If \[x=\sqrt{3+\sqrt{3+\sqrt{3+}}}\]...... , then the value of x is:
A)
\[\frac{1\underline{+}\sqrt{12}}{2}\]
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B)
\[\frac{1\underline{+}\sqrt{13}}{2}\]
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C)
\[\frac{1\underline{+}\sqrt{11}}{2}\]
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D)
\[\frac{1\underline{+}\sqrt{14}}{2}\]
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E)
None of these
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The zeroes of the polynomial \[3{{y}^{2}}+y-4\]are:
A)
\[\frac{4}{3}and\,\,1\]
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B)
\[-\frac{4}{3}and\,\,1\]
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C)
\[\frac{4}{3}and\,\,-1\]
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D)
\[-\frac{4}{3}and\,\,-1\]
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E)
None of these
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The equation \[lo{{g}_{a}}x+lo{{g}_{a}}\left( 1+x \right)=0\]is same as:
A)
\[{{x}^{2}}+x=0\]
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B)
\[{{x}^{2}}-1=0\]
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C)
\[{{x}^{2}}+x-1=0\]
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D)
\[{{x}^{2}}+x-2=0\]
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E)
None of these
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Which of the following values does not satisfies \[\frac{x}{2}+\frac{y}{4}=15\]?
A)
(30, 0)
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B)
(0, 60)
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C)
(10, 40)
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D)
(20, 15)
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E)
None of these
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If LP, MQ and NR are the medians of \[\Delta LMN\], then which of the following condition is correct?
A)
(LM + MN + NP) < (LP + MQ + NR)
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B)
(LM + MN + NP) > (NP + MQ + NR)
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C)
(LM + MN + LN) > (LP +MQ + NR)
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D)
(d)\[(L{{M}^{2}}+M{{N}^{2}}+N{{P}^{2}})>(L{{P}^{2}}+M{{Q}^{2}}+N{{R}^{2}})\]
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E)
None of these
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The angles of a quadrilateral are respectively\[100{}^\circ \],\[98{}^\circ \] and\[92{}^\circ \]. The fourth angle of the quadrilateral is:
A)
\[36{}^\circ \]
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B)
\[48{}^\circ \]
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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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The length of tangent from a point A at a distance of 5 cm from the centre of a circle is 4 cm. What is the radius of the circle?
A)
2 cm
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B)
3 cm
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C)
4 cm
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D)
5 cm
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E)
None of these
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Find the value of x, if the distance between the points \[\left( x,\text{ }-1 \right)\] and \[\left( 3,\text{ }2 \right)\] is 5.
A)
8
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B)
\[-1\]
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C)
7
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D)
Both [b] and [c]
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E)
None of these
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From a point P on the ground the angle of elevation of a 30 m tall building is \[45{}^\circ \]. A flag is hoisted at the top of the building and the angle of elevation of the top of the flag staff from point P is \[60{}^\circ \]. The length of flag staff and the distance of the building from the point P are respectively:
A)
21.96m and 30m
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B)
51.96 m and 30 m
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C)
30 m and 30 m
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D)
21.56 m and 30 m
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E)
None of these
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A bucket is in the form of a frustum of a cone. Its depth is 15 cm and the diametres of the top and bottom are 56 cm and 42 cm respectively. Find how many litres of water can the bucket hold.
A)
14.24 litres
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B)
28.49 litres
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C)
36.52 litres
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D)
51.32 litres
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E)
None of these
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In a football team, there are 3 groups of 3 players each, a captain and a goalkeeper. The mean age of these three groups are 25 years, 26 years and 32 years and mean age of entire team is 26 years. If the captain is thirteen years older than the goalkeeper, then age of the captain is:
A)
12 years
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B)
25 years
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C)
14 years
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D)
24 years
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E)
None of these
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A toy seller uses a spinner which has 4 equal sectors coloured yellow, blue, green and red for selling the toy of different colours. Maria wants to purchase a toy of red colour from the toy seller. Find the probability that Maria purchases a red coloured toy from the toy seller.
A)
\[\frac{1}{4}\]
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B)
\[\frac{1}{2}\]
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C)
\[\frac{1}{3}\]
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D)
\[\frac{2}{3}\]
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E)
None of these
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Find the value of x, \[\sqrt[3]{3x-2}=4\].
A)
20
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B)
25
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C)
22
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D)
30
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E)
None of these
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Simplify: \[4\sqrt{2}-2\sqrt{8}+\frac{3}{\sqrt{2}}\]
A)
\[\frac{3}{2}\sqrt{3}\]
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B)
\[\frac{3}{4}\sqrt{2}\]
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C)
\[\frac{3}{2}\sqrt{2}\]
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D)
\[\frac{4}{3}\sqrt{3}\]
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E)
None of these
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Find the remainder when \[{{x}^{3}}+3{{x}^{2}}+3x+1\] is divided by \[x-\frac{1}{2}\]
A)
\[\frac{8}{27}\]
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B)
\[\frac{-8}{27}\]
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C)
\[\frac{27}{8}\]
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D)
\[\frac{-27}{8}\]
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E)
None of these
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Factories: \[\frac{1}{2}{{x}^{2}}+4x+6\]
A)
\[(x+6)\left( \frac{x}{2}-1 \right)\]
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B)
\[(x+6)\left( \frac{x}{2}+1 \right)\]
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C)
\[(x+6)\left( \frac{x}{3}-1 \right)\]
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D)
\[(x-6)\left( \frac{x}{3}+1 \right)\]
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E)
None of these
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Evaluate:\[25x-19-\{3-(4x-5)\}=3x-(6x-5)\]
A)
x = 1
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B)
x = 5
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C)
x = 2
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D)
x = 4
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E)
None of these
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Simplify: \[\sqrt{{{m}^{2}}{{n}^{2}}}\times \sqrt[6]{{{m}^{2}}{{n}^{2}}}\times \sqrt[3]{{{m}^{2}}{{n}^{2}}}\]
A)
\[{{m}^{2}}{{n}^{2}}\]
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B)
\[{{m}^{3}}{{n}^{2}}\]
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C)
\[{{m}^{2}}{{n}^{2}}\]
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D)
\[m{{n}^{2}}\]
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E)
None of these
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Which of the following is an irrational number?
A)
\[7\sqrt{3}\]
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B)
\[\sqrt{2}\]
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C)
\[3\sqrt{5}\]
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D)
All of these
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E)
None of these
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Solve for x and y: \[4x-15y=65\] \[3x+2y=9\]
A)
\[(-5,-3)\]
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B)
\[(5,-3)\]
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C)
\[(2,\,\,3)\]
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D)
\[(-2,\,\,3)\]
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E)
None of these
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If angles of a triangle are in the ratio\[1:4:7\], then find the largest angle.
A)
\[135{}^\circ \]
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B)
\[84{}^\circ \]
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C)
\[105{}^\circ \]
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D)
\[75{}^\circ \]
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E)
None of these
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The edge of a cube is doubled. What will be the new volume?
A)
3 times
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B)
2 times
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C)
4 times
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D)
8 times
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E)
None of these
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If \[x=\sqrt{3+\sqrt{3+\sqrt{3+---}}}\], then the value of x is:
A)
\[\frac{2\underline{+}\sqrt{13}}{2}\]
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B)
\[\frac{3\underline{+}\sqrt{13}}{2}\]
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C)
\[\frac{4\underline{+}\sqrt{13}}{2}\]
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D)
\[\frac{1\underline{+}\sqrt{13}}{2}\]
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E)
None of these
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