question_answer 1)
Which one of the following is a polynomial?
A)
\[\frac{{{x}^{3}}}{9}-\frac{3}{{{x}^{-\,3}}}+\sqrt{x}\] done
clear
B)
\[{{x}^{3}}-\frac{3{{x}^{7/3}}}{^{3}\sqrt{x}}+\frac{{{x}^{-\,1/2}}}{{{x}^{1/2}}}\] done
clear
C)
\[{{x}^{2}}-3\sqrt{5x}+\sqrt{2}+{{x}^{-\,1}}\] done
clear
D)
\[\frac{{{x}^{3/2}}}{{{x}^{1/2}}}+\frac{2{{x}^{7/5}}}{{{x}^{2/5}}}+\frac{8{{x}^{2}}}{{{x}^{-1}}}\] done
clear
E)
None of these done
clear
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question_answer 2)
If \[A{{x}^{n}}+B{{x}^{n-2}}+C{{x}^{n-8}}+D\]is a polynomial such that \[\mathbf{A + B + C + D = 0}\] degree of the polynomial is ___________
A)
n done
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B)
0 done
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C)
1 done
clear
D)
not defined done
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E)
None of these done
clear
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question_answer 3)
Which among the following statements is true?
A)
\[\sqrt{3}x+\frac{{{x}^{4}}}{x}+5{{x}^{2}}\] is a quadratic polynomial done
clear
B)
Every real number is a zero of the zero polynomial. done
clear
C)
A non-zero constant polynomial has one zero. done
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D)
The degree of the polynomial, \[P(x)=\frac{\sqrt{3{{x}^{n}}}}{{{x}^{n-5}}}+\frac{\sqrt{5}{{x}^{n-2}}}{{{x}^{n-3}}}-\frac{7}{2}\frac{{{x}^{n-9}}}{{{x}^{n-15}}}+ {{x}^{4}}+ 8{{x}^{3}} + 5x + 2\]is 5 done
clear
E)
None of these done
clear
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question_answer 4)
\[7{{8}^{3}} - 3{{3}^{3}} - 4{{5}^{3}}\] is equal to
A)
347490 done
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B)
247280 done
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C)
387490 done
clear
D)
387280 done
clear
E)
None of these done
clear
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question_answer 5)
One of the factors of \[(225{{x}^{2}} - 1)\text{ }+\text{ }{{(1\text{ }+ 15x)}^{2}}\] is
A)
\[(15x-1)\] done
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B)
\[(5x+1)\] done
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C)
\[(5x-1)\] done
clear
D)
30x done
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E)
None of these done
clear
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question_answer 6)
\[{{\mathbf{(}\sqrt{\mathbf{P}}\mathbf{-}\sqrt{\mathbf{Q}}\mathbf{)}}^{\mathbf{3}}}\mathbf{+(}\sqrt{\mathbf{Q}}\mathbf{-}\sqrt{\mathbf{R}}{{\mathbf{)}}^{\mathbf{3}}}\mathbf{+(}\sqrt{\mathbf{R}}\mathbf{-}\sqrt{\mathbf{P}}{{\mathbf{)}}^{\mathbf{3}}}\] equals to _______
A)
\[3(P-Q)(Q-R)(R-P)\] done
clear
B)
\[3(\sqrt{P}-\sqrt{Q})(\sqrt{Q}-\sqrt{R})(\sqrt{R}-\sqrt{P})\] done
clear
C)
\[\sqrt{3}(\sqrt{P}-\sqrt{Q})(\sqrt{Q}-\sqrt{R})(\sqrt{R}-\sqrt{P})\] done
clear
D)
All the above done
clear
E)
None of these done
clear
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question_answer 7)
Find the square root of \[4{{a}^{6}}-12{{a}^{5}}+9{{a}^{4}}+8{{a}^{3}}-12{{a}^{2}}+4\]
A)
\[{{a}^{3}}-3{{a}^{2}}+2\] done
clear
B)
\[2{{a}^{3}}+3{{a}^{2}}-2\] done
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C)
\[2{{a}^{3}}-3{{a}^{2}}+2\] done
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D)
\[2{{a}^{3}}+3{{a}^{2}}+2\] done
clear
E)
None of these done
clear
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question_answer 8)
The LCM and HCF of the polynomials \[\mathbf{p(x)=51 }{{\mathbf{x}}^{\mathbf{2}}}\mathbf{ (x+3}{{\mathbf{)}}^{\mathbf{3}}}\mathbf{ (x-2}{{\mathbf{)}}^{\mathbf{2}}}\] and \[\mathbf{q(x)=34x (x-1}{{\mathbf{)}}^{\mathbf{5}}}\mathbf{ (x-2}{{\mathbf{)}}^{\mathbf{3}}}\] are respectively.
