Which is the correct decimal form of\[3\frac{1}{8}\]?
A)
4.125
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B)
3.225
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C)
3.125
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D)
\[0.\overline{18}\]
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E)
None of these
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Simplify: \[{{\left[ 5\times {{\left( {{8}^{\frac{1}{3}}}+{{27}^{\frac{1}{3}}} \right)}^{3}} \right]}^{\frac{1}{4}}}\]
A)
25
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B)
5
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C)
15
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D)
125
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E)
None of these
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Consider the following statements:
1. Product of two irrational numbers is an irrational number 2. Product of any two rational numbers is a rational number 3. Product of any two natural numbers is a natural number. Which of the above statements are correct?
A)
1 and 2
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B)
2 and 3
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C)
1 and 3
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D)
1, 2 and 3
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E)
None of these
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Factories:\[{{x}^{4}}-625\]
A)
\[{{\left( {{x}^{2}} \right)}^{2}}-{{\left( 5 \right)}^{2}}\]
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B)
\[{{\left( {{x}^{3}} \right)}^{2}}-{{\left( 125 \right)}^{2}}\]
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C)
\[(x+5)\,\,(x-5)\,\,({{x}^{2}}+25)\]
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D)
\[{{x}^{2}}-25\]
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E)
None of these
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Factorise: \[{{(a-b)}^{3}}+{{(b-c)}^{3}}+{{(c-a)}^{3}}\]
A)
\[2\,(a-b)\,\,(b-c)\,\,(c-a)\]
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B)
\[3\,\,(a-b)\,\,(b+c)\,\,(c+a)\]
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C)
\[3\,(a-b)\,\,(b-c)\,\,(c-a)\]
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D)
\[4\,(a-b)\,\,(b-c)\,\,(c-a)\]
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E)
None of these
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Solve the system of equations : \[4x-7y+28=0\]and \[5y-7x+9=0\]
A)
x = 6 and y = 3
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B)
x = 2 and y = 8
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C)
x = 7 and y = 8
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D)
x = 7 and y = 7
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E)
None of these
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Solve the equation: \[\frac{1}{x+5}+\frac{1}{x-5}=\frac{1}{{{x}^{2}}-25}\]
A)
1
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B)
2
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C)
\[\frac{1}{2}\]
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D)
\[\frac{1}{3}\]
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E)
None of these
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In figure, coordinates of P are
A)
\[(-\,4,-\,4)\]
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B)
\[(-\,3,-\,5)\]
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C)
\[(-\,5,3)\]
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D)
(3, 5)
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E)
None of these
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Determine the point on the graph of the equation \[2x+6y=36,\] whose \[x-\]coordinate is \[\frac{3}{2}\] times its ordinate.
A)
(5, 2)
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B)
(4, 6)
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C)
(6, 4)
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D)
(2, 5)
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E)
None of these
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Which one of the following pair of linear equations has inconsistent solution?
A)
\[15x+13y+27=0\] and \[\frac{15}{2}x+\frac{13}{2}y+\frac{27}{2}=0\]
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B)
\[30x+26y+54=0\] and \[20x+13y+5=0\]
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C)
\[15x+13y+27=0\]and \[45x+39y+29=0\]
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D)
\[x+5y+10=0\] and \[2x+10y+20=0\]
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E)
None of these
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Find the remainder, when polynomial \[f\,(x)\,={{x}^{4}}-{{x}^{3}}-11{{x}^{2}}-x-24\] is divided by\[x+3\].
A)
12
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B)
\[-\,24\]
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C)
24
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D)
\[-\,12\]
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E)
None of these
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Amit is two years older than Yogesh who is twice as old as Suresh. If the sum of their ages is 27 years, then how old is Yogesh?
A)
5 years
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B)
6 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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A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number increased by 99 if its digits are reversed. The number is:
A)
145
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B)
253
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C)
387
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D)
423
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E)
None of these
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It is given that \[\Delta \,ABC\cong \Delta \,FDE,\] \[AB=4cm,\]\[\,\angle \,B=45{}^\circ \] and \[\angle \,A=80{}^\circ \]. Then which of the following is true?
A)
\[DF=4\,cm,\,\angle F=55{}^\circ \]
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B)
\[DF=4\,cm,\,\angle E=55{}^\circ \]
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C)
\[DE=4\,cm,\,\angle E=55{}^\circ \]
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D)
\[DE=4\,cm,\,\angle D=60{}^\circ \]
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E)
None of these
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Find the perimeter of a rhombus whose diagonals are 16 cm and 30 cm long.
A)
17 cm
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B)
69 cm
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C)
63 cm
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D)
68 cm
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E)
None of these
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In the given figure \[\ell \parallel m\] and \[\ell \parallel n\]. Find the value of x.
A)
\[50{}^\circ \]
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B)
\[60{}^\circ \]
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C)
\[120{}^\circ \]
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D)
\[45{}^\circ \]
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E)
None of these
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In the given figure line I meets sides AB and AC of \[\Delta \,ABC\] at their mid-points D and E respectively. If \[\angle \,A=60{}^\circ \] and \[\angle \,B=70{}^\circ ,\] then find\[\angle \,AED\].
A)
\[130{}^\circ \]
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B)
\[60{}^\circ \]
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C)
\[50{}^\circ \]
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D)
\[70{}^\circ \]
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E)
None of these
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The ratio of two sides of parallelogram is 3 : 5 and its perimetre is 48 m. Find the long side of the parallelogram.
A)
25 m
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B)
10 m
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C)
12 m
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D)
15 m
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E)
None of these
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Which of the following parts are sufficient to construct a quadrilateral?
