If \[x=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}\] and \[y=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}},\] then find the value of \[{{x}^{2}}+{{y}^{2}}\].
A)
88
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B)
96
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C)
98
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D)
78
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E)
None of these
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\[x=3+{{3}^{\frac{1}{3}}}+{{3}^{\frac{2}{3}}},\] then find the value of\[{{x}^{3}}-9{{x}^{2}}+18x-12\].
A)
1
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B)
2
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C)
3
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D)
0
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E)
None of these
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Simplify :\[\sqrt{9+2x}-\sqrt{2x}=\frac{5}{\sqrt{9+2x}}\]
A)
4
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B)
8
done
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C)
10
done
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D)
11
done
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E)
None of these
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If \[x=\frac{7-\sqrt{45}}{2},\] find the value of\[{{x}^{3}}+\frac{1}{{{x}^{3}}}\].
A)
47
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B)
298
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C)
322
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D)
428
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E)
None of these
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If \[{{(2.5)}^{x}}={{(0.025)}^{y}}={{10}^{3}},\] find the value of \[\frac{1}{x}-\frac{1}{y}.\]
A)
\[\frac{3}{2}\]
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B)
\[\frac{1}{3}\]
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C)
\[\frac{5}{3}\]
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D)
\[\frac{2}{3}\]
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E)
None of these
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Solve: \[{{5}^{\log x}}+{{x}^{\log 5}}=50\]
A)
10
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B)
50
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C)
100
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D)
200
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E)
None of these
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A cylindrical solid with base radius 5 cm and height 8 cm is melted down to form 12 identical cones with base radii 4 cm. Calculate the height of each cone.
A)
\[3\frac{1}{8}\,\,cm\]
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B)
\[2\frac{1}{8}\,\,cm\]
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C)
\[1\frac{1}{8}\,\,cm\]
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D)
\[4\frac{3}{8}\,\,cm\]
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E)
None of these
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Three cubes with sides in the ratio 3 : 4 : 5 are melted to form a single cube whose diagonal is\[12\sqrt{3}\,cm\]. The sides of the cubes are:
A)
3 cm, 4 cm, 5 cm
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B)
6 cm, 8 cm, 10 cm
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C)
9 cm, 12 cm, 15 cm
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D)
7 cm, 9 cm, 14 cm
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E)
None of these
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If \[a+b+c=0,\] then find the value of\[\frac{{{a}^{2}}}{bc}+\frac{{{b}^{2}}}{ca}+\frac{{{c}^{2}}}{ab}\].
A)
5
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B)
4
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C)
3
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D)
1
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E)
None of these
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If \[ab{{x}^{2}}={{(a-b)}^{2}}\,\,(x+1),\] then the value of \[1+\frac{4}{x}+\frac{4}{{{x}^{2}}}\] is:
A)
\[{{\left( \frac{a-b}{a+b} \right)}^{2}}\]
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B)
\[{{\left( \frac{a+b}{a-b} \right)}^{2}}\]
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C)
\[{{\left( \frac{a}{a+b} \right)}^{2}}\]
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D)
\[{{\left( \frac{b}{a+b} \right)}^{2}}\]
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E)
None of these
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Find the fourth vertex of the parallelogram whose three consecutive vertices are (8, 8), (6, 1) and\[(-\,1,1)\].
A)
(1, 8)
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B)
(8, 8)
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C)
\[(-\,7,\,8)\]
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D)
(2, 7)
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E)
None of these
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Angles A, B, C of a \[\Delta \,ABC\] satisfy \[B-A=30{}^\circ \] and \[C-B=45{}^\circ \]. Find the value of angle C.
A)
\[55{}^\circ \]
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B)
\[84{}^\circ \]
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C)
\[100{}^\circ \]
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D)
\[125{}^\circ \]
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E)
None of these
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In the figure given below, ABCD is a parallelogram in which \[AB\parallel CD\]. If \[x=\frac{3}{5}y\] and\[y=\frac{5}{7}z\]. Find the value of z.
