A merchant has 120 litres of oi1 of one kind, 180 litres of another kind and 240 litres of third kind. He wants to sell the oil by filling the three kinds of oils in tins of equal capacity. The greatest capacity of such a tin is-
A)
50 litres
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B)
60 litres
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C)
55 litres
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D)
65 litres
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E)
None of these
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If \[\beta \], \[\gamma \]and \[\delta \]are the roots of s(t)=\[{{t}^{3}}-p{{t}^{2}}+qt-r\], then \[\frac{1}{\beta \gamma }+\frac{1}{\gamma \delta }+\frac{1}{\beta \delta }\]is equal to-
A)
\[\frac{r}{p}\]
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B)
\[\frac{p}{r}\]
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C)
\[\frac{-p}{r}\]
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D)
\[\frac{q}{r}\]
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E)
None of these
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A fraction becomes\[\frac{1}{3}\], if l is subtracted from both its numerator and denominator b. If 1 is added to numerator and denominator both it becomes\[\frac{1}{2}\], the fraction is:
A)
\[\frac{4}{7}\]
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B)
\[\frac{2}{7}\]
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C)
\[\frac{3}{7}\]
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D)
\[\frac{1}{7}\]
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E)
None of these
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The sum of ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Find son's present age.
A)
9 years
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B)
7 years
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C)
10 years
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D)
12 years
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E)
None of these
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If the \[{{3}^{rd}}\]and \[{{9}^{th}}\]term of an A.P. are 4 and \[-8\] respectively, then which term of this A.P. is zero?
A)
4
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B)
1
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C)
9
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D)
5
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E)
None of these
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Radius of two ends of a bucket are 8 cm and 20 cm. If its height is 16 cm, then find the volume of milk it can hold.
A)
\[10,459.43\,\,c{{m}^{3}}\]
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B)
\[10549.55\,\,c{{m}^{3}}\]
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C)
\[94134.8\,\,c{{m}^{3}}\]
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D)
\[1398.6\,\,c{{m}^{3}}\]
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E)
None of these
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The areas of two similar triangles are \[121\,\,c{{m}^{2}}\]and \[64\,\,c{{m}^{2}}\]respectively. If the median of the first triangle is 12.1cm, find the corresponding median of the other.
A)
8 cm
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B)
9.5 cm
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C)
8.8 cm
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D)
12.1 cm
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E)
None of these
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In the figure given below, if O is the centre of the circle, then find the value of\[\angle DAC\].
A)
\[{{85}^{o}}\]
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B)
\[{{40}^{o}}\]
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C)
\[{{50}^{o}}\]
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D)
\[{{80}^{o}}\]
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E)
None of these
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If \[a\cot q+\]\[b\cos ecq=p\] and \[b\cot q+\]\[a\cos ecq=q\], then \[{{p}^{2}}-{{q}^{2}}\]is equal to:
A)
\[{{a}^{2}}-{{b}^{2}}\]
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B)
\[{{b}^{2}}-{{a}^{2}}\]
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C)
\[{{a}^{2}}+{{b}^{2}}\]
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D)
\[b-a\]
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E)
None of these
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Four points \[A(4,-2),\text{ }B(-3,5),\text{ }C(4,-2)\]and D (k, 3k) are given in such a way that\[\frac{ar(\Delta DBC)}{ar(\Delta ABC)}=\frac{1}{2}\] The value of k is:
A)
\[\frac{8}{11}\]
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B)
\[\frac{11}{8}\]
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C)
\[\frac{7}{4}\]
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D)
\[\frac{4}{7}\]
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E)
None of these
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Find the mode of the data: 25, 16, 19, 48, 19, 20, 34, 15, 19, 20, 21, 24, 19, 16, 22, 16, 18, 20, 16, 19
A)
17
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B)
20
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C)
19
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D)
21
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E)
None of these
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A bag contains 8 red balls, 2 black balls and 5 white balls. One ball is drawn at random from the bag, what is the probability that the ball drawn is black?
