The sum of the successors of two numbers is 42 and the difference of their predecessors is 12. Find the numbers.
A)
62 and 41
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B)
26 and 14
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C)
54 and 30
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D)
45 and 30
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E)
None of these
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A two-digit number is formed by either subtracting 17 from nine times the sum of the digits or by adding 21 to 13 times the difference of the digits. Find the number.
A)
37
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B)
73
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C)
71
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D)
Cannot be determined
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E)
None of these
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Find the three consecutive terms in A. P., whose sum is 36 and the product is 960.
A)
4, 12 and 20
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B)
20, 12 and 4
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C)
6, 9 and 15
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D)
Both A and B
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E)
None of these
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If\[{{\mathbf{x}}^{-\mathbf{2}}}=\mathbf{64}\], then find the value of\[{{\mathbf{x}}^{\mathbf{3}}}+{{\mathbf{x}}^{0}}\].
A)
\[\frac{3}{2}\]
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B)
\[\frac{2}{3}\]
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C)
3
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D)
2
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E)
None of these
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Find the value of x, in\[\frac{{{5}^{x+2}}-6\times {{5}^{x+1}}}{13\times {{5}^{x}}-2\times {{5}^{x+1}}}\]
A)
\[\frac{3}{5}\]
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B)
\[-\frac{5}{3}\]
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C)
\[\frac{5}{3}\]
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D)
\[\frac{5}{2}\]
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E)
None of these
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If\[sin\,\theta =\frac{b}{a}\], then find \[\sqrt{\frac{a-b}{a+b}}+\sqrt{\frac{a+b}{a-b}}\]
A)
0
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B)
1
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C)
\[cos\theta \]
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D)
\[\frac{1}{cos\theta }\]
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E)
None of these
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If \[\mathbf{tanA}=\mathbf{n}\,\mathbf{tanB}\]and\[\mathbf{sin}\text{ }\mathbf{A}=\mathbf{n}\text{ }\mathbf{sinB}\], then find the value of\[\mathbf{co}{{\mathbf{s}}^{\mathbf{2}}}\mathbf{A}\].
A)
\[\frac{{{m}^{2}}+1}{{{n}^{2}}+1}\]
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B)
\[\frac{{{m}^{2}}+1}{{{n}^{2}}-1}\]
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C)
\[\frac{{{m}^{2}}-1}{{{n}^{2}}+1}\]
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D)
\[\frac{{{m}^{2}}-1}{{{n}^{2}}-1}\]
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E)
None of these
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If\[\theta \]is an acute angle and\[\mathbf{tan}\theta +\mathbf{cot}\theta =\mathbf{2}\], find the value of\[\mathbf{ta}{{\mathbf{n}}^{\mathbf{7}}}\theta +\mathbf{co}{{\mathbf{t}}^{\mathbf{7}}}\theta \].
A)
5
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B)
2
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C)
4
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D)
1
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E)
None of these
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If the mean of 6 observations\[\mathbf{x},\mathbf{x}+\mathbf{3},\mathbf{x}+\mathbf{6},\mathbf{x}+\mathbf{9},\mathbf{x}+\mathbf{12},\mathbf{x}+\mathbf{15}\] is 18, find the mean of first 4 observations.
A)
25
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B)
18
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C)
15
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D)
36
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E)
None of these
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If\[{{\mathbf{2}}^{x+\mathbf{1}}}+{{\mathbf{2}}^{\mathbf{2}x}}=\mathbf{4}-{{\mathbf{2}}^{x}}\], then find the value of\[\mathbf{3x}\].
A)
0
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B)
1
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C)
3
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D)
4
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E)
None of these
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Find the area of the shaded region, given that the radius of each circle is equal to 5 cm.
