to the vector space of all 3 $\times$ 3
$M$ (ℝ)
3 real lower triangular matrices over ℝ under usual matrix addition and scalar multiplication.
d.
The quotient space 3 ⁄ $T$ (ℝ) is isomorphic to the vector space of all 3 $\times$ 3
$M$ (ℝ)
3 real matrices with trace zero over ℝ under usual matrix addition and scalar multiplication.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $I$ be the integral defined as follows:
1 $y$ 2 1 $I$ = $\int \int √ dx dy$ + $\int \int dx dy$
0 0 1 $\sqrt{y}-1$ If the order of the integration is changed, then which one of the following is the correct expression for $I?$ 1/2 $x$
a.
$\int$ 0
b.
$\int \int$ 2 0 $x$
c.
$\int \int$ 2 0 $x$
d.
$\int \int$ 2 1 $x$ -1 $dy dx$ 0 $x$
2
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $C$ denote the Cantor set and $f:$ [0,1] $\to$ ℝ be defined as follows:
$x$ 2026 for $x$ ∈ $C$
$f(x)$ = 2
$cos(πx)$ for $x$ ∈ [ 0, ] $\C$
{ $sin(πx)$ for $x$ ∈ [, 1 ] $\C$ 2
1
1 The value of the Lebesgue integral of $f(x)$ over the interval [0,1] is equal to
a.
2 $π$
b.
1 $π$
c.
3 $π$
d.
0
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $u(x, t)$ be the solution of the initial value problem for the heat equation on the real line:
$∂u ∂$ 2 $u$
$=k$, $-\infty$ < $x$ < $\infty, t$ > 0, $k∈R$
$∂t ∂x$ 2 with the initial condition
$u(x,$ 0) = $e -a|x|$, $a$ > 0.
$\infty$ If $û(w, t)$ = $\int u(x, t)e iwx dx$ is the Fourier transform of $u(x, t)$ with respect
$-\infty$ to $x,$ then $û(w, t)$ is equal to
a.
$2a$ $a$ 2 $+w$
b.
$a$ $a$ 2 $+w$
c.
$2a$ $a$ 2 $+w$
d.
1 $\sqrt{4} πkt$
$e 4kt$
$-w2$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $D$ = ${z$ ∈ ℂ | $|z|$ < 1} denote the unit disc in the complex plane ℂ. Let $f: D \to D$ be an analytic function which satisfies $f(0)$ = 0. Then which one of the following is a possible value of $f′(0)?$
a.
5 2
b.
$i$ 10
c.
3 2
d.
5 - $i$ 2
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $X$ be the space of all continuously differentiable real valued functions on [0,1]. Define the following norms on $X:$
$p$ 1 $(x)$ = $sup{|x(t)|$ ∶ $t$ ∈ [0,1]}
$d$
$p$ 2 $(x)$ = sup {| $x(t)|$ ∶ $t$ ∈ [0,1]}
$dt$
and $p$ 3 $(x)$ = $p$ 1 $(x)$ + $p$ 2 $(x).$ Which one of the following is TRUE?
a.
$(X, p$ 1) is a Banach space.
b.
$(X, p$ 2) is a Banach space.
c.
$(X, p$ 3) is not a Banach space.
d.
$(X, p$ 3) is a Banach space.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $f:$ ℝ 2 $\to$ ℝ be a function defined as follows:
$x \sqrt{x}$ 2 + $y$ 2
$f(x, y)$ = { $|x|$
0 for $x$ = 0
for $x ≠$ 0 Which of the following statements is/are TRUE?
a.
$f(x, y)$ is continuous at (0,0).
b.
For any $u$ ∈ ℝ 2, the directional derivative of $f$ at (0,0) in the direction of $u$ exists.
c.
$∂f$ $∂x$
d.
$f(x, y)$ is differentiable at (0,0).
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let ℤ 11 be the ring of integers modulo 11. Let ℤ 11 $[x]$ be the ring of all polynomials with coefficients in ℤ 11. Which of the following statements is/are TRUE?
a.
The polynomial $x$ 2 + $x$ + 4 is irreducible over ℤ 11.
b.
ℤ 11 $[x]$
⁄ $〈x$ 2 + $x$ + 4〉 is a field.
c.
The ideal $〈x$ 2 + $x$ + 4〉 is maximal.
d.