A)
\[102{{x}^{2}} {{(x-1)}^{5}}{{(x-2)}^{3}}{{(x+3)}^{3}} and 17{{x}^{2}}{{(x-2)}^{2}}\] done
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B)
\[204{{x}^{2}} {{(x-1)}^{5}}{{(x-2)}^{3}}{{(x+3)}^{3}} and 17x(x-2)\] done
clear
C)
\[102{{x}^{2}} {{(x-1)}^{5}}{{(x-2)}^{3}}{{(x+3)}^{3}} and 17x{{(x-2)}^{2}}\] done
clear
D)
\[102{{x}^{2}} {{(x-1)}^{5}}{{(x-2)}^{2}}{{(x+3)}^{3}} and 17x{{(x-2)}^{2}}\] done
clear
E)
None of these done
clear
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question_answer 9)
If \[\frac{\mathbf{p}}{\mathbf{q}}\mathbf{+}\frac{\mathbf{q}}{\mathbf{p}}\mathbf{=-1}\], then find the value of \[{{\mathbf{p}}^{\mathbf{3}}}\mathbf{-}{{\mathbf{q}}^{\mathbf{3}}}\] _______
A)
0 done
clear
B)
2pq done
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C)
1 done
clear
D)
-1 done
clear
E)
None of these done
clear
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question_answer 10)
\[\sqrt{\mathbf{(}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-x-2)(2}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+5x+3)(2}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-x-6)}}\]equals to ________
A)
\[(x-1)(x+2)(x-3)\] done
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B)
\[(x+1)(x-2)(x-3)\] done
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C)
\[(x+1)(2x+3)(x-2)\] done
clear
D)
\[(x-1)(x+2)(2x+3)\] done
clear
E)
None of these done
clear
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question_answer 11)
If \[\sqrt{3{{x}^{4}}-4\sqrt{3}{{x}^{3}}-2{{x}^{2}}+4\sqrt{3}x+3}\]\[=(a{{x}^{2}}+bx+c)\] Then which one of the following is incorrect?
A)
a and b are of different sign done
clear
B)
\[{{b}^{2}}+2ac=2\] done
clear
C)
\[2bc=4\sqrt{3}\] done
clear
D)
\[ab=-\,2\sqrt{3}\] done
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E)
None of these done
clear
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question_answer 12)
Factorize: \[{{\mathbf{p}}^{\mathbf{3}}}\mathbf{+}{{\mathbf{q}}^{\mathbf{3}}}\mathbf{+3pq-1}\]
A)
\[(p-q+1)({{p}^{2}}+{{q}^{2}}-pq)\] done
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B)
\[(p+q-1)({{p}^{2}}+{{q}^{2}}+1-pq+q+p)\] done
clear
C)
\[{{(p-1)}^{3}}(p+q)\] done
clear
D)
\[{{(p-1)}^{3}}(p-q)\] done
clear
E)
None of these done
clear
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question_answer 13)
If \[{{\mathbf{x}}^{\mathbf{4}}}\mathbf{-}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{+a}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+x+b}\]is exactly divisible by \[\mathbf{(x+2)}\] as well as \[\mathbf{(x-2)}\] then ______
A)
\[a+b=1\] done
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B)
\[a+2b=5\] done
clear
C)
\[a=b+1\] done
clear
D)
All the above done
clear
E)
None of these done
clear
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question_answer 14)
If \[\mathbf{p(x)=}{{\mathbf{x}}^{\mathbf{6}}}\mathbf{-7}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{-8}\] then which of the following is /are factor(s) of p(x)?
