Find the smallest number which, when divided by 8, 12 and 30 leaves remainder 3, 7 and 25 respectively.
A)
105
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B)
110
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C)
115
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D)
120
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E)
None of these
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Find the smallest four digit number which is exactly divisible by 6, 8, 12.
A)
1000
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B)
1024
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C)
1008
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D)
1168
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E)
None of these
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Three person A, B, C run along a 40 km long circular field. They start their race at 5 AM at same time and from same point at the speed of 12 km/hr, 16 km/hr and 20 km/hr respectively. After how much time they will meet again?
A)
15 hours
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B)
13 hours
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C)
12 hours
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D)
10 hours
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E)
None of these
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Four bells ring at an interval of 6, 8, 12, 18 respectively. If they had last rang at 12: 40 PM, then at what time they will ring together again?
A)
1 : 15 PM
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B)
1 : 30 PM
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C)
1 : 45 PM
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D)
1 : 52 PM
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E)
None of these
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Length \[\times \] Breadth of a room is 13 m \[\times \]7.5 m. Floor of a room is to be paved by square tiles of same size. What will be the greatest size of tiles and the Number of tiles?
A)
0.5 m, 350 tiles
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B)
0.7 m, 390 tiles
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C)
0.5 m, 390 tiles
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D)
0.5 m, 320 tiles
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E)
None of these
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Express 2.1\[\overline{36}\]in the form\[\frac{p}{q}\].
A)
\[\frac{24}{22}\]
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B)
\[\frac{47}{22}\]
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C)
\[\frac{29}{45}\]
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D)
\[\frac{31}{22}\]
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E)
None of these
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Find the zeros of the polynomial \[f(x)={{x}^{2}}+\sqrt{2}\,x-4\]
A)
\[x=\sqrt{2}\]
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B)
\[x=\sqrt{3}\]
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C)
\[x=\sqrt{5}\]
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D)
\[x=\sqrt{7}\]
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E)
None of these
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The cubic polynomial whose three roots are 3, \[-\,1\] and \[-\,3\]is:
A)
\[{{n}^{3}}+{{n}^{2}}-9n-9\]
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B)
\[{{n}^{3}}-{{n}^{2}}-9n-9\]
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C)
\[{{n}^{3}}+{{n}^{2}}+9n+9\]
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D)
\[{{n}^{3}}-{{n}^{2}}+9n+9\]
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E)
None of these
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Katherine studies in a senior secondary school. A math test was conducted as a part of monthly routine and she scores 50 marks, getting 4 marks for each correct answer and losing 2 marks for each wrong answer. Had she been awarded 5 marks for each correct answer and deducted 3 marks for each wrong answer, she would have scored 60 marks. The total number of questions in the test was:
A)
25
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B)
5
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C)
15
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D)
20
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E)
None of these
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If \[\alpha \] and \[\beta \] are real and \[{{\alpha }^{2}}\] and \[-\,{{\beta }^{2}}\] are the roots of \[4{{y}^{2}}+y+3=0,\] then find the value of\[{{\beta }^{2}}\]
A)
\[\left( \frac{5}{8},\,-1 \right)\]
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B)
\[\left( 1,-1 \right)\]
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C)
\[\left( 1,\,\,\frac{3}{4} \right)\]
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D)
\[\left( 1,\frac{-3}{4} \right)\]
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E)
None of these
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If the 15th term of an AP is 121 and 25th term is 201, then find the 35th term of the AP.
A)
292
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B)
281
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C)
264
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D)
275
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E)
None of these
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Sum of 20 terms of the series given by 3 + 7 + 11 + _____ is:
A)
840
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B)
760
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C)
780
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D)
820
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E)
None of these
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If the radius of cylinder is doubled, but height is reduced by \[50%\], what is the percentage change in volume?
