The HCF of two numbers is 16 and their product is 3072. Find their LCM.
A)
190
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B)
192
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C)
188
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D)
170
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E)
None of these
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If \[\alpha \] and \[\beta \] are the zeroes of the polynomial \[f\,\,\left( x \right)={{x}^{2}}-px+q,\] then find the value of \[{{\alpha }^{2}}+{{\beta }^{2}}\].
A)
\[{{p}^{2}}+q\]
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B)
\[{{p}^{2}}-2q\]
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C)
\[{{p}^{2}}+{{q}^{2}}\]
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D)
\[{{p}^{2}}-5q\]
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E)
None of these
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Solve: \[\begin{align} & 2x+3y=9 \\ & 3x+4y=5 \\ \end{align}\]
A)
\[x=21\,\,and\,\,y=12\]
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B)
\[x=28\,\,and\,\,y=21\]
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C)
\[x=-\,21\,\,and\,\,y=17\]
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D)
\[x=2\,\,and\,\,y=25\]
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E)
None of these
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Find the value of 'a' such that y = 2 is a root of the equation \[a{{y}^{2}}+2ay-3=0\]
A)
\[\frac{1}{4}\]
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B)
\[\frac{3}{8}\]
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C)
\[\frac{3}{4}\]
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D)
\[0\]
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E)
None of these
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How many terms are there in the sequence 3, 6, 9, 12, _______111?
A)
35 terms
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B)
37 terms
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C)
42 terms
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D)
40 terms
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E)
None of these
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In a given\[\Delta \,ABC,\] \[DE\parallel BC\] and \[\frac{AD}{DB}=\frac{3}{5}\] . If AC = 5.6 cm, then find AE.
A)
2.1 cm
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B)
2.4 cm
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C)
1.2 cm
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D)
3.1 cm
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E)
None of these
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Find the value of ?k? for which the points A (1, 2) B (3, k) and C (4, 5) are collinear.
A)
\[\frac{1}{2}\]
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B)
\[\frac{14}{3}\]
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C)
\[\frac{1}{3}\]
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D)
\[4\]
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E)
None of these
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If \[5\tan \theta =4,\] then find the value\[\frac{5\sin \theta -3\cos \theta }{5\sin \theta +2\cos \theta }\]
A)
\[\frac{1}{3}\]
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B)
\[\frac{1}{2}\]
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C)
\[\frac{1}{6}\]
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D)
\[\frac{2}{3}\]
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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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The length of tangent drawn from a point P to a circle of radius 8 cm is 15 cm. The distance of P form the centre of the circle is:
A)
17 cm
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B)
14 cm
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C)
13 cm
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D)
7 cm
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E)
None of these
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The radius of wheel is 25 cm. The number of revolutions it will make to travel a distance of 11km will be.
A)
2800
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B)
6250
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C)
7250
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D)
6300
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E)
None of these
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The radii of two spheres are in the ratio 1 : 2. Find the ratio of their surface areas.
A)
1 : 4
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B)
2 : 3
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C)
5 : 4
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D)
6 : 1
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E)
None of these
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If \[2x,\] \[x+21,\] \[5x+2\] are in AP. Find the value of x.
A)
5
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B)
8
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C)
6
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D)
10
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E)
None of these
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If the sum of the zeroes of the polynomials \[f\,\,\left( t \right)=k{{t}^{2}}+2t+3k\] is equal to their product, then find the value of k.
A)
\[\frac{2}{3}\]
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B)
\[\frac{-2}{3}\]
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C)
\[\frac{2}{5}\]
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D)
\[0\]
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E)
None of these
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Find k such that \[3x+y=1\] and \[\left( 2k-1 \right)x+\left( k-1 \right)y=2k+1\] has no solution.
A)
k = 3
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B)
k = 2
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C)
k = 4
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D)
k = 7
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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 length of the diagonals of a rhombus are 16 cm and 12 cm, then the length of the side of the rhombus is:
A)
9 cm
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B)
10 cm
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C)
8 cm
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D)
20 cm
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E)
None of these
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In the adjoining figure, AB is a tangent from A to the circle and BOC is a diametre. If \[\angle AOC=125{}^\circ ,\] then\[\angle BAO=?\]
A)
\[40{}^\circ \]
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B)
\[35{}^\circ \]
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C)
\[50{}^\circ \]
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D)
\[45{}^\circ \]
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E)
None of these
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Find the area of the triangle whose vertices are \[A\,\,\left( -\,5,-\,1 \right),\] \[B\,\,\left( 3,-\,5 \right)\] and \[C\,\,\left( 5,\text{ }3 \right)\].
A)
18 sq. units
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B)
24 sq. units
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C)
32 sq. units
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D)
36 sq. units
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E)
None of these
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A card is drawn from a well shuffled pack of 52 cards. The probability that the card is a black or a club is:
A)
\[\frac{1}{3}\]
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B)
\[\frac{1}{4}\]
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C)
\[\frac{1}{2}\]
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D)
\[\frac{3}{13}\]
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E)
None of these
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If 10th term of an A.P. is 52 and 16th term is 82. Find the 32nd term.