A)
\[60{}^\circ \]
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B)
\[36{}^\circ \]
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C)
\[84{}^\circ \]
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D)
\[92{}^\circ \]
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E)
None of these
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ABC is a triangle where AN is perpendicular to CB and BM is perpendicular to AC. The length of BC is 10 cm, that of AC is 12 cm and that of AN is 8 cm. Find the length of BM (approx).
A)
5.76 cm
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B)
6.67 cm
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C)
7.76 cm
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D)
8.77 cm
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E)
None of these
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If the sum of the interior angles of a regular polygon measures up to 1440 degrees, how many sides does the polygon have?
A)
10 sides
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B)
8 sides
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C)
12 sides
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D)
9 sides
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E)
None of these
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Vertices of a quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9) and D(5, 4). What is the shape of the quadrilateral?
A)
Square
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B)
Rectangle but not a square
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C)
Rhombus
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D)
Parallelogram but not a rhombus
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E)
None of these
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What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40 and 41?
A)
6
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B)
4
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C)
24.5
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D)
20.5
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E)
None of these
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A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?
A)
240 m
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B)
360 m
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C)
420 m
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D)
600 m
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E)
None of these
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Find the values of x from the figure given below, if \[DE\parallel BC.\]
A)
\[x=1\]
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B)
\[x=5\]
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C)
\[x=-\,1\]
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D)
\[x=2\]
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E)
None of these
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From the given figure, find out the values of x and y.
A)
x = 26, y = 19
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B)
x = 26, y = 29
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C)
x = 25, y = 20
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D)
x = 40, y = 25
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E)
None of these
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Find the ratio of radii of two circles, if arc of equal length subtend angles \[30{}^\circ \] and \[45{}^\circ \] at their centre.
A)
2 : 3
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B)
4 : 3
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C)
3 : 2
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D)
3 : 4
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E)
None of these
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In what ratio are the volumes of a cylinder, a cone and a sphere, if each has the same radius and the same height?
A)
1 : 3 : 2
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B)
2 : 3 : 1
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C)
3 : 1 : 2
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D)
3 : 2 : 1
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E)
None of these
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In the given figure \[\angle \,A=50{}^\circ \] and \[\angle \,ABC=75{}^\circ \]. Find the value of \[\angle DPC\] and\[\angle BQC\].
A)
\[40{}^\circ ,\,50{}^\circ \]
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B)
\[50{}^\circ ,\,60{}^\circ \]
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C)
\[55{}^\circ ,\,25{}^\circ \]
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D)
\[55{}^\circ ,\,35{}^\circ \]
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E)
None of these
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Five years ago, A was three times as old as B and ten years later A shall be twice as old as B. What are the present ages of A and B.
A)
A = 15 years, B = 45 years
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B)
A = 10 years, B = 40 years
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C)
A = 20 years, B = 50 years
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D)
A = 50 years, B = 20 years
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E)
None of these
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If code for 'TAMILNADU' = ?UDANLIMAT?, then code for 'KARNATAKA' = '?'
A)
AAKTANRAK
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B)
AKTAANRAK
done
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C)
AKATANRAK
done
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D)
ATKAANRAK
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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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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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A bag contains 8 red, 2 black and 5 white balls. One ball is drawn at random. What is the probability that the ball drawn is not black?
A)
\[\frac{2}{15}\]
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B)
\[\frac{3}{15}\]
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C)
\[\frac{8}{15}\]
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D)
\[\frac{1}{3}\]
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E)
None of these
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If a = 4.965, b = 2.343 and c = 2.622 then the value of \[{{a}^{3}}-{{b}^{3}}-{{c}^{3}}-3abc\] is
A)
\[-\,2\]
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B)
\[-\,1\]
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C)
0
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D)
9.93
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E)
None of these
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An aeroplane leaves an airport and flies due north at a speed of 1000 km/h. At same time, another plane flies due west at a speed of 1200 km/h from the same place. The approximate distance between the two planes after 1.5 hours will be:
A)
2400 km
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B)
2520 km
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C)
2343 km
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D)
2434 km
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E)
None of these
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Robert tosses a coin three times. The probability that he gets atleast two heads is:
A)
\[\frac{1}{2}\]
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B)
\[\frac{1}{3}\]
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C)
\[\frac{1}{4}\]
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D)
\[\frac{1}{5}\]
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E)
None of these
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Out of four persons, B is taller than C, A is taller than D but not as tall as C. Who among them is the tallest?