The ideal $〈x$ 2 + $x$ + 4〉 is not a prime ideal.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Consider the following partial differential equation:
$∂$ 2 $f(x,$
$y)$
$∂$ 2 $f(x,$
$a$
+
$b$
$∂x$
2
$∂y$
where $a$ and $b$ are distinct positive real numbers. The combination(s) of the values of the real parameters $ξ$ and $η$ for which $f(x, y)$ = $e 2ξx+ηy$ is a solution of the given partial differential equation, is/are
a.
$ξ=$ 1, $η=$ 2 $\sqrt{a} \sqrt{b}$
b.
$ξ=$ 0, $η=$ 0
c.
$ξ=$
d.
2 $ξ$ = 0, $η$ = 2 $√$ $b$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $T:$ ℝ 3 $\to$ ℝ 3 be the linear transformation which reflects every vector in ℝ 3 through a two-dimensional subspace of ℝ 3. Let $P$ ∈ ℝ $3\times3$ be the matrix
1 0 0 representation of $T$ using the basis { (0), (1), (0) }.
0 0 1 Then the value of 2 $\times trace(P)$ - 3 $\times determinant(P)$ is equal to. (answer in integer)
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $x$ 3 - $x$ + 1 ∈ ℤ 3 $[x],$ where ℤ 3 $[x]$ is the ring of all polynomials with coefficients in ℤ 3. Then the degree of the field extension 3 ⁄ $〈x$ 3 - $x$ + 1〉 of ℤ 3 is equal to. (answer in integer)
ℤ $[x]$
$dy$
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Consider the differential equation = $x$ + $y$ with the initial condition $y(0)$ = 1.
$dx$ Using the modified Euler’s method, the second approximation to $y(h),$ where ℎ = 0.05 (step size), is equal to. (rounded off to TWO decimal places)
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
. (answer in integer) $x$ Let $X$ =, ‖ ⋅ ‖ 1) where ‖($y$)‖ = $|x|$ + $|y|$ + $|z|$ and $T: X \to X$ be a linear (ℝ 3 $z$ 1 transformation defined as $x$ 1 $x$ 1 3 $T$ ($y$) = (2 2 -2) ($y$). $z$ 1 3 -3 $z$ Then the operator norm of $T$ is equal to. (answer in integer)
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Consider the following Linear Programming Problem (LPP):
maximize $z$ = $10x$ 1 + $20x$ 2
subject to
$x$ 1 $\le$ 36
$x$ 2 $\ge$ 42
$x$ 1 + $x$ 2 $\ge$ 48
$5x$ 1 + $x$ 2 $\le$ 150
$x$ 1, $x$ 2 $\ge$ 0 The maximum value of $z$ in the above LPP is equal to. (answer in integer)
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
For $a n$ ∈ ℂ, $n$ = 0,1,2, …, the power series
$\infty$
∑ $a n (z$ - 2) $n$
$n=0$ converges at $z$ = 5 and diverges at $z$ = -1. Then the radius of convergence of this power series is equal to. (answer in integer)
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
1 0 0 Let $P$ = (0 9 0). Define an inner product on ℝ 3 with respect to $P$ as 0 0 16
$〈x, y〉 P$ = $x$ ⊤ $Py,$ for all $x, y$ ∈ ℝ 3.
1 1 Consider the subspace $V$ = span { (0), (1) }. Which one of the following sets is
0 1 an orthonormal basis of $V$ with respect to $〈x, y〉 P$ ?
a.
1 0 { (0), (1) } 0 1
b.
0 0 { (1), (1) } 0 1
c.
0 1 1 { (0), (5) } 1 0 5
d.
0 1 1 { (0), ($\sqrt{2}$) } 1 0 $\sqrt{2}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The value of the contour integral
(1 - $z)(3cosz$ + $5sinz)$
$dz$, $\int$
1 - $z$ 101
Γ
7 where Γ = ${z$ ∈ ℂ ∶ $|z|$ = }, oriented in the counter-clockwise direction, is equal
9 to
a.
$2πi$
b.
$-2πi$
c.
0
d.
$4πi$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $δ(t)$ be the unit impulse function defined by $δ(x$ - $x$ 0) = 0 when $x ≠ x$ 0 and
$\infty$
$\int δ(x$ - $x$ 0) $dx$ = 1.
$-\infty$ Consider the following initial value problem
2 + + $2y$ = $δ(x$ - 5)
$d$ 2 $y dy$
$dx$ 2 $dx$
$dy$ with $y(0)$ = 0 and (0) = 0. Which one of the following is TRUE?
$dx$
a.
b.
c.
d.