A)
\[{{x}^{2}}+2x+4\] done
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B)
\[{{x}^{2}}-x+1\] done
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C)
both A and B done
clear
D)
\[(x+2)\] done
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E)
None of these done
clear
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question_answer 15)
\[{{\mathbf{l}}^{\mathbf{3}}}{{\mathbf{(m-n)}}^{\mathbf{3}}}\mathbf{+}{{\mathbf{m}}^{\mathbf{3}}}{{\mathbf{(n-l)}}^{\mathbf{3}}}\mathbf{+}{{\mathbf{n}}^{\mathbf{3}}}{{\mathbf{(l-m)}}^{\mathbf{3}}}\]equals to _________
A)
\[{{(lmn)}^{3}}(l-m)(m-n)(n-l)\] done
clear
B)
\[(lm+mn+nl)(3{{l}^{2}}{{m}^{2}}{{n}^{2}})\] done
clear
C)
\[3lmn(m-n)(n-l)(l-m)\] done
clear
D)
0 done
clear
E)
None of these done
clear
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question_answer 16)
If P and Q are two polynomials of degree 5 and 4 respectively, then find the degree of\[\mathbf{P-Q}\].
A)
1 done
clear
B)
5 done
clear
C)
4 done
clear
D)
Cannot be determined done
clear
E)
None of these done
clear
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question_answer 17)
The square root of \[{{\mathbf{(ab+ac-bc)}}^{\mathbf{2}}}\mathbf{-4abc(a-b)}\]is ________
A)
\[(bc+ca-ab)\] done
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B)
\[(ab+bc-ca)\] done
clear
C)
\[(ab+bc+ca)\] done
clear
D)
\[(ab-bc+ca)\] done
clear
E)
None of these done
clear
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question_answer 18)
Which one among the following statements is/ are correct?
A)
Point \[(-\,5, 0)\]lies in the II quadrant. done
clear
B)
A point lies on x-axis at a distance of 5 units from y-axis, Its coordinate can be \[(-\,5, 0)\] or \[(5, 0)\] done
clear
C)
A point lies on y-axis lies on y-axis at a distance of 3 units from the x-axis. Its coordinate are \[(3, 0)\] done
clear
D)
All the above done
clear
E)
None of these done
clear
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question_answer 19)
The perpendicular distance of the point \[\mathbf{(6, -8)}\] from the x-axis is _______
A)
8 Units done
clear
B)
6 units done
clear
C)
10 units done
clear
D)
2 units done
clear
E)
None of these done
clear
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question_answer 20)
In the graph as shown, the equation of the line l is
A)
\[x=-\,3\] done
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B)
\[y=-\,3\] done
clear
C)
\[x-3=0\] done
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D)
\[y-3=0\] done
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E)
None of these done
clear
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question_answer 21)
A line passes through the points \[\mathbf{A(-2, -2),}\] \[\mathbf{B(-5, -5)}\]and \[\mathbf{C(-10, -10)}\]. The equation of this line will be ________
A)
\[x+y=0\] done
clear
B)
\[x-y=0\] done
clear
C)
\[x= -y\] done
clear
D)
\[x= y+1\] done
clear
E)
None of these done
clear
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question_answer 22)
The equation of a line passing through the points \[\mathbf{(-6, -4)}\] \[\mathbf{(0, 2)}\] and \[\mathbf{(-2, 0)}\] is _________
A)
\[y+x=2\] done
clear
B)
\[y-x=2\] done
clear
C)
\[x-y=2\] done
clear
D)
\[x+y=-\,2\] done
clear
E)
None of these done
clear
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question_answer 23)
The area of a square whose opposite vertices are \[\mathbf{(0, 0)}\]and \[\mathbf{(6, 6)}\]is _______
A)
\[36\text{ }unit{{s}^{2}}\] done
clear
B)
\[30\text{ }unit{{s}^{2}}\] done
clear
C)
\[34\text{ }unit{{s}^{2}}\] done
clear
D)
Cannot be determined done
clear
E)
None of these done
clear
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question_answer 24)