A)
A
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B)
B
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C)
C
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D)
D
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E)
None of these
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If the number 117A49 is completely divisible by 7, then the smallest natural number in place of A will be:
A)
2
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B)
5
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C)
6
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D)
7
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E)
None of these
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The ratio of the corresponding sides of two similar squares is 1 : 4. What is the ratio of the area of the smaller square to the area of the larger square?
A)
1 : 2
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B)
1 : 4
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C)
1 : 8
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D)
1 : 16
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E)
None of these
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Which of the following formula is correct for the computation of mode for a continuous frequency distribution?
A)
\[l+\frac{f-{{f}_{1}}}{2f-{{f}_{1}}-{{f}_{2}}}\times h\]
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B)
\[l-\frac{f-{{f}_{1}}}{2L-{{f}_{1}}-{{f}_{2}}}\times h\]
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C)
\[l-\frac{f-{{f}_{1}}}{2L+{{f}_{1}}-{{f}_{2}}}\times h\]
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D)
\[l+\frac{f-{{f}_{1}}}{{{f}_{1}}-{{f}_{2}}}\times h\]
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E)
None of these
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Direction: Refer to the following table. Read the table answer the questions. Food Grain Production in various state of a Country in 1999 (in lakh tons)
State Rice Wheat Jawar Pulses Others P 45 103 - 27 29 Q 48 86 73 19 15 R 59 32 67 14 31 S 41 37 59 21 15 T 37 22 41 13 11 U 68 15 12 - 18 V 57 8 7 12 10 W 38 28 31 22 45
Which State had the highest grain production?
A)
P
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B)
Q
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C)
R
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D)
S
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E)
None of these
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View Answer play_arrow
Direction: Refer to the following table. Read the table answer the questions. Food Grain Production in various state of a Country in 1999 (in lakh tons)
State Rice Wheat Jawar Pulses Others P 45 103 - 27 29 Q 48 86 73 19 15 R 59 32 67 14 31 S 41 37 59 21 15 T 37 22 41 13 11 U 68 15 12 - 18 V 57 8 7 12 10 W 38 28 31 22 45
What was the proportion of rice production to wheat production in the country?
A)
1 : 1
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B)
0.8 : 1
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C)
1.2 : 1
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D)
2 : 1
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E)
None of these
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Direction: Refer to the following table. Read the table answer the questions. Food Grain Production in various state of a Country in 1999 (in lakh tons)
State Rice Wheat Jawar Pulses Others P 45 103 - 27 29 Q 48 86 73 19 15 R 59 32 67 14 31 S 41 37 59 21 15 T 37 22 41 13 11 U 68 15 12 - 18 V 57 8 7 12 10 W 38 28 31 22 45
Jawar was the most important food grain in the State/States
A)
O, R, S
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B)
Q
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C)
R, S
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D)
R, S, T
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E)
None of these
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Direction: Refer to the following table. Read the table answer the questions. Food Grain Production in various state of a Country in 1999 (in lakh tons)
State Rice Wheat Jawar Pulses Others P 45 103 - 27 29 Q 48 86 73 19 15 R 59 32 67 14 31 S 41 37 59 21 15 T 37 22 41 13 11 U 68 15 12 - 18 V 57 8 7 12 10 W 38 28 31 22 45
State P alone accounted for approximately what percentage of wheat production in the country?
A)
73%
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B)
50%
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C)
41%
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D)
30%
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E)
None of these
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The value of \[(0.34\overline{67}+0.13\overline{33})\] is
A)
0.48
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B)
\[0.48\overline{01}\]
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C)
\[0.\overline{48}\]
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D)
\[0.4\overline{8}\]
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E)
None of these
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