A)
\[50%\]
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B)
\[100%\]
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C)
\[150%\]
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D)
\[200%\]
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E)
None of these
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The ratio of the volume of a right circular cylinder and a right circular cone of the same base and height will be:
A)
2 : 3
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B)
1 : 3
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C)
3 : 1
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D)
9 : 1
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E)
None of these
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In the figure \[AB\parallel QR,\] find the length of PB:
A)
2 cm
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B)
3 cm
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C)
2.5 cm
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D)
4 cm
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E)
None of these
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In the given figure AB = 12 cm, AC = 15 cm and AD = 6 cm. \[BC\parallel DE\], find the length of AE:
A)
6 cm
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B)
7.5 cm
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C)
9 cm
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D)
10 cm
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E)
None of these
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If \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=xy+yz+zx,\] then the triangle is
A)
isosceles
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B)
right angled
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C)
Equilateral
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D)
scalene
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E)
None of these
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In a right angled triangle ABC, CD is perpendicular on the hypotenuse AB. Which of the following is correct?
A)
\[CD=\frac{AC\times BC}{A\,B}\]
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B)
\[AD=\frac{AC\times AC}{A\,B}\]
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C)
\[BD=\frac{BC\times BC}{AB}\]
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D)
All of the above
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E)
None of these
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In the given figure, AB is the diameter of the circle. Find the value of\[\angle ACD\].
A)
\[30{}^\circ \]
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B)
\[60{}^\circ \]
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C)
\[45{}^\circ \]
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D)
\[25{}^\circ \]
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E)
None of these
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Two circles of radii 13 cm and 5 cm touch internally each other. Find the distance between their centres.
A)
18 cm
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B)
12 cm
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C)
9 cm
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D)
8 cm
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E)
None of these
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Vertical angles of two isosceles triangles are equal. Then corresponding altitudes are in the ratio 4 : 9. Find the ratio of their areas.
A)
16 : 44
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B)
16 : 81
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C)
16 : 65
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D)
16 : 91
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E)
None of these
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If \[x=\frac{4ab}{a+b},\] find the value of \[\frac{x+2a}{x-2a}+\frac{x+2b}{x-2b}\]
A)
4
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B)
3
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C)
6
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D)
2
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E)
None of these
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If \[x=\frac{\sqrt{3}}{2},\] calculate value of\[\sqrt{1+x}-\sqrt{1-x}\]
A)
1
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B)
2
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C)
3
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D)
4
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E)
None of these
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In figure, ABC is a right triangle, right angled at B. AD and CE are two medians drawn from A and C respectively. If AC = 5 cm and \[AD=\frac{3\sqrt{5}}{2}\]cm, find the length of CE.
A)
\[2\,\sqrt{5}cm\]
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B)
2.5 cm
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C)
5 cm
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D)
\[4\,\sqrt{2}cm\]
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E)
None of these
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What is the maximum value of \[3-4{{x}^{2}}+2x?\]
A)
\[\frac{13}{-\,5}\]
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B)
\[\frac{13}{-\,4}\]
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C)
\[\frac{13}{5}\]
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D)
\[\frac{13}{4}\]
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E)
None of these
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In the given figure, AP = 3 cm, BA = 5 cm and CP = 2 cm. Find CD.
A)
12 cm
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B)
10 cm
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C)
9 cm
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D)
6 cm
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E)
None of these
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In a circle of radius 5 cm, AB and AC are the two chords such that AB = AC = 6 cm. Find the length of the chord BC.
A)
4.8 cm
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B)
10.8 cm
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C)
9.6 cm
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D)
6.8 cm
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E)
None of these
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In a circle of diameter 60 m, the length of a chord is 30 m. Find the length of the minor arc on one side of the chord.
A)
29.42 m
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B)
30.50 m
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C)
31.42 m
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D)
32.50 m
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E)
None of these
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Find the value of \[\frac{4}{3}{{\cot }^{2}}30{}^\circ +3{{\sin }^{2}}60{}^\circ -2{{\operatorname{cosec}}^{2}}60{}^\circ -\frac{3}{4}{{\tan }^{2}}30{}^\circ \]
A)
\[\frac{10}{3}\]
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B)
\[\frac{11}{3}\]
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C)
4
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D)
5
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E)
None of these
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The angle of elevation of the top of a tower at a distance of 150 m from its foot on a horizontal plane is found to be\[60{}^\circ \]. Find the height of the tower.