$y(10)$ = 2 $5\sqrt{15} e$ 5/4 sin ()
$\sqrt{15}$ 4
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let ℓ $\infty$ = ${x$ = $(x n$) $n\ge1$ | $x n$ ∈ ℝ, sup ${|x n$ |: $n$ = 1,2, … } < $\infty}$ with the
$x x$ supremum norm. Let $T:$ ℓ $\infty \to$ ℓ $\infty$ be given by $T(x$, $x$, $x$, …) = $(x$, 2, 3, …).
1 2 3 1 2 3 Which one of the following is TRUE?
a.
$T$ is bounded but not one-to-one.
b.
$T$ is one-to-one but not bounded.
c.
$T$ is bounded and the inverse (from the range of $T)$ exists but not bounded.
d.
$T$ is bounded and the inverse (from the range of $T)$ is bounded.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $u(x, t)$ satisfy the wave equation
∂ 2 $u$ ∂ 2 $u$
2 = $c$, - $\infty$ < $x$ < $\infty, t$ > 0, $c>0$
$∂t$ 2 $∂x$ 2 with
1 if $|x|$ < 1
$u(x,$ 0) = {
0 otherwise
and
$∂u$
$(x,$ 0) = 0.
$∂t$ By using D’Alembert’s formula, the maximum value of $u(0, t)$ for $t$ > 0 is
a.
1
b.
1 2
c.
1 4
d.
0
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $E$ 1 and $E$ 2 be subsets of a normed linear space $X,$ and
$E$ 1 + $E$ 2 = ${x$ + $y$ ∶ $x$ ∈ $E$ 1, $y$ ∈ $E$ 2 }
$E$ 1 $\times E$ 2 = ${(x, y)$ ∶ $x$ ∈ $E$ 1, $y$ ∈ $E$ 2 }. Which one of the following is NOT TRUE?
a.
If either of $E$ 1 or $E$ 2 is open, then $E$ 1 + $E$ 2 is open.
b.
If $E$ 1 and $E$ 2 are convex, then $E$ 1 + $E$ 2 is convex.
c.
If $E$ 1 and $E$ 2 are closed, then $E$ 1 + $E$ 2 is closed.
d.
If $E$ 1 and $E$ 2 are connected, then $E$ 1 $\times E$ 2 is connected.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
For a transportation problem, let $c ij$ denote the unit cost of the cell $(i, j).$ Assume that $c$ 11 = 10, $c$ 12 = 12, $c$ 21 = 11 and $c$ 22 = 13. Let α $i$ and β $j$, $i, j$ = 1,2,3, represent the simplex multipliers associated with any basis corresponding to the unit cost $c ij$. Assume that α 1 = $x,$ α 2 = $x$ + 1, β 1 = $y$ and β 2 = $y$ + 2. The relative cost coefficient $d ij$ is the difference between the current solution and the new improved solution. If $x$ = 4, $c$ 13 = 19 and β 3 = $y$ + 5, then which one of the following is TRUE?
a.
$y$ = 6 and $d$ 13 = 7
b.
$y$ = 6 and $d$ 13 = 4
c.
$y$ = 5 and $d$ 13 = 7
d.
$y$ = 5 and $d$ 13 = 4
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $P$ and $Q$ be 3 $\times$ 3 nonzero real matrices. Assume that there exists a 3 $\times$ 3 real nonsingular matrix $S$ such that $S$ -1 $PS$ and $S$ -1 $QS$ are both upper triangular. Which of the following statements is/are TRUE?
a.
The matrix $PQ$ - $QP$ is invertible.
b.
The matrix $PQ$ - $QP$ is nilpotent.
c.
The matrix $I$ + $PQ$ - $QP$ is invertible, where $I$ is the 3 $\times$ 3 identity matrix.
d.
If $PQ$ - $QP$ is a nonzero matrix, then $PQ$ - $QP$ is diagonalizable.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$z 1+z$ Let $f(z)$ = and $g(z)$ = be two Mӧbius transformations defined on the $1-z 1-z$ unit disc $D$ = ${z$ ∈ ℂ ∶ $|z|$ < 1}. Consider the following statements: $S$ 1: $f(D)$ ⊆ $g(D)$ $S$ 2: $g(D)$ ⊆ $f(D)$ Which of the following statements is/are CORRECT?
a.
$S$ 1 is true.
b.
$S$ 2 is true.
c.
$S$ 2 is true and $S$ 1 is false.
d.
Neither $S$ 1 is true nor $S$ 2 is true.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let α and β be the roots of the indicial equation obtained in the method of finding Frobenius series solution to the differential equation:
$2x$ 2 - $x$ + (1 - $x$ 2 $)y$ = 0.
$d$ 2 $y dy$
$dx$ 2 $dx$ Which of the following statements is/are TRUE?
a.
