What is the number nearest to 110000 but greater than 100000 which is exactly divisible by each of 8, 15 and 21.
A)
100100
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B)
100800
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C)
110400
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D)
102400
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E)
None of these
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What must be subtracted from \[8{{x}^{4}}+14{{x}^{3}}-\]\[2x+7x-8\]so that the resulting polynomial is exactly divisible by \[4{{x}^{2}}+3x-2.\]
A)
\[10x-14\]
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B)
\[14x-10~\]
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C)
\[~2x+3~\]
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D)
\[4x+6\]
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E)
None of these
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The difference between two numbers is 26 and one number is three times the other. Find them.
A)
40 and 14
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B)
42 and 16
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C)
39 and 13
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D)
36 and 20
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E)
None of these
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The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is\[2\frac{16}{21}\], find the fraction.
A)
\[\frac{2}{5}\]
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B)
\[\frac{3}{5}\]
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C)
\[\frac{3}{7}\]
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D)
\[\frac{10}{7}\]
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E)
None of these
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Sum of first n terms of an A.P. is\[\frac{3{{n}^{2}}}{2}+\frac{5n}{2}\]. Find its 25th term.
A)
72
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B)
76
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C)
80
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D)
82
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E)
None of these
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A hollow container in the shape of a hemisphere is surmounted by a cylinder having radius 7 cm and height 6 cm. Find the volume of water it can hold.
A)
\[1594\,\,c{{m}^{3}}\]
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B)
\[1424\,\,c{{m}^{3}}\]
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C)
\[1642.6\,\,c{{m}^{3}}\]
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D)
\[1398.6\,\,c{{m}^{3}}\]
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E)
None of these
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Two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 25. Find the ratio of their corresponding heights.
A)
5 : 4
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B)
4 : 5
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C)
2 : 3
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D)
16 : 25
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E)
None of these
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P and Q are the points on the minor arc of a circle with centre O. If T is a point on the major arc of the circle and\[\angle AOP={{75}^{o}}\], then find the value of\[\angle PTQ\].
A)
\[{{67.5}^{o}}\]
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B)
\[~{{37.5}^{o}}\]
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C)
\[~{{47.5}^{o}}\]
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D)
\[~{{85}^{o}}\]
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E)
None of these
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\[\frac{\sin \alpha }{1-\cot \alpha }+\frac{\cos \alpha }{1-\tan \alpha }\]in its simplest form is equal to:
A)
0
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B)
1
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C)
\[\sin \alpha +\cos \alpha \]
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D)
\[\sin \alpha -\cos \alpha \]
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E)
None of these
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The distance of point \[(x\sin \theta ,\,\,x\cos \theta )\]from the origin is:
A)
\[x\]
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B)
\[{{x}^{2}}\]
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C)
\[\sqrt{x}\]
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D)
\[{{x}^{3}}\]
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E)
None of these
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If the mean of the following distribution is 27, then find the value of p.
Class 0-10 10-20 20-30 30-40 40-50 Frequency 8 P 12 13 10
A)
6
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B)
7
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C)
5
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D)
2
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E)
None of these
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There are 10 tickets numbered from 1, 2, 3, ---, 10. One ticket is drawn at random, what is the probability that the number on the ticket is a prime number?
A)
\[\frac{1}{4}\]
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B)
\[\frac{9}{10}\]
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C)
\[\frac{2}{5}\]
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D)
\[\frac{7}{10}\]
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E)
None of these
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Solve the equations. \[\begin{array}{*{35}{l}} x+y=3 \\ 3x-2y=4 \\ \end{array}\]
A)
\[x=3,\text{ }y=1\]
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B)
\[x=1,\text{ }y=3\]
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C)
\[x=2,\text{ }y=1\]
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D)
\[~x=2,\text{ }y=2\]
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E)
None of these
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Solve the equations. \[\frac{x}{a}+\frac{y}{b}=2\] \[ax-by={{a}^{2}}-{{b}^{2}}\]
A)
\[x={{a}^{2}}\,\,,y={{b}^{2}}\]
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B)
\[x=-a,\,\,y=-b\]
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C)
\[x=2,\,\,y=-2\]
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D)
\[x=a,\,\,y=b\]
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E)
None of these
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Which term of the arithmetic progression 5, 15, 25-----will be 130 more than its 31st term?
A)
22
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B)
33
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C)
44
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D)
51
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E)
None of these
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If\[\tan \theta =\frac{a}{b}\], find the value of\[\frac{\cos \theta +\sin \theta }{\cos \theta -\sin \theta }\].
A)
\[\frac{{{a}^{2}}-{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}\]
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B)
\[\frac{a-b}{b-a}\]
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C)
\[\frac{b+a}{b-a}\]
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D)
\[\frac{b}{a-b}\]
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E)
None of these
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If radius of the circle given below is 7.5 cm. Find the area of the shaded region\[(use\pi =3.14)\].
A)
\[84.375\,\,c{{m}^{2}}\]
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B)
\[48.753\,\,c{{m}^{2}}\]
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C)
\[44.375\,\,c{{m}^{2}}\]
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D)
\[48.375\,\,c{{m}^{2}}\]
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E)
None of these
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If \[\sin \theta =\frac{a}{b}\], then \[\cos \theta \]is equal to
A)
\[\frac{a}{b}\]
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B)
\[\frac{b}{\sqrt{{{b}^{2}}-{{a}^{2}}}}\]
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C)
\[\frac{a}{\sqrt{{{b}^{2}}-{{a}^{2}}}}\]
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D)
\[\frac{\sqrt{{{b}^{2}}-{{a}^{2}}}}{b}\]
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E)
None of these
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Choose the correct option to replace the blank box.
A)
\[\frac{1+\sqrt{3}}{2}\]
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B)
\[\frac{1-\sqrt{3}}{2\sqrt{2}}\]
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C)
\[\frac{\sqrt{3}}{2\sqrt{2}}\]
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D)
\[\frac{2}{\sqrt{3}}\]
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E)
None of these
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If\[{{2}^{2x}}+{{2}^{x+1}}=4-{{2}^{x}}\], then find the value of\[x\].
A)
1
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B)
0
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C)
2
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D)
4
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E)
None of these
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\[\frac{{{\left[ \frac{1}{216} \right]}^{\frac{-2}{3}}}}{{{\left[ \frac{1}{27} \right]}^{\frac{-4}{3}\,\,}}}\]?
A)
\[\frac{2}{3}\]
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B)
\[\frac{1}{8}\]
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C)
\[\frac{3}{4}\]
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D)
\[\frac{4}{9}\]
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E)
None of these
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If\[\sqrt[2]{\sqrt[3]{Xx.000001}}=0.2\], then find the value of\[X\].
A)
4
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B)
16
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C)
32
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D)
64
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E)
None of these
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Find the value of x in the equation,\[{{x}^{2}}-(\sqrt{3}+1)x+\sqrt{3}=0\]
A)
\[-1,\,\,-\sqrt{3}\]
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B)
\[1,\,\,-\sqrt{3}\]
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C)
\[-1,\,\,\sqrt{3}\]
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D)
\[1,\,\,\sqrt{3}\]
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E)
None of these
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