A)
\[\frac{2}{15}\]
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B)
\[\frac{13}{15}\]
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C)
\[\frac{8}{15}\]
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D)
\[\frac{1}{3}\]
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E)
None of these
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If x=2 and x=3 are roots of the equation\[3{{x}^{2}}-2kx+2m=0\], find the value of K and m.
A)
\[m=\frac{15}{2}\ \ and\ \ k=9\]
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B)
\[m=\frac{7}{3}\ \ and\ \ k=\frac{15}{2}\]
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C)
\[m=9\ \ and\ \ k=\frac{15}{2}\]
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D)
\[m=7\ \ and\ \ k=3\]
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E)
None of these
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Find the value of x in the following equation\[\frac{2}{{{x}^{2}}}-\frac{5}{x}+2=0\]
A)
\[-2,\,\,\frac{1}{2}\]
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B)
\[-3,\,\,\frac{1}{3}\]
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C)
\[-3,\,-\,\frac{1}{3}\]
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D)
\[2,\,\,\frac{1}{2}\]
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E)
None of these
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If \[5\tan \theta =4\], then evolution \[\frac{5\sin \theta -3\cos \theta }{5\sin \theta +2\cos \theta }\]
A)
\[\frac{7}{6}\]
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B)
\[\frac{1}{6}\]
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C)
\[\frac{5}{6}\]
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D)
\[\frac{3}{4}\]
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E)
None of these
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Find the value of x in\[~\tan 3x=\sin {{45}^{o}}\cos {{45}^{o}}+\sin {{30}^{o}}\]
A)
\[{{5}^{o}}\]
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B)
\[{{10}^{o}}\]
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C)
\[{{15}^{o}}\]
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D)
\[{{25}^{o}}\]
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E)
None of these
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If \[\theta \] is an acute angle and\[\sin \theta =\cos \theta \], then find the value of \[2{{\tan }^{2}}\theta +{{\sin }^{2}}\theta -1\]
A)
\[\frac{7}{2}\]
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B)
\[\frac{2}{3}\]
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C)
\[\frac{2}{7}\]
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D)
\[\frac{3}{2}\]
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E)
None of these
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If \[\tan \theta =\frac{a}{b}\], then \[\frac{a\sin \theta +b\cos \theta }{a\sin \theta -b\cos \theta }\]is equal to
A)
\[\frac{{{a}^{2}}-{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}\]
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B)
\[\frac{a+b}{a-b}\]
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C)
\[\frac{{{a}^{2}}+{{b}^{2}}}{{{a}^{2}}-{{b}^{2}}}\]
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D)
\[\frac{a-b}{{{a}^{2}}-{{b}^{2}}}\]
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E)
None of these
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Find the value of \[6{{\tan }^{2}}\theta -\frac{6}{{{\cos }^{^{2}}}\theta }\].
A)
36
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B)
\[-6\]
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C)
\[-8\]
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D)
64
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E)
None of these
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The arithmetic mean of 1, 2, 3-----n is:
A)
\[\frac{n+1}{2}\]
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B)
\[\frac{n-1}{2}\]
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C)
\[\frac{n}{2}\]
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D)
\[\frac{n}{2}+1\]
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E)
None of these
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The mode of a frequency distribution can be determined graphically from
A)
frequency polygon
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B)
histogram
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C)
ogive
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D)
frequency curve
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E)
None of these
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The area of a largest triangle that can be inscribed in a semi-circle of radius r, is
A)
\[2{{r}^{3}}\]
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B)
\[2{{r}^{2}}\]
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C)
\[{{r}^{2}}\]
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D)
\[2r\]
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E)
None of these
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If the radius of a circle is diminished by 10%, then its area is diminished by
A)
10%
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B)
20%
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C)
19%
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D)
36%
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E)
None of these
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