A)
4 sides and 1 diagonal
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B)
4 sides and 1 angle
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C)
3 sides and 2 included angles
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D)
All of these
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E)
None of these
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If D is the mid-point of the straight line joining\[A\,(-\,3,9),\] and B (5, 3), then the coordinates of D is:
A)
(2, 12)
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B)
(8, 6)
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C)
\[(-\,10,-\,4)\]
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D)
(1, 6)
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E)
None of these
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In the given figure, O is the centre of circle. If\[\angle \,OAB=50{}^\circ ,\] then \[\angle \,ACB\]is equal to:
A)
\[50{}^\circ \]
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B)
\[40{}^\circ \]
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C)
\[60{}^\circ \]
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D)
\[70{}^\circ \]
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E)
None of these
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Find the value of x in given figure:
A)
\[60{}^\circ \]
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B)
\[50{}^\circ \]
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C)
\[55{}^\circ \]
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D)
\[70{}^\circ \]
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E)
None of these
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If each interior angle of a regular octagon is \[135{}^\circ ,\]then each exterior angle of octagon will be:
A)
\[65{}^\circ \]
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B)
\[75{}^\circ \]
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C)
\[45{}^\circ \]
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D)
\[90{}^\circ \]
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E)
None of these
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In the given figure, a star is shown. What is the sum of the angles A, B, C, D and E?
A)
\[120{}^\circ \]
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B)
\[240{}^\circ \]
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C)
\[180{}^\circ \]
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D)
\[360{}^\circ \]
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E)
None of these
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How many metres of cloth 10 metre wide will be required ot make a conical tent having the radius of base 7 m and height 24 metre.
A)
55 m
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B)
50 m
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C)
75 m
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D)
150 m
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E)
None of these
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A sphere, a cylinder and a cone have same radius and same height. Find the ratio of the areas of their curved surfaces.
A)
\[5:4:\sqrt{5}\]
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B)
\[4:4:\sqrt{5}\]
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C)
\[4:5:\sqrt{5}\]
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D)
\[5:5:\sqrt{5}\]
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E)
None of these
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A cube of edge 8 cm is immersed completely in a cuboidal vessel containing water and water does not overflow. If the dimensions of the base are 16 cm and 10 cm. Find the rise in the water level in the vessel.
A)
1.8 cm
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B)
2.2 cm
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C)
3.2 cm
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D)
4.2 cm
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E)
None of these
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The area of a triangular sign board of sides 5 cm, 12 cm and 13 cm is
A)
\[\frac{65}{2}\,\,c{{m}^{2}}\]
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B)
\[\frac{65}{2}\,\,c{{m}^{2}}\]
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C)
\[60\,\,c{{m}^{2}}\]
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D)
\[12\,\,c{{m}^{2}}\]
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E)
None of these
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The circumference of a circle is 88 metre. Find the area of the circle.
A)
\[156\,\,{{m}^{2}}\]
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B)
\[616\,\,{{m}^{2}}\]
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C)
\[516\,\,{{m}^{2}}\]
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D)
\[448\,\,c{{m}^{2}}\]
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E)
None of these
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The sides of a triangle are in the ratio of 25 : 14 : 12 and its perimetre is 1530 m. The smallest side of triangle is?
A)
120 m
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B)
240 m
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C)
360 m
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D)
370 m
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E)
None of these
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The area of trapezium in the adjoining figure is
A)
\[286\,{{m}^{2}}\]
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B)
\[306\,{{m}^{2}}\]
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C)
\[316\,{{m}^{2}}\]
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D)
\[296\,{{m}^{2}}\]
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E)
None of these
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In \[\Delta \,ABC\] and \[\Delta \,DEF,\] AB = DF,\[\angle \,ACB=70{}^\circ ,\]\[\angle \,ABC=50{}^\circ ,\] \[\angle \,DEF=70{}^\circ \] and \[\angle EDF=60{}^\circ \]. By which of the following congruence conditions are the two triangles congruent?
A)
SSS
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B)
ASA
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C)
SAS
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D)
RHS
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E)
None of these
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The mean of 15 numbers is 10. If 2 is added to every number, what will be the new mean?
A)
11
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B)
12
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C)
15
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D)
20
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E)
None of these
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Seven houses were sold last week in Indrapuram. Here are the selling prices: $94,900, $97,900, $99,900, $100,900, $102,900, $107,900 and $1,250,000. Find the median selling price.
A)
$99,900
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B)
$102,900
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C)
$100,900
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D)
$107,900
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E)
None of these
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A number from 1 to 11 is chosen at random. What is the probability of choosing an odd number?
A)
\[\frac{6}{11}\]
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B)
\[\frac{5}{11}\]
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C)
\[\frac{4}{11}\]
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D)
\[\frac{3}{11}\]
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E)
None of these
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Which one of the following numbers cannot be a probability?
A)
5
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B)
0.5
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C)
0.005
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D)
0.85
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E)
None of these
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Find the value of \[\sqrt[4]{121}\,\,\times \,\,\sqrt[4]{121}\]
A)
12
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B)
21
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C)
19
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D)
11
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E)
None of these
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The value of\[\frac{1}{3+\frac{2}{2+\frac{1}{2}}}\]is:
A)
\[\frac{4}{5}\]
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B)
\[\frac{5}{4}\]
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C)
\[\frac{5}{19}\]
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D)
\[\frac{19}{5}\]
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E)
None of these
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Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages?
A)
45 years
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B)
35 years
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C)
40 years
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D)
50 years
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E)
None of these
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Find the missing number.
A)
25
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B)
26
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C)
27
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D)
29
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E)
None of these
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