If a straight line \[\mathbf{ax+by=c}\] cuts x and y-axis at the points P and Q, then the area of the triangle OPQ where O is the point of intersection of coordinate axes, is _________
A)
\[\frac{{{a}^{2}}}{2bc}\] done
clear
B)
\[\frac{{{c}^{2}}}{2ab}\] done
clear
C)
\[\frac{2ac}{{{b}^{2}}}\] done
clear
D)
\[\frac{2ac}{{{c}^{2}}}\] done
clear
E)
None of these done
clear
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question_answer 25)
In a group of cows and hens m the total number of legs is 12 more than twice the total number of heads. The number cows is __________
A)
2 done
clear
B)
4 done
clear
C)
6 done
clear
D)
Cannot be determined done
clear
E)
None of these done
clear
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question_answer 26)
In a fraction, if numerator is increased by 2 and denominator is increased by 3, it becomes \[\frac{\mathbf{3}}{\mathbf{4}}\] and if numerator is decreased by 3 and denominator is decreased by 6, it becomes\[\frac{\mathbf{4}}{\mathbf{3}}\]. Find the sum of the numerator and denominator.
A)
12 done
clear
B)
15 done
clear
C)
19 done
clear
D)
16 done
clear
E)
None of these done
clear
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question_answer 27)
Any solution of the linear equation \[\mathbf{-7x+0}\mathbf{.y-14=0}\]in two variables is of the form ________
A)
\[(-\,2, 0)\] done
clear
B)
\[(-\,2, n)\] done
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C)
\[(0, -2)\] done
clear
D)
\[(n, -2)\] done
clear
E)
None of these done
clear
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question_answer 28)
The equation \[\mathbf{5x-3y-2=0}\]has a unique solution, if x, y are _________
A)
Rational numbers done
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B)
Real numbers done
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C)
Integers done
clear
D)
Natural numbers done
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E)
None of these done
clear
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question_answer 29)
The graph of \[\frac{\mathbf{5x}}{\mathbf{2}}\mathbf{=7+}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{x-15}\] is a line _________
A)
parallel to x-axis at a distance of 4 units from the origin. done
clear
B)
parallel to y-axis at a distance of 8 units from the origin. done
clear
C)
making an intercept 4 on the y-axis. done
clear
D)
making an intercept 4 on the y-axis done
clear
E)
None of these done
clear
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question_answer 30)
The solution of a linear equation does not remain same when
A)
we add same number in both sides of the equation. done
clear
B)
parallel to y-axis at a distance of 8 units from the origin. done
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C)
we multiply both sides of the equation by zero. done
clear
D)
we divide both sides of the equation by same non zero number. done
clear
E)
None of these done
clear
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question_answer 31)
\[\mathbf{x=-5}\] and \[\mathbf{y=1}\] is a solution of the linear equation _______
A)
\[x-2y= 7\] done
clear
B)
\[3y-x=-\,8\] done
clear
C)
\[6y-x=11\] done
clear
D)
\[3x=15y\] done
clear
E)
None of these done
clear
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question_answer 32)
Which among the following is not a solution of the equation \[\mathbf{-7x+2y=-}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{x-}\frac{\mathbf{3}}{\mathbf{2}}\mathbf{y+5}\]
A)
\[(3, 7)\] done
clear
B)
\[(-\,4, -6)\] done
clear
C)
\[(9, 18)\] done
clear
D)
\[(4, \frac{62}{7})\] done
clear
E)
None of these done
clear
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question_answer 33)
The coordinates given in following table represents the solution of the equation _______.