$α≠β$
b.
α-β∈ℤ
c.
α-β ∉ℤ
d.
α= β
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $Q[x]$ be the ring of all polynomials with coefficients in ℚ under the usual polynomial addition and multiplication. Let $T: Q[x] \to Q[x]$ be defined by
$T(p(x))$ = $p(x$ 2), for all $p(x)$ ∈ $Q[x]$. Which of the following statements is/are TRUE?
a.
$T$ is a ring homomorphism.
b.
$T$ is one-to-one.
c.
$T$ is onto.
d.
$T$ is a ring isomorphism.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let (ℤ $n$, +) be the group of integers modulo $n.$ Let $G$ = ℤ 30 ⨁ ℤ 12 be the external direct product of ℤ 30 and ℤ 12. Then which of the following statements is/are TRUE?
a.
$G$ is not a cyclic group.
b.
The order of the element (14,7) in $G$ is 98.
c.
The order of the element (14,7) in $G$ is 60.
d.
There is an element in $G$ of order 360.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let α = ∬ $F⃗$ ∙ $n̂ dS,$ where $F⃗$ = $(2x$ + $3z)î$ + $(xz$ - $y)ĵ$ + $(y$ 2 + $2z)k̂$ and $S$ is
$S$ the sphere with centre at (3, -1, 2) and radius 9. Here, $n̂$ is the unit normal drawn outward and $î$, $ĵ$, $k̂$ are unit vectors.
1 Then the value of α is equal to
36 $π$
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $P$ 3 (ℝ) be the vector space of all polynomials of degree at most three with the real coefficients under usual polynomial addition and scalar multiplication. Let $T: P$ 3 (ℝ) $\to$ ℝ 2 be the linear transformation defined as
$T(p)$ = $(p(1), p$ ′ (1)) for all $p$ ∈ $P$ 3 (ℝ), where $p$ ′ is the derivative of $p.$ Then the nullity of $T$ is equal to
. (answer in integer)
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $L$ 2 [0, π] denote the space of all real valued Lebesgue square integrable functions on [0, π]. Let $T: L$ 2 [0, π] $\to L$ 2 [0, π] be defined as follows:
$π π$
$T(f(x))$ = $sinx \int f(t)cost dt$ + $cosx \int f(t)sint dt$.
0 0
4 Then the value of $‖T‖$ is equal to
$π$
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
. (answer in integer) Let Ω = ${(x, y)$ ∈ ℝ 2: $x$ 2 + $y$ 2 < 1} be the open unit disc and ∂Ω be its boundary. If $u(x, y)$ is the solution of the following Dirichlet problem
∂ 2 $u$
∂ 2 $u$
+
= 0
$∂x$ 2
$∂y$ 2
$u(x,$
= $x$
2 - $y$
1 1 then the value of 4 $(u$ (, 0) - $u$ (0,)) is 2 2
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Ω . (answer in integer) Let $X$ = {5, 6, 7, 8, 9, 10} be equipped with the topology τ = ${φ, X,$ {5,6,7}, {8,9,10}}. Then the number of subsets of $X$ which are neither open nor closed is. (answer in integer)
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let α, β ∈ ℝ. If (4, 0, 2, β) is an optimal solution of the Linear Programming Problem:
minimize $x$ 1 + $3x$ 2 + $2x$ 3 - $αx$ 4
subject to
$4x$ 1 + $x$ 2 + $x$ 3 = 18
$-3x$ 1 + $2x$ 3 + $x$ 4 = 2
$x$ 1, $x$ 2, $x$ 3, $x$ 4 $\ge$ 0, then the maximum value of 22(α + β) is equal to
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
. (answer in integer) Let $D$ = ${(x, y)$ ∈ ℝ 2 ∶ 0 $\le x \le$ 2, 0 $\le y \le$ 2} and let $f(t)$ denote the smallest integer greater than or equal to $t.$ Then the value of the integral ∬ $f(x$ + $y)dxdy$ $D$ is
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
. (answer in integer) If Jacobi method is used to solve the following system of linear equations
1 2 1 $x$ 1 2
(0 2 2) ($x$ 2) = (2)
1 1 1 $x$ 3 2
$(i) x$
1 0
(0) $(i)$ with the initial guess $x$ = (0) and $x$ = ($x 2(i)$), $i$ = 1,2,3 …, denotes the
$(i)$ 0 $x$ $th$ (2) (2) (2) iterate, then the value of | $x$ + $x$ + $x$ | is equal to $i$. (answer in
3
1 2 3 integer)
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
