If \[\frac{6+\sqrt{5}}{6-\sqrt{5}}=\frac{a+b\sqrt{5}}{31}\], then which one of the following represents the values of a and b?
A)
a = 41 and b = 12
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B)
a = 25 and b = 13
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C)
a = 36 and b = 5
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D)
a = 14 and b = 21
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E)
None of these
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\[{{x}^{3}}\left( y-z \right)+{{y}^{3}}\left( z-x \right)+{{z}^{3}}(x-y)\] is equal to:
A)
\[(x+y+z)(x-y)(y-z)(z-x)\]
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B)
\[(x+y+z)(x-y-z)(x-y)(y-z)\]
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C)
\[(x+y+z)(x-y)(y-z)(x-z)\]
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D)
\[({{x}^{3}}+{{y}^{3}}+{{z}^{3}})(x-y)(y-z)(z-x)\]
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E)
None of these
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If, \[{{\log }_{4}}x+{{\log }_{2}}x=6\] then x must be equal to:
A)
16
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B)
10
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C)
\[-2\]
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D)
1
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E)
None of these
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Find x and y which satisfies: \[x\text{ }+\text{ }y\text{ }=\text{ }7\]and \[2x-\text{3}y\text{ }=\text{ 4}\]
A)
\[x\text{ }=\text{ }16\text{ }and\text{ }y\text{ }=-9\]
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B)
(b)\[x\text{ }=-16\text{ }and\text{ }y\text{ }=\text{ }9\]
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C)
\[x\text{ }=-2\text{ }and\text{ }y\text{ }=\text{ }3\]
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D)
\[x\text{ }=\text{ }5\text{ }and\text{ }y\text{ }=2\]
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E)
None of these
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In a right-angled triangle ABC, right-angled at B, AB = 12 cm and BC = 5 cm. If D is the mid-point of side AC, then the length of BD is equal to:
A)
11 cm
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B)
12 cm
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C)
6.5 cm
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D)
5 cm
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E)
None of these
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Which one of the following statements is incorrect?
A)
The quadrilateral formed by joining the mid-points of adjacent sides of a rectangle is always a rhombus
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B)
The quadrilateral formed by joining the mid-points of the pair of adjacent sides of a rhombus is always a rectangle
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C)
The line segment joining the mid-points of the sides of a triangle divide it into three congruent triangle
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D)
The quadrilateral formed by joining the mid points of the pairs of adjacent sides of a square is always a square
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E)
None of these
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A circle in inscribed in a \[\Delta ABC\] having AB = 12 cm, BC =8 cm and CA = 10 cm touching AB at D, BC at E and AC at F. Find the length of AD.
A)
3 cm
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B)
5 cm
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C)
6 cm
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D)
7 cm
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E)
None of these
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The ratio in which the line \[3x\text{ }+\text{ }y\text{ }-\text{ }9\text{ }=\text{ }0\]divides the segment joining the points (1, 3) and 2, 7) is:
A)
2 : 3
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B)
3 : 4
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C)
1 : 2
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D)
4 : 5
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E)
None of these
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A helicopter is flying at an altitude of 1500 m. The angle of depression of two cars moving in same direction as observed from the helicopter are \[60{}^\circ \]and\[30{}^\circ \]. The distance between two cars is:
A)
1435 m
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B)
1732 m
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C)
4325 m
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D)
1712 m
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E)
None of these
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A river 1.5 m deep and 36 m wide is flowing at the rate of 3.5 km per hour. Calculate the amount of water that runs into the sea per minute.
A)
(a)\[1870\,\,{{m}^{3}}\]
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B)
\[2280\,\,{{m}^{3}}\]
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C)
\[3150\,\,{{m}^{3}}\]
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D)
\[2890\,\,{{m}^{3}}\]
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E)
None of these
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The mean of the following frequency distribution is 29.8 and the sum of all frequencies is 25. Compute the missing frequencies x and y
Class interval Frequency Class interval Frequency 0-10 5 30-40 3 10-20 x 40-50 y 20-30 4 50-60 2
A)
x = 12 and y = 6
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B)
x = 3 and y = 6
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C)
x = 2 and y = 6
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D)
x = 2 and y = 5
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E)
None of these
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A bag contains 3 white, 4 red and 5 black balls. One ball is drawn at random. What is the probability that the ball drawn is neither black nor white.
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)
\[\frac{3}{4}\]
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E)
None of these
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If sum of x and x + 3 is greater than 20, find the possible value of x.
A)
\[-\]9
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B)
6\[-\]
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C)
\[-\]2
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D)
10
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E)
None of these
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The mean of 10 numbers is 20. If 5 is subtracted from every number, what will be the new mean?
A)
10
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B)
15
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C)
25
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D)
22
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E)
None of these
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In a group of 26 girls Gatita?s position is 7th from the bottom. What is the position of Gatita from the top of the group?
A)
19th
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B)
21st
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C)
20th
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D)
27th
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E)
None of these
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Speed of a boat in still water is 10 km/hr and the speed of a river is 3 km/hr. Find the distance covered by the boat upstream lasting 3 hours is:
A)
13 km
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B)
20 km
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C)
21 km
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D)
15 km
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E)
None of these
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If \[{{7}^{1+x}}+{{7}^{1-x}}=50\], then x is:
A)
\[\underline{+}\]2
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B)
\[\underline{+}\]3
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C)
\[\underline{+}\]1
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D)
\[\underline{+}\]5
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E)
None of these
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If \[{{\left( \frac{a}{b} \right)}^{x-1}}={{\left( \frac{b}{a} \right)}^{x-3}}\], then find the value of x.
A)
1
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B)
\[-\]1
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C)
2
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D)
3
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E)
None of these
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\[\frac{50}{x}=\frac{x}{12\frac{1}{2}}\], then x is:
A)
\[\frac{25}{2}\]
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B)
4
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C)
25
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D)
\[\frac{3}{25}\]
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E)
None of these
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Factorise: \[{{(a-b)}^{3}}+{{(b-c)}^{3}}+{{(c-a)}^{3}}\]
A)
\[3(a+b)(a+c)+(c-a)\]
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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)
\[3(a-b)(b-c)(c-a)\]
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E)
None of these
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If \[x\text{ }+\text{ }y\text{ }=\text{ }2\], then the value of \[{{x}^{3}}+6xy+{{y}^{3}}-8\] is equal to:
A)
1
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B)
0
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C)
3
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D)
7
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E)
None of these
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When \[(4{{a}^{3}}+4{{a}^{2}}-a-1)\] is divided by \[\left( 2a\text{ }+\text{ }1 \right)\], the remainder will be:
A)
2
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B)
1
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C)
0
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D)
5
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E)
None of these
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Simplify: \[\frac{\sqrt{3}-1}{\sqrt{3}+1}+\frac{\sqrt{3}+1}{\sqrt{3}-1}\]
A)
\[2+\sqrt{3}\]
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B)
\[2-\sqrt{3}\]
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C)
2
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D)
4
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E)
None of these
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