A)
\[3y=4x+2\] done
clear
B)
\[3y+4x=1\] done
clear
C)
\[4x-3y=1\] done
clear
D)
\[4x-8y=9\] done
clear
E)
None of these done
clear
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question_answer 34)
If the point \[\mathbf{(-3, 8)}\] lies on the line \[\mathbf{3y-7x+a=0}\], then the value of \[\frac{\mathbf{3a}}{\mathbf{5}}\] is _________ .
A)
27 done
clear
B)
\[-\]27 done
clear
C)
18 done
clear
D)
\[-\]18 done
clear
E)
None of these done
clear
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question_answer 35)
For what value of k, the linear equation \[\mathbf{3x-ky=9}\] has equal values of x and y for its solution.
A)
\[\frac{9-3x}{2}\] done
clear
B)
\[\frac{3x+9}{x}, x\ne 0\] done
clear
C)
0 done
clear
D)
\[\frac{3x-9}{x}, x\ne 0\] done
clear
E)
None of these done
clear
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question_answer 36)
The point on the graph of the linear equation \[\mathbf{6x+5y=18}\], whose ordinate is \[\mathbf{3}\frac{\mathbf{1}}{\mathbf{2}}\] times its abscissa, is _______
A)
\[\left( \frac{16}{19},\frac{56}{19} \right)\] done
clear
B)
\[\left( \frac{36}{19},\frac{126}{19} \right)\] done
clear
C)
\[\left( \frac{36}{47},\frac{126}{47} \right)\] done
clear
D)
\[\left( \frac{18}{47},\frac{63}{47} \right)\] done
clear
E)
None of these done
clear
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question_answer 37)
The point, at which the graph of the linear equation \[\mathbf{x-y=9}\]meets a line which is parallel to the y-axis, at a distance of 3 units from the origin and in the positive direction of x-axis, is _______
A)
\[(3, 0)\] done
clear
B)
\[(-\,3, 6)\] done
clear
C)
\[(6, -3)\] done
clear
D)
\[(3, -6)\] done
clear
E)
None of these done
clear
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question_answer 38)
The point on the graph of the equation \[\mathbf{3x+4y=15}\] whose abscissa is \[\frac{\mathbf{3}}{\mathbf{4}}\] times its ordinate, is
A)
\[\left( \frac{12}{5},\frac{9}{5} \right)\] done
clear
B)
\[\left( \frac{9}{5},\frac{12}{5} \right)\] done
clear
C)
\[\left( \frac{12}{5},\frac{9}{20} \right)\] done
clear
D)
\[\left( \frac{9}{20},\frac{15}{5} \right)\] done
clear
E)
None of these done
clear
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question_answer 39)
Directions: The temperature of a liquid can be measured in kelvin units as\[\mathbf{x{}^\circ K}\] or in Fahrenheit units Units as\[\mathbf{y{}^\circ F}\], the relation between the two system of measurement of temperature is given by the linear equation\[\mathbf{y-32=}\frac{\mathbf{9}}{\mathbf{2}}\mathbf{(x-273)}\]. Based on this information, answer the following questions:
Find the temperature of the liquid in Fahrenheit if the temperature of the liquid is \[\mathbf{333{}^\circ K}\]
A)
\[-\,140{}^\circ F\] done
clear
B)
\[140{}^\circ F\] done
clear
C)
\[158{}^\circ F\] done
clear
D)
\[-\,158{}^\circ F\] done
clear
E)
None of these done
clear
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question_answer 40)
Directions: The temperature of a liquid can be measured in kelvin units as\[\mathbf{x{}^\circ K}\] or in Fahrenheit units Units as\[\mathbf{y{}^\circ F}\], the relation between the two system of measurement of temperature is given by the linear equation\[\mathbf{y-32=}\frac{\mathbf{9}}{\mathbf{2}}\mathbf{(x-273)}\]. Based on this information, answer the following questions:
If at a value, the temperature in Fahrenheit equals to temperature in kelvin then this value is ________
A)
374.25 done
clear
B)
574.25 done
clear
C)
385 done
clear
D)
485 done
clear
E)
None of these done
clear
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