A)
150 m
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B)
\[100\,\sqrt{3}\,m\]
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C)
\[150\,\sqrt{3}\,m\]
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D)
50 m
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E)
None of these
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A tree AC, has broken down from point B because of the wind. The angle of side BD from earth is \[45{}^\circ ,\] where point D touches ground. If AD = 10 m, then find the height of tree.
A)
\[5\,(1+\sqrt{2})\,m\]
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B)
\[10\,(\sqrt{2}-1)\,m\]
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C)
\[10\,(\sqrt{2}+1)\,m\]
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D)
\[5\,(\sqrt{2}-1)\,m\]
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E)
None of these
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The angle of elevation of a jet plane from a point P on the ground is \[60{}^\circ \]. After 15 second of flight the angle becomes \[30{}^\circ \]. If the height of the jet plane is 1500 m, then find the speed of the jet plane.
A)
\[300\,m/s\]
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B)
\[400\sqrt{3}\,m/s\]
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C)
\[150\,m/s\]
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D)
\[200/\sqrt{3}\,m/s\]
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E)
None of these
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Find the value of \[{{\sin }^{2}}(120{}^\circ -A)+{{\sin }^{2}}A+{{\sin }^{2}}(120{}^\circ +A).\]
A)
\[\frac{2}{3}\]
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B)
\[\frac{3}{2}\]
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C)
\[\frac{5}{2}\]
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D)
\[\frac{\sqrt{3}}{2}\]
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E)
None of these
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A bus travels from A to B and from B to C at the speeds of 30 km/hr and 20 km/hr respectively. If the distance from A to B and B to C both are 150 km, then what was the average speed of the bus (in km/hr)?
A)
24
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B)
25
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C)
26
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D)
27
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E)
None of these
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The distance between a rabbit and a dog is 500 meters. Having seen the dog the rabbit runs at a speed of 100 m/min and the dog chases the rabbit at a speed of 120 m/min. After how many minutes the rabbit will be caught?
A)
12.5 min
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B)
50 min
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C)
25 min
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D)
75 min
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E)
None of these
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A tradesman bought 500 metres of electric wire @ 75 paisa per meter. He sold \[60%\] of it at a profit of \[8%\]. At what gain percent should he sell the remainder so as to gain \[12%\] on the We transaction?
A)
\[20%\]
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B)
\[15%\]
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C)
\[18%\]
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D)
\[16%\]
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E)
None of these
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Find the value of \[\tan A+\tan \,B+tan\,C,\] if\[A+B+C=\pi .\]
A)
\[tanA\text{ }tanB\text{ }tanC\]
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B)
1
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C)
0
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D)
\[cotA\text{ }cotB\text{ }cotC\]
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E)
None of these
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Which one of the following pairs is correctly matched? If then
A)
\[x=\frac{1+\sin 60{}^\circ -\cos 60{}^\circ }{1+\sin 60{}^\circ +\cos 60{}^\circ }\,\,\,\,\,\,\,x=\tan 60{}^\circ \]
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B)
\[x=\frac{1+\sin 90{}^\circ -\cos 90{}^\circ }{1+\sin 90{}^\circ -\cos 90{}^\circ }\,\,\,\,\,\,\,x=\tan 30{}^\circ \]
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C)
\[x=\frac{2\tan 30{}^\circ }{1+{{\tan }^{2}}30{}^\circ }\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=\tan 60{}^\circ \]
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D)
\[x=\frac{1-{{\tan }^{2}}30{}^\circ }{1+{{\tan }^{2}}30{}^\circ }\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=\cos 60{}^\circ \]
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E)
None of these
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10 years ago, Chandravati's mother was 4 times older than her daughter. After 10 years, the mother will be twice older than the daughter. The present age of Chandravati is:
A)
5 years
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B)
10 years
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C)
20 years
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D)
12 years
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E)
None of these
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If L stands for +, M stands for \[-,\] N stands for x, P stands for \[\div ,\] then 14 N 10 L 42 P 2 M 8 = ?
A)
153
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B)
216
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C)
248
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D)
251
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E)
None of these
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