Find the value of \[\frac{{{X}^{a(b-c)}}}{{{X}^{b(a-c)}}}\div {{\left( \frac{{{X}^{b}}}{{{X}^{a}}} \right)}^{c}}.\]
A)
0
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B)
1
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C)
3
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D)
\[\frac{1}{2}\]
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E)
None of these
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If a, m and n are positive integers, then \[{{\left\{ \sqrt[m]{\sqrt[n]{a}} \right\}}^{mn}}\]is equal to:
A)
am n
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B)
a
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C)
\[{{a}^{\frac{m}{n}}}\]
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D)
1
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E)
None of these
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\[\sqrt{6+\sqrt{6+\sqrt{6+----}}}\] to \[\infty \]is equal to:
A)
6
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B)
3
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C)
-3
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D)
2
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E)
None of these
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Which one of the following is equal to a?
A)
\[{{a}^{\frac{7}{5}}}-{{a}^{\frac{12}{7}}}\]
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B)
\[{{a}^{\frac{12}{7}}}+{{a}^{\frac{5}{7}}}\]
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C)
\[{{a}^{\frac{12}{7}}}\times {{a}^{\frac{7}{12}}}\]
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D)
\[{{\left( \sqrt{{{a}^{3}}} \right)}^{\frac{2}{3}}}\]
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E)
None of these
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If\[{{7}^{1+x}}+{{7}^{1-x}}=50\], then find the value of x.
A)
\[\pm 3\]
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B)
\[\pm 1\]
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C)
\[\pm 2\]
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D)
\[\pm 5\]
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E)
None of these
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The following table shows the blood groups of 40 students of a class.
Blood group A B O AB Number of students 13 7 14 6
One student of the class is chosen at random. What is the probability that the chosen student has blood group O?
A)
2.85
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B)
0.35
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C)
0.2
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D)
2.35
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E)
None of these
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Mean of 8 numbers is 25. If 5 is subtracted from each number, what will be the new mean?
A)
35
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B)
15
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C)
20
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D)
54
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E)
None of these
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Factories: \[{{\mathbf{x}}^{\mathbf{2}}}-\mathbf{2x}+\frac{7}{16}\].
A)
\[\left( 4x-7 \right)\left( 4x-1 \right)\]
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B)
\[\left( 4x+7 \right)\left( 4x+1 \right)\]
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C)
\[\frac{1}{16}\left( 4x-7 \right)\left( 4x+1 \right)\]
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D)
\[\frac{1}{16}\left( 4x-7 \right)\left( 4x-1 \right)\]
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E)
None of these
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In a\[\Delta \mathbf{ABC}\], if \[\mathbf{2}\angle \mathbf{A}=\mathbf{3}\angle \mathbf{B}=\mathbf{6}\angle C\] miscalculate the measure of \[\angle \mathbf{A}\].
A)
\[90{}^\circ \]
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B)
\[45{}^\circ \]
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C)
30°
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D)
\[60{}^\circ \]
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E)
None of these
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Find the measure of the complement of an angle of\[\mathbf{48}{}^\circ \text{ }\mathbf{36}'\text{ }\mathbf{24}''\].
A)
\[36{}^\circ 23'41''\]
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B)
\[41{}^\circ 36'23''\]
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C)
\[41{}^\circ \text{ }23'36''\]
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D)
\[23{}^\circ 4r36''\]
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E)
None of these
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By what number should \[{{\left( -\mathbf{15} \right)}^{-\mathbf{1}}}\] be divided so that the quotient may be \[{{\left( \frac{5}{9} \right)}^{-1}}\]?
A)
\[\frac{1}{27}\]
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B)
\[\frac{-1}{27}\]
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C)
\[\frac{1}{9}\]
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D)
\[\frac{-1}{9}\]
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E)
None of these
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Solve: \[\sqrt{8+\sqrt{773+\sqrt{116+\sqrt{9+\sqrt{250+\sqrt{36}}}}}}\].
A)
3
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B)
6
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C)
3
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D)
2
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E)
None of these
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Find the value of \[\sqrt{\frac{4}{1+{{x}^{p-q}}}+\frac{4}{1+{{x}^{q-p}}}}\].
A)
\[\pm 2\]
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B)
\[\pm 4\]
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C)
\[\pm 1\]
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D)
\[\pm 3\]
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E)
None of these
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Which one of the following relations is false?
A)
\[\frac{3{{\pi }^{c}}}{2}=270{}^\circ \]
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B)
\[\frac{7{{\pi }^{c}}}{4}=315{}^\circ \]
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C)
\[\frac{{{\pi }^{c}}}{3}=60{}^\circ \]
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D)
\[\frac{4{{\pi }^{c}}}{16}=90{}^\circ \]
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E)
None of these
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A tree grows yearly by\[\frac{1}{6}\]of its height. How much will it increase in 2 years if it is 12 m high today?
A)
\[\frac{3}{4}m\]
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B)
\[5\frac{7}{7}m\]
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C)
\[4\frac{1}{3}m\]
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D)
\[5\frac{12}{15}m\]
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E)
None of these
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If the number 117B49 is completely divisible by 7, then the smallest natural number in place of B will be:
A)
2
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B)
5
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C)
7
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D)
6
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E)
None of these
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The mean of 10 observations is 18.25. On rechecking it was found that 16 was misread as 21. Find the correct mean if it is replaced by 16.
A)
16.5
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B)
17.75
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C)
15.25
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D)
15.75
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E)
None of these
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Find the length of a chord which is at a distance of 8 cm from the centre of a circle of radius 17 cm.
A)
15cm
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B)
30cm
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C)
20cm
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D)
25cm
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E)
None of these
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The greatest number among \[{{3}^{30}},{{4}^{40}},\,{{5}^{30}},{{6}^{20}}\] is:
A)
440
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B)
530
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C)
620
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D)
350
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E)
None of these
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Find the remainder obtained when \[\mathbf{4}{{\mathbf{x}}^{\mathbf{4}}}-\mathbf{3}{{\mathbf{x}}^{\mathbf{3}}}-\mathbf{2}{{\mathbf{x}}^{\mathbf{2}}}+\mathbf{x}-\mathbf{7}\]is divided by\[~\mathbf{x}+\frac{2}{3}\].
A)
- 3
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B)
\[\frac{-57}{8}\]
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C)
\[\frac{-557}{81}\]
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D)
\[\frac{221}{7}\]
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E)
None of these
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If\[x=17+12\sqrt{2}\], then the value of\[{{x}^{\frac{1}{4}}}-{{x}^{\frac{-1}{4}}}\]is equal to:
A)
0
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B)
1
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C)
2
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D)
3
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E)
None of these
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If the mean of 5 observations\[\mathbf{x},\text{ }\mathbf{x}+2,\mathbf{x}+\mathbf{4},\text{ }\mathbf{x}+\mathbf{6}\]and\[\mathbf{x}+\mathbf{8}\]is 14, then find the value of x.
A)
8
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B)
9
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C)
15
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D)
12
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E)
None of these
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lf\[\mathbf{x}+\mathbf{y}=\mathbf{2}\],then find the value of\[{{\mathbf{x}}^{\mathbf{3}}}+\mathbf{6xy}+{{\mathbf{y}}^{\mathbf{3}}}-\mathbf{8}\].
A)
2
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B)
1
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C)
0
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D)
3
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E)
None of these
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