The graphical representation of the equation\[f(x)=2{{x}^{2}}+3x+5\] is:
A)
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B)
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C)
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D)
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E)
None of these
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The zeroes of the polynomials \[f(x)={{x}^{2}}+x-6\] is ________.
A)
\[\left( 1,-\,3 \right)\]
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B)
\[\left( 2,-\,3 \right)\]
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C)
\[\left( 2,-\,2 \right)\]
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D)
\[\left( 3,-\,3 \right)\]
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E)
None of these
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If a and b are the roots of the given equation\[12{{x}^{2}}+7x-10=0,\] then the value of a + b is _______.
A)
\[0\]
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B)
\[\frac{7}{12}\]
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C)
\[\frac{-\,7}{12}\]
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D)
\[\frac{12}{7}\]
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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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What types of solution have the pair of linear equation \[3x+4y=7\] and \[4x-3y=7\] ?
A)
Unique solution
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B)
No solution
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C)
Infinitely many solution
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D)
All of these
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E)
None of these
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The value of m for which the given system of equation \[mx-5y=10\] and \[8x+9y=24\] has no solution.
A)
\[\left( m\ne \frac{40}{9}\And m=\frac{10}{3} \right)\]
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B)
\[\left( m=-\frac{40}{9}\And m\ne \frac{10}{3} \right)\]
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C)
\[\left( m=\frac{40}{9}\And m=\frac{10}{3} \right)\]
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D)
\[\left( m\ne \frac{40}{9}\And m\ne \frac{10}{3} \right)\]
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E)
None of these
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Solve the system of equations: \[\begin{align} & 4x-7y+28=0 \\ & 5x-7y+9=0 \\ \end{align}\]
A)
\[x=19\,\,\And \,\,y=3\]
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B)
\[x=2\,\,\And \,\,y=\frac{104}{7}\]
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C)
\[x=19\,\,\And \,\,y=\frac{104}{7}\]
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D)
\[x=7\,\,\And \,\,y=7\]
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E)
None of these
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Find the value of \[{{\log }_{2}}8\] is.
A)
3
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B)
2
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C)
1
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D)
4
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E)
None of these
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The number of positive integers having characteristic 2 and base 3 is.
A)
18
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B)
9
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C)
27
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D)
36
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E)
None of these
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If the 15th term of an AP is 45 and 20th term is 60, and then find the 30th term of the AP.
A)
70
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B)
90
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C)
110
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D)
120
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E)
None of these
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Find the mean of the data: 2, 4, 10, 12, 18, 16, 14, 20
A)
12
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B)
14
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C)
15
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D)
18
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E)
None of these
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The score of 10 students of a class test is given as 44, 54, 46, 63, 55, 42, 34, 48, 70, 38. Calculate the median of the data.
A)
47
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B)
46
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C)
48
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D)
44
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E)
None of these
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Find the mean of the data:
\[{{x}_{i}}=\] 3 9 17 23 27 \[{{f}_{i}}=\] 8 10 12 9 5
A)
14.2
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B)
15
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C)
15.5
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D)
13.6
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E)
None of these
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The distance between two points A(2, 1) and\[B\,\,\left( 4,-\,3 \right)\] is
A)
\[3\,\sqrt{5}\,units\]
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B)
\[2\,\sqrt{5}\,units\]
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C)
\[\sqrt{5}\,units\]
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D)
\[4\,\sqrt{5}\,units\]
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E)
None of these
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The point \[\left( 2,-\,5 \right)\] lies in which one of the following quadrant?
A)
1st
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B)
2nd
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C)
3rd
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D)
4th
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E)
None of these
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The co-ordinate of the point which divides the line Segment joining the points \[\left( 5,-\,2 \right)\] and (9, 6) internally in the ratio 1 : 2 is:
A)
\[\left( \frac{19}{3},\frac{2}{3} \right)\]
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B)
\[\left( \frac{1}{3},\frac{2}{3} \right)\]
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C)
\[\left( \frac{1}{3},\frac{22}{3} \right)\]
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D)
\[\left( \frac{13}{3},\frac{22}{3} \right)\]
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E)
None of these
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The co-ordinates of one end of a diameter of a circle are\[\left( 5,-\,7 \right)\]. If co-ordinates of the centre be (7, 3) then the co-ordinate of the other end of the diameter is.
A)
(9, 1)
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B)
(9, 3)
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C)
(9, 13)
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D)
(4, 13)
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E)
None of these
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The angles of a triangle are in the ratio 2 : 3 : 7. Find the measure of largest angle of the triangle.
A)
\[105{}^\circ \]
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B)
\[45{}^\circ \]
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C)
\[30{}^\circ \]
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D)
\[85{}^\circ \]
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E)
None of these
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Which one of the following options is a quadratic equation?
A)
\[{{x}^{2}}+\frac{1}{{{x}^{2}}}=2\]
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B)
\[{{y}^{2}}+2\,\sqrt{y}-3=0\]
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C)
\[3{{y}^{2}}-4y+2=2{{y}^{2}}-2y-4\]
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D)
\[x+\frac{1}{x}=4{{x}^{8}}\]
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E)
None of these
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Find the value of a and b if y = 2 and y = 3 are roots of equation \[4{{y}^{2}}-3ay+2b=0.\]
A)
\[b=12,a=\frac{20}{3}\]
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B)
\[a=12,b=20\]
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C)
\[a=20,b=4\]
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D)
\[a=4,b=4\]
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E)
None of these
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The quadrilateral which is formed by joining the mid points of a given quadrilateral is always _______.
