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\[f(x)={{x}^{2}}-px+q,\]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: \[\begin{matrix} 2x+3y=9 \\ 3x+4y=5 \\ \end{matrix}\]
A)
\[x=21\text{ }and\text{ }y=12\]
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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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The length of tangent drawn from a point P to a circle of radius 8 cm is 15 cm. The distance of P from 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 11 km 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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If \[2x,\] \[x+21,\] \[5x+2\] are in AP, then 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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Find k such that \[3x+y=1\] and \[(2k-\text{1})x+\left( k-\text{1} \right)y=2k+1\] 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 the numbers.
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 value of K, if K35624 is divisible by 11 is:
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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If x be a rational number and y be an irrational number, then:
A)
Both x + y and xy are necessarily irrational
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B)
Both x + y and xy are necessarily rational
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C)
xy is necessarily irrational, but x + y can be either rational or irrational
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D)
x + y necessarily irrational, but xy can be either rational or irrational
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E)
None of these
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The sum of two numbers is 18. The greatest product of these two numbers can be:
A)
17
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B)
81
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C)
80
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D)
84
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E)
None of these
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If the 15th term of an A.P is 45 and 20th term is 60, then find the 30th term of the A.P.
A)
70
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B)
90
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C)
110
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D)
120
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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 and 38. Calculate the median of the data.
A)
47
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B)
46
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C)
48
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D)
44
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E)
None of these
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The sum and the product of zeros of a quadratic equation are \[\frac{9}{2}\] and 2 respectively. The quadratic equation is:
A)
\[{{x}^{2}}-9x+4=0\]
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B)
\[2{{x}^{2}}-9x+4=0\]
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C)
\[5{{x}^{2}}+9x+4=0\]
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D)
\[3{{x}^{2}}+9x+2=0\]
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E)
None of these
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Find k such that \[5x+2y=k\] and \[10x+4y=3\]has infinitely many solutions.
A)
\[\frac{1}{2}\]
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B)
\[\frac{2}{3}\]
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C)
\[\frac{3}{2}\]
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D)
\[\frac{4}{9}\]
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E)
None of these
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The co-ordinate of the point which divides the line segment joining the points \[\left( 5,-2 \right)\] and (9, 6) internally in the ratio 1 : 2 is:
A)
\[\left( \frac{19}{3},\frac{2}{3} \right)\]
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B)
\[\left( \frac{1}{3},\frac{2}{3} \right)\]
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C)
\[\left( \frac{1}{3},\frac{22}{3} \right)\]
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D)
\[\left( \frac{13}{3},\frac{22}{3} \right)\]
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E)
None of these
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Find a point on x-axis which is equidistant from \[A\,\,\left( 2,-\,5 \right)\] and \[B\,\,\left( -\,2,9 \right)\].
A)
\[\left( -\,9,\text{ }0 \right)\]
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B)
\[\left( -\,7,\text{ }0 \right)\]
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C)
\[\left( 0,-\,7 \right)\]
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D)
(5, 3)
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E)
None of these
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The coach of a cricket team buys 3 bats and 7 balls for Rs. 1395. Later, he buys 4 bats and 5 balls for Rs. 1665. Find the cost of each bat and each ball.
A)
Rs. (500, 50)
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B)
Rs. (360, 45)
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C)
Rs. (450, 120)
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D)
Rs. (850, 150)
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E)
None of these
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In\[\Delta \,ABC,\] if,\[\angle B=90{}^\circ ,\] AB = 10 cm and AC = 20 cm, then find the angle\[\angle C\].
A)
\[60{}^\circ \]
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B)
\[30{}^\circ \]
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C)
\[90{}^\circ \]
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D)
\[45{}^\circ \]
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E)
None of these
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In the given figure, PT is a tangent at P and ABCP is a quadrilateral.\[\angle BAP\] is \[60{}^\circ ,\] then the value of \[\angle PCB\] is:
A)
\[60{}^\circ \]
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B)
\[90{}^\circ \]
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C)
\[120{}^\circ \]
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D)
\[140{}^\circ \]
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E)
None of these
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The value of \[\frac{{{\sin }^{2}}45{}^\circ +{{\cos }^{2}}45{}^\circ }{{{\sin }^{2}}30{}^\circ }\] is:
A)
\[\frac{1}{2}\]
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B)
\[\frac{1}{4}\]
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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 \[\cos \theta =\frac{1}{\sqrt{2}},\] 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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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 horse is placed for grazing inside a rectangular field 40 m by 36 m. It is tethered to one corner by a rope 14 m long. On how much area can it graze?
A)
\[154{{m}^{2}}\]
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B)
\[124\,\,{{m}^{2}}\]
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C)
\[164\,\,{{m}^{2}}\]
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D)
\[2824\,\,{{m}^{2}}\]
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E)
None of these
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The value of \[{{\cos }^{2}}30{}^\circ \,\,{{\cos }^{2}}45{}^\circ +4{{\sec }^{2}}60{}^\circ +\frac{1}{2}\,{{\cos }^{2}}90{}^\circ -2{{\tan }^{2}}60{}^\circ \] is:
A)
\[\frac{10}{3}\]
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B)
\[\frac{83}{8}\]
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C)
\[\frac{79}{8}\]
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D)
\[\frac{59}{9}\]
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E)
None of these
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Find the probability that a number chosen 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° 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 \[B\,\,\left( -\,4,6 \right)\] 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 perimeter of two similar triangles are 42 cm and 63 cm respectively. If one side of first triangle is 12 cm, then find the corresponding side of other triangle.
A)
12 cm
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B)
16 cm
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C)
18 cm
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D)
9 cm
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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,
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D)
8, 8
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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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Find the area of the sector of a circle with radius 7 cm and of angle \[108{}^\circ \].
A)
\[14.7\,\pi \,\,c{{m}^{2}}\]
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B)
\[15.2\,\pi \,\,c{{m}^{2}}\]
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C)
\[18.5\,\pi \,\,c{{m}^{2}}\]
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D)
\[20.8\,\pi \,\,c{{m}^{2}}\]
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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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The area of a trapezium is \[441\text{ }c{{m}^{2}}\]and the ratio of parallel side is 5 : 9. Also the perpendicular distance between them is 21 cm. Find the longest parallel side.
A)
36 cm
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B)
28 cm
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C)
18 cm
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D)
27 cm
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E)
None of these
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