If \[x=\frac{1}{2+\sqrt{3}},\] find the value of \[{{x}^{3}}-{{x}^{2}}-11x+3\]
A)
0
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B)
3
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C)
x
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D)
x+3
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If \[x=3\sqrt{3}+\sqrt{26}\] find the value of \[\frac{1}{2}\left( x+\frac{1}{x} \right)\]
A)
\[\frac{1}{2}\]
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B)
\[\sqrt{3}\]
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C)
3
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D)
\[3\sqrt{3}\]
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If \[x=2+{{2}^{1/3}}+{{2}^{2/3}}\] find \[{{x}^{3}}-6{{x}^{2}}+6x-2.\]
A)
0
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B)
1
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C)
2
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D)
6
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Express \[1.272727.....=1.\overline{27}\] in the form \[\frac{p}{q},\]where p and q are integers and \[q\ne 0.\]
A)
\[\frac{1}{27}\]
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B)
\[\frac{1}{11}\]
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C)
\[\frac{14}{11}\]
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D)
\[\frac{14}{27}\]
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The value of x, when \[{{2}^{x+4}}{{.3}^{x+1}}=288.\]
A)
1
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B)
\[-1\]
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C)
0
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D)
None
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When simplified the product \[\left( 1+\frac{1}{2} \right)\left( 1+\frac{1}{3} \right)\left( 1+\frac{1}{4} \right).....\left( 1+\frac{1}{n} \right)\] becomes
A)
\[n\]
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B)
\[\frac{n-1}{2}\]
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C)
\[\frac{n+1}{2}\]
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D)
\[\frac{n}{2}\]
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If \[a=2+\sqrt{3}\] and & \[b=2-\sqrt{3}\] then \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}\] is equal to
A)
14
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B)
\[-14\]
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C)
\[8\sqrt{3}\]
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D)
\[-8\sqrt{3}\]
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Rationalizing factor of \[(2+\sqrt{3})=\]
A)
\[2-\sqrt{3}\]
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B)
\[\sqrt{3}\]
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C)
\[2+\sqrt{3}\]
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D)
\[3+\sqrt{3}\]
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Which of the following is equal to x?
A)
\[{{x}^{\frac{12}{7}}}-{{x}^{\frac{5}{7}}}\]
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B)
\[\sqrt[12]{{{\left( {{x}^{4}} \right)}^{\frac{1}{3}}}}\]
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C)
\[{{\left( \sqrt{{{x}^{3}}} \right)}^{\frac{2}{3}}}\]
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D)
\[{{x}^{\frac{12}{19}}}+{{x}^{\frac{7}{19}}}\]
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If \[\frac{1}{x+1}+\frac{1}{x+4}=0\]then x=
A)
\[2\frac{1}{2}\]
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B)
\[-2\frac{1}{2}\]
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C)
3
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D)
\[-\,3\]
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If \[\frac{x}{pq}+\frac{x}{qr}+\frac{x}{pr}=p+q+r,\] then x=
A)
\[pqr\]
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B)
\[\frac{pq}{r}\]
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C)
\[\frac{p}{qr}\]
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D)
\[\frac{q}{pr}\]
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The equation \[\frac{12x+1}{4}=\frac{13x-1}{5}+3\] is true for
A)
\[x=\frac{1}{8}\]
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B)
\[x=2\]
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C)
\[x=5/8\]
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D)
\[x=\frac{3}{4}\]
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If \[\frac{a}{2}+b=0.8\] and \[\frac{7}{a+\frac{b}{2}}=10,\] then (a, b) are
A)
(0.2, 0.4)
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B)
(0.3, 0.5)
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C)
(0.4, 0.6)
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D)
(0.4, 0.5)
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A bag contains 50P, 25P and 10P coins in the ratio 2 : 3 : 4 amounting to Rs. 129. Find the number of coins of each type
A)
120, 180, 240
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B)
180, 150, 200
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C)
200, 180, 120
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D)
180, 200, 140
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Monthly incomes of two persons are in the ratio 4 : 5 and their monthly expenses are in the ratio 7 : 9. If each saves Rs. 50 per month, their monthly incomes (in rupees) are :
A)
(500, 400)
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B)
(300, 600)
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C)
(400, 500)
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D)
none of these
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If \[6x+3y=7xy\] and \[3x+9y=11xy,\] then the value of x and y are
A)
\[\left( 1,\frac{3}{2} \right)\]
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B)
\[\left( 2,\frac{3}{2} \right)\]
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C)
\[\left( \frac{3}{2},1 \right)\]
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D)
\[\left( \frac{3}{2},2 \right)\]
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The angle A of a triangle ABC is equal to the sum of the two other angles. Also the ratio of the angle B to angle C is 4 : 5. The three angles are
A)
\[90{}^\circ ,\]\[40{}^\circ ,\]\[50{}^\circ \]
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B)
\[90{}^\circ ,\]\[55{}^\circ ,\]\[35{}^\circ \]
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C)
\[90{}^\circ ,\]\[60{}^\circ ,\]\[30{}^\circ \]
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D)
None of these
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If a is a natural number then \[{{a}^{2}}+\frac{1}{{{a}^{2}}}\] is always greater than or equal to
A)
5
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B)
4
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C)
3
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D)
2
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If \[\sqrt{0.04\times 0.4\times a}=0.4\times 0.04\times \sqrt{b},\] then value of \[\frac{b}{a}\] is
A)
0.016
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B)
\[\frac{125}{2}\]
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C)
0.16
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D)
None of these.
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If 'x' is any natural number, then \[{{x}^{3}}-\frac{1}{{{x}^{3}}^{{}}}\] will always be greater than or equal to
A)
\[x+\frac{1}{x}\]
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B)
\[3\left( x-\frac{1}{x} \right)\]
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C)
\[3\left( x+\frac{1}{x} \right)\]
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D)
\[\left( {{x}^{3}}+\frac{1}{{{x}^{3}}} \right)\]
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