Express \[0.5\overline{7}\] as a fraction in simplest form.
A)
\[\frac{1}{45}\]
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B)
\[\frac{13}{45}\]
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C)
\[\frac{26}{90}\]
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D)
\[\frac{26}{45}\]
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E)
None of these
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If both a and b are rational numbers, find the value of a and b in equation: \[\left( \frac{3+\sqrt{5}}{3-\sqrt{5}}=a+b\sqrt{5} \right)\]
A)
\[a=\frac{2}{7}\] and \[b=\frac{3}{2}\]
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B)
\[a=\frac{7}{2}\] and \[b=\frac{2}{3}\]
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C)
\[a=\frac{7}{2}\] and \[b=\frac{3}{2}\]
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D)
\[a=\frac{3}{7}\] and \[b=\frac{7}{3}\]
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E)
None of these
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Evaluate: \[\sqrt{\frac{81}{64}\sqrt{\frac{81}{64}\sqrt{\frac{81}{64}.........to\,\infty }}}\]
A)
\[\frac{9}{8}\]
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B)
\[\frac{81}{64}\]
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C)
\[\frac{3}{2\sqrt{2}}\]
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D)
\[\frac{2}{3}\]
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E)
None of these
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If Gatita can type one page in?t? minutes then in 10 minutes how many pages can she type?
A)
\[\frac{t}{10}\]
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B)
\[\frac{10}{t}\]
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C)
t+10
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D)
t-10
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E)
None of these
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Two circles of radii 5 cm and 3 cm intersect each other at two points and the distance between their centers is 4 cm. Find the length of the common chord.
A)
7cm
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B)
6cm
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C)
4cm
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D)
11cm
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E)
None of these
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A cone, a hemisphere and a cylinder stand on equal base and have the same height. The ratio of their volumes is:
A)
1:2:3
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B)
2:1:3
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C)
2:3:1
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D)
3 : 2 :1
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E)
None of these
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Factorize. \[\mathbf{a}-b-{{\mathbf{a}}^{\mathbf{2}}}+{{b}^{\mathbf{2}}}\]
A)
\[\left( a+b \right)\left( 1-a-b \right)\]
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B)
\[\left( a+b \right)\left( 1+a+b \right)\]
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C)
\[\left( a-b \right)\left( 1+a+b \right)\]
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D)
\[\left( a-b \right)\left( 1-a-b \right)\]
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E)
None of these
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Find out the values of x and y in the following figure where \[\angle A=\left( 2x+4 \right){}^\circ ,\,\,\angle B=\left( x+10 \right){}^\circ \] \[\angle C=\left( 4y-4 \right){}^\circ \text{ }and\text{ }\angle D=\left( 5y+5 \right){}^\circ \]
A)
\[x=25{}^\circ and\,y=40{}^\circ \]
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B)
\[x=40{}^\circ \text{ }and\text{ }y=25{}^\circ \]
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C)
\[x=14{}^\circ \text{ }and\text{ }y=41{}^\circ \]
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D)
\[x=41{}^\circ \text{ }and\text{ }y=14{}^\circ \]
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E)
None of these
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A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
A)
180m
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B)
342m
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C)
150m
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D)
120m
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E)
None of these
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When a scooter is sold for Rs. 18700, the owner loses 15 %. At what price must that scooter be sold in order to gain 15 %?
A)
Rs. 22,500
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B)
Rs. 21,000
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C)
Rs. 25,800
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D)
Rs. 25,300
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E)
None of these
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A man has some ducks and dogs. If the number of their heads taken together be 48 and that of their feet be 140, then the number of ducks will be:
A)
23
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B)
26
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C)
24
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D)
22
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E)
None of these
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Which one of the following numbers is neither prime nor composite?
A)
4
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B)
3
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C)
2
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D)
1
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E)
None of these
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The probability that it will rain today is 0.84. What is the probability that it will not rain today?
A)
0.48
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B)
0.61
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C)
0.16
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D)
0.84
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E)
None of these
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A bag contains 8 red, 2 black and 5 white balls. One ball is drawn at random, what is the probability that the ball drawn is not black?
A)
\[\frac{8}{15}\]
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B)
\[\frac{1}{3}\]
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C)
\[\frac{2}{15}\]
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D)
\[\frac{13}{15}\]
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E)
None of these
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If\[{{\mathbf{2}}^{\mathbf{5}}}+{{\mathbf{2}}^{\mathbf{5}}}+{{\mathbf{2}}^{5}}+{{\mathbf{2}}^{\mathbf{5}}}={{\mathbf{2}}^{\mathbf{X}}}\], then find the value of x
A)
20
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B)
5
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C)
7
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D)
9
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E)
None of these
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If \[\mathbf{a}+\mathbf{b}=\mathbf{7}\]and\[\mathbf{ab}=\mathbf{12}\], then find the value of \[\left( {{\mathbf{a}}^{\mathbf{2}}}-\mathbf{ab}+{{\mathbf{b}}^{\mathbf{2}}} \right)\]
A)
31
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B)
13
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C)
15
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D)
21
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E)
None of these
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Which one of the following is correct?
A)
Mode = 2 Median ? 3 Mean
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B)
Mode = 3 Median + 2 mean
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C)
Mode =3 Median ? 2 Mean
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D)
Mode = 2 Median ? 2 Mean
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E)
None of these
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If mean of \[\left( \mathbf{x}+\mathbf{2} \right),\left( \mathbf{2x}+\mathbf{3} \right),\left( \mathbf{3x}+\mathbf{4} \right)\] and\[\left( \mathbf{4x}+\mathbf{5} \right)\]is \[\mathbf{x}+\mathbf{2}\], find x.
A)
1
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B)
-1
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C)
2
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D)
0
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E)
None of these
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The mean of 8 numbers is 25. If 5 is subtracted from each number, what will be the new mean?
A)
40
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B)
15
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C)
18
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D)
20
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E)
None of these
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The sides BA and DC of quadrilateral ABCD are produced as shown in the given figure.
then which of the following is correct?
A)
\[x+y>a+b\]
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B)
\[~x+y<a+b\]
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C)
\[x+y\ne a+b\]
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D)
\[x+y=a+b\]
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E)
None of these
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Find the measurement of the supplement angle of\[\mathbf{87}{}^\circ \text{ }\mathbf{28}'\,\,\mathbf{43}'\].
A)
\[91{}^\circ 41'17'\]
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B)
\[90{}^\circ 42'18'\]
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C)
\[92{}^\circ 31'17'\]
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D)
\[81{}^\circ 41'18'\]
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E)
None of these
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If \[\frac{x}{y}=\frac{4}{5}\], then find \[\frac{8}{9}+\frac{y-x}{y+x}\].
A)
- 1
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B)
1
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C)
4
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D)
0
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E)
None of these
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In the given \[\Delta \mathbf{DEF},\text{ }\mathbf{GH}\parallel \mathbf{EF}\]if,\[\frac{DG}{DE}=\frac{8}{11}\] and \[\mathbf{DF}=\mathbf{19}\text{ }\mathbf{cm}\]then find the value of HF
A)
8cm
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B)
11cm
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C)
9cm
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D)
7 cm
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E)
None of these
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