A)
160
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B)
175
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C)
162
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D)
169
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E)
None of these
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If 2 is a root of the equation \[{{x}^{2}}+bx+12=0\] and\[{{x}^{2}}+bx+k\] has equal roots, then k is equal to:
A)
8
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B)
16
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C)
\[-\,8\]
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D)
\[-\,16\]
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E)
None of these
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Sum of first n terms in 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 bag contains 5 black balls, 4 white balls and 3 red balls. If a ball is selected randomly, then the probability that it is a black or red ball is:
A)
\[\frac{1}{3}\]
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B)
\[\frac{1}{4}\]
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C)
\[\frac{5}{12}\]
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D)
\[\frac{2}{3}\]
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E)
None of these
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In the given figure AD = 4 cm, BD = 3 cm and CB = 12 cm. Find \[\cot \theta \].
A)
\[\frac{5}{12}\]
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B)
\[\frac{12}{5}\]
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C)
\[\frac{11}{5}\]
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D)
\[\frac{4}{3}\]
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E)
None of these
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If \[\cos \theta =\frac{1}{\sqrt{2}},\] then \[\frac{\sin \theta \cos \theta +{{\sin }^{2}}\theta +\cos \theta }{\sin \theta \cos \theta +{{\cos }^{2}}\theta -\cos \theta }\] is equal to:
A)
\[1\]
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B)
\[-1\]
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C)
\[\sqrt{2}\]
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D)
\[\frac{\sqrt{2}+1}{\sqrt{2}-1}\]
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E)
None of these
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In the given figure, AB and CD are two common tangents to the two touching circles. If DC = 4 cm, than find AB.
A)
6 cm
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B)
8 cm
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C)
12 cm
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D)
4 cm
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E)
None of these
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Find the probability of that a number at random from the numbers 1, 2, 3, _____, 35 is a multiple of 3 or 5.
A)
\[\frac{36}{35}\]
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B)
\[\frac{26}{35}\]
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C)
\[\frac{16}{35}\]
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D)
\[\frac{6}{35}\]
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E)
None of these
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If \[\alpha \] and \[\beta \] are the zeroes of the polynomial\[f(x)=a{{x}^{2}}+bx+c\], then what is the value of\[\frac{1}{\alpha }+\frac{1}{\beta }-2\alpha \beta \] ?
A)
\[\frac{-b}{c}+a\]
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B)
\[\frac{bc}{a}+3a\]
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C)
\[-\left( \frac{b}{c}+\frac{2c}{a} \right)\]
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D)
\[\frac{-c}{a}\]
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E)
None of these
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A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of \[30{}^\circ \] with the ground. The distance between the foot of the tree to the point where the top touches the ground is 8 m. What is the height of the tree?
A)
\[8\,\sqrt{3}\,m\]
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B)
\[2\,\sqrt{5}\,m\]
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C)
\[5\,\sqrt{2}\,m\]
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D)
\[3\,\sqrt{2}\,m\]
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E)
None of these
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Find the ratio in which the line joining A (2, 3) and \[\left( -\,4,\,\,6 \right)\] is divided by x-axis.
A)
1 : 2 internally
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B)
1 : 2 externally
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C)
2 : 3 internally
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D)
2 : 5 externally
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E)
None of these
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The score of 10 students of a class test is given as 44, 54, 46, 63, 55, 42, 34, 48, 70, 38. Calculate the median.
A)
48
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B)
46
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C)
47
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D)
49
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E)
None of these
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The perimetre of two similar triangles are 25 cm and 15 cm respectively. If one side of first triangle is 9 cm, find the corresponding side of the second triangle.
A)
9 cm
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B)
5.4 cm
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C)
7.5 cm
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D)
5.5 cm
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E)
None of these
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Three metallic cubes whose edges 3 cm, 4 cm and 5 cm respectively are melted and recast to form a single large cube. Find the surface area of the resulting cube.
A)
\[210\,\,c{{m}^{2}}\]
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B)
\[216\,\,c{{m}^{2}}\]
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C)
\[214\,\,c{{m}^{2}}\]
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D)
\[343\,\,c{{m}^{2}}\]
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E)
None of these
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A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.
A)
\[\frac{1}{2}\]
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B)
\[\frac{2}{3}\]
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C)
\[\frac{2}{1}\]
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D)
\[\frac{1}{3}\]
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E)
None of these
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If A (4, 2), B (a, 0), C (6, b) and D (2, 6) are the vertices of a parallelogram, then find the values of a and b.
A)
\[a=3,\,\,b=-3\]
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B)
\[a=3,\,\,b=5\]
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C)
\[a=1,\,\,b=-3\]
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D)
\[a=8,\,\,b=4\]
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E)
None of these
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Find the area of the sector of a circle with radius 7 cm and of angle\[108{}^\circ \].
A)
\[46.2\,\,c{{m}^{2}}\]
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B)
\[45.2\,\,c{{m}^{2}}\]
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C)
\[43.2\,\,c{{m}^{2}}\]
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D)
\[44.2\,\,c{{m}^{2}}\]
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E)
None of these
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A man has some hens and cows. If the number of heads be 48 and number of feet equals 140, the number of hens will be:
A)
24
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B)
26
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C)
22
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D)
25
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E)
None of these
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The system of equations \[x+2y=3\] and \[2x+4y=3\] has
A)
Exactly two solutions
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B)
No solution
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C)
Infinitely many solutions
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D)
A unique solution
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E)
None of these
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The sum of two numbers is 16 and the sum their reciprocals is\[\frac{1}{3}\]. Find the numbers.
A)
6, 10
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B)
4, 12
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C)
5, 11
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D)
8, 8
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E)
None of these
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