A)
A parallelogram
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B)
A trapezium
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C)
A rhombus
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D)
A rectangle
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E)
None of these
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In the figure given below \[QN\parallel LM\]
A)
5, 11
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B)
5, 8
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C)
8, 5
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D)
18, 5
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E)
None of these
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The length of tangent from point P to a circle of radius 5 cm, is 12 cm. The distance P from the centre of circle is_______.
A)
17 cm
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B)
14 cm
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C)
13 cm
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D)
7 cm
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E)
None of these
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In the figure given below the value of y is_______.
A)
\[135{}^\circ \]
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B)
\[45{}^\circ \]
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C)
\[130{}^\circ \]
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D)
\[115{}^\circ \]
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E)
None of these
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In the figure given below 0 is the centre of the circle and \[\angle PQR=40{}^\circ \]. Find the value of y
A)
\[100{}^\circ \]
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B)
\[120{}^\circ \]
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C)
\[140{}^\circ \]
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D)
\[80{}^\circ \]
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E)
None of these
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The circumcenter of a triangle whose vertices are \[\left( -1,\text{ }0 \right),\] \[(7,-\,6)\] and \[\left( -\,2,3 \right)\] is__.
A)
\[\left( 5,0 \right)\]
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B)
\[\left( 3,-\,3 \right)\]
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C)
\[\left( -\,3,3 \right)\]
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D)
\[\left( 4,\text{3} \right)\]
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E)
None of these
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The coordinate of centroid of a triangle whose vertices are \[\left( 3,2 \right),\] \[\left( -\,3,-\,1 \right)\] and \[\left( 0,-\,1 \right)\] is _______.
A)
\[\left( 0,0 \right)\]
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B)
\[\left( 0,3 \right)\]
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C)
\[\left( 3,0 \right)\]
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D)
\[\left( 0,-\,5 \right)\]
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None of these
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The distance travelled by the tip of minute hand in 10 minutes when the length of minute hand is 20 cm, is________.
A)
201.95 m
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B)
20.9 cm
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C)
2.095 cm
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D)
209.5 cm
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E)
None of these
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If \[\sec 60{}^\circ +\tan 30{}^\circ =p\] then the value of p is _______.
A)
3.265
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B)
2.578
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C)
1.896
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D)
2.111
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None of these
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The value of \[\frac{{{\sin }^{2}}45{}^\circ +{{\cos }^{2}}45{}^\circ }{{{\sin }^{2}}30{}^\circ }\] is _______.
A)
\[\frac{1}{2}\]
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B)
\[\frac{1}{4}\]
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C)
\[4\]
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D)
\[1\]
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E)
None of these
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If \[2\sin 2\theta =\sqrt{3}\] then the value of \[\theta \] is_______.
A)
\[\frac{\pi }{3}\]
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B)
\[\frac{\pi }{6}\]
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C)
\[\frac{\pi }{4}\]
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D)
\[\frac{\pi }{2}\]
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E)
None of these
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If \[x\cos 60{}^\circ .\sin 30{}^\circ =\tan 30{}^\circ .\cot 60{}^\circ \] then the value of x is ________.
A)
\[\frac{1}{2}\]
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B)
\[\frac{1}{4}\]
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C)
\[\frac{4}{3}\]
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D)
2
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E)
None of these
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A tree is broken at a height of 40 m from the horizontal ground in such a way that its tip touches the ground with an angle of \[60{}^\circ \]. Find the distance of tip from the base to the point where it touches the ground.
A)
23.09 m
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B)
18.67 m
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C)
10.372 m
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D)
10.432 m
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E)
None of these
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Find the distance PQ, if PR and QS are of equal heights.
A)
102.37
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B)
105.55
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C)
103.8
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D)
104.99
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E)
None of these
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Find the mean of the following data:
Class Interval Frequency 0 - 10 16 10 - 20 12 20 - 30 9 30 - 40 6 40 - 50 7
A)
20.2
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B)
21.3
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C)
45.5
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D)
43.2
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E)
None of these
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Find the area of the triangle whose base = 25 cm and height = 10.8 cm.
A)
\[125\text{ }c{{m}^{3}}\]
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B)
\[135\text{ }c{{m}^{2}}\]
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C)
\[124\text{ }c{{m}^{2}}\]
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D)
\[199\text{ }c{{m}^{2}}\]
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E)
None of these
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A chord of a circle of radius 14 cm makes a right angle at the centre. Find the area of the major segments of the circle.
A)
\[590\,\,c{{m}^{2}}\]
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B)
\[560\,\,c{{m}^{2}}\]
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C)
\[595\,c{{m}^{3}}\]
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D)
\[995\,\,c{{m}^{2}}\]
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E)
None of these
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A solid toy is in the form of a right circular cylinder with a hemisphere at one end and a cone at the other end (as shown in the figure). Their common diametre is 4.2 cm. The height of the cylindrical land conical part are 12 cm and 7 cm respectively. Find the volume of the given toy.
A)
\[217.865\,\,c{{m}^{3}}\]
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B)
\[957.532\,\,c{{m}^{3}}\]
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C)
\[125.632\,\,c{{m}^{3}}\]
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D)
\[669.157\,\,c{{m}^{3}}\]
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E)
None of these
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From a solid cylinder whose height is 12 cm and diametre 10 cm a conical cavity of same height and of same diametre is curved out. Find the total surface area of the remaining Solid.
A)
\[670\,\,c{{m}^{2}}\]
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B)
\[770\,\,c{{m}^{3}}\]
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C)
\[660\,\,c{{m}^{2}}\]
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D)
\[780\,\,c{{m}^{2}}\]
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E)
None of these
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Find the probability of getting head, if the coin is two headed.
A)
\[1\]
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B)
\[\frac{1}{2}\]
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C)
\[\frac{1}{3}\]
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D)
\[\frac{1}{4}\]
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E)
None of these
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