A)
\[\left( 400-50\pi \right)c{{m}^{2}}\]
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B)
\[\left( 360-100\pi \right)c{{m}^{2}}\]
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C)
\[\left( 400-100\pi \right)c{{m}^{2}}\]
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D)
\[\left( 100-50\pi \right)c{{m}^{2}}\]
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E)
None of these
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lf\[\mathbf{tan}\theta =\frac{a}{b},\], find the value of \[\frac{\cos \theta +\sin \theta }{\cos \theta -\sin \theta }\]
A)
\[\frac{a-b}{b-a}\]
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B)
\[\frac{b+a}{b-a}\]
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C)
\[\frac{{{a}^{2}}-{{b}^{2}}}{{{a}^{2}}-{{b}^{2}}}\]
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D)
\[\frac{b}{a-b}\]
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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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Find the value of x in the given equation. \[~\mathbf{tan}\,\mathbf{3x}=\mathbf{sin}\,\mathbf{45}{}^\circ \times \mathbf{cos45}{}^\circ +\mathbf{sin30}{}^\circ \]
A)
\[15{}^\circ \]
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B)
\[10{}^\circ \]
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C)
\[5{}^\circ \]
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D)
\[25{}^\circ \]
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E)
None of these
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If the radius of a circle is reduced by 20%, then its area is reduced by:
A)
20%
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B)
36%
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C)
19%
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D)
15%
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E)
None of these
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A bag contains 8 red balls, 2 black balls and 3 white balls. One ball is drawn at random from the bag what is the probability the ball drawn is white?
A)
\[\frac{2}{13}\]
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B)
\[\frac{5}{13}\]
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C)
\[\frac{3}{13}\]
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D)
\[\frac{7}{13}\]
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E)
None of these
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If\[\alpha \]and\[\beta \]are the roots of the polynomial\[\mathbf{a}{{\mathbf{x}}^{\mathbf{2}}}+\mathbf{bx}+\mathbf{c}\], then find the value of\[{{\alpha }^{\mathbf{2}}}+{{\beta }^{\mathbf{2}}}\]
A)
\[\frac{{{b}^{2}}-2ac}{{{a}^{2}}}\]
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B)
\[\frac{b+2ac}{a}\]
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C)
\[\frac{b-2ac}{a}\]
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D)
\[\frac{{{b}^{2}}+2ac}{{{a}^{2}}}\]
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E)
None of these
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\[\mathbf{Tan5}{}^\circ \mathbf{x}\text{ }\mathbf{tan25}{}^\circ \mathbf{x}\text{ }\mathbf{tan30}{}^\circ \mathbf{x}\text{ }\mathbf{tan65}{}^\circ \mathbf{x}\text{ }\mathbf{tan85}{}^\circ \]=?
A)
\[\sqrt{3}\]
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B)
\[1\]
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C)
\[\frac{1}{\sqrt{3}}\]
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D)
\[\frac{1}{2}\]
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E)
None of these
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Find the sum of first 24 terms of the list of numbers whose nth term is given by\[{{\mathbf{a}}_{n}}=\mathbf{3}+\mathbf{2n}\].
A)
627
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B)
762
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C)
276
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D)
672
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E)
None of these
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In an AP if \[\mathbf{a}=-\mathbf{7}.\mathbf{2},\text{ }\mathbf{d}=\mathbf{3}.\mathbf{6}\]and\[{{a}_{n}}=7.2\], then find n.
A)
3
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B)
4
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C)
2
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D)
5
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E)
None of these
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If \[\mathbf{a}-\mathbf{b}=\mathbf{5}\]and\[{{\mathbf{a}}^{\mathbf{2}}}-{{\mathbf{b}}^{\mathbf{2}}}=\mathbf{65}\], then find the value of\[{{\mathbf{a}}^{\mathbf{2}}}+{{\mathbf{b}}^{\mathbf{2}}}\].
A)
10
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B)
47
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C)
85
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D)
95
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E)
None of these
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The area of a rectangle is\[{{\mathbf{x}}^{\mathbf{2}}}+\mathbf{12xy}+\mathbf{27}{{\mathbf{y}}^{\mathbf{2}}}\] and its length is\[\left( \mathbf{x}+\mathbf{9y} \right)\], then find the breadth of the rectangle.
A)
\[\left( x-3y \right)\]
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B)
\[\left( x+3y \right)\]
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C)
\[\left( 3-3y \right)\]
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D)
\[\left( 3+3y \right)\]
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E)
None of these
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If\[x=2+\sqrt{2}\]and\[~\mathbf{y}=\mathbf{2}\text{ }-\sqrt{\mathbf{2}}\], then find the value of\[\left( {{\mathbf{x}}^{\mathbf{2}}}+{{\mathbf{y}}^{\mathbf{2}}} \right)\].
A)
6
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B)
14
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C)
12
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D)
18
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E)
None of these
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