If \[\mathbf{n}\left( \mathbf{U} \right)=\mathbf{700},\mathbf{n}\left( \mathbf{A} \right)=\mathbf{200},\mathbf{n}\left( \mathbf{B} \right)=\mathbf{300}\], and \[\mathbf{n}\left( \mathbf{A}\cap \mathbf{B} \right)=\mathbf{100}\], then \[\mathbf{n}\left( \mathbf{A}'\cap \mathbf{B}' \right)=\]
A)
400
done
clear
B)
350
done
clear
C)
300
done
clear
D)
600
done
clear
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If \[\mathbf{A}=\left\{ \mathbf{1},\mathbf{2},\mathbf{3} \right\},\mathbf{B}=\left\{ \mathbf{3},\mathbf{4} \right\}\]and \[\mathbf{C}=\left\{ \mathbf{4},\mathbf{5},\mathbf{6} \right\}\]then \[\left( \mathbf{A}\times \mathbf{B} \right)\cap \left( \mathbf{B}\times \mathbf{C} \right)\]is equal to
A)
\[\left\{ \left( 1,4 \right),\left( 2,3 \right) \right\}\]
done
clear
B)
\[\left\{ \left( 4,4 \right),\left( 3,2 \right) \right\}\]
done
clear
C)
\[\left\{ \left( 3,5 \right),\left( 3,4 \right) \right\}\]
done
clear
D)
\[\left\{ \left( 3,4 \right) \right\}\]
done
clear
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If A and B are two independent events such that \[\mathbf{P}\left( A \right)=\frac{3}{10},\mathbf{P}\left( \mathbf{B}' \right)=\mathbf{x}\]and \[\mathbf{P}\left( \mathbf{A}\cup \mathbf{B} \right)=\frac{8}{10}\], then x is equal to
A)
\[\frac{2}{7}\]
done
clear
B)
\[\frac{3}{7}\]
done
clear
C)
\[\frac{4}{7}\]
done
clear
D)
\[\frac{5}{7}\]
done
clear
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The sum of the series: \[1+\frac{3}{2}+\frac{5}{4}+\frac{7}{6}+......\infty \]is equal to
A)
3e
done
clear
B)
2e
done
clear
C)
e
done
clear
D)
5e
done
clear
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The 4th term from the end in the expansion of\[{{\left( \mathbf{x}+\frac{2}{x} \right)}^{9}}\]
A)
\[\frac{5376}{{{x}^{4}}}\]
done
clear
B)
\[\frac{{{x}^{3}}}{5376}\]
done
clear
C)
\[\frac{5376}{{{x}^{3}}}\]
done
clear
D)
\[\frac{{{x}^{4}}}{5376}\]
done
clear
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Multiplicative inverse of \[\frac{3+4i}{4-4i}\]is
A)
\[\frac{8}{25}-\frac{31}{25}i\]
done
clear
B)
\[\frac{-8}{25}-\frac{31}{25}i\]
done
clear
C)
\[\frac{-8}{25}+\frac{31}{25}i\]
done
clear
D)
None of these
done
clear
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If \[\mathbf{cos}\left( \mathbf{x}-\mathbf{y} \right),\mathbf{cosx}\] and \[\mathbf{cos}\left( \mathbf{x}+\mathbf{y} \right)\]are in H.P. then \[cosx.\sec \left( \frac{y}{2} \right)\]is equal to
A)
\[\pm \sqrt{3}\]
done
clear
B)
\[\pm \sqrt{2}\]
done
clear
C)
\[\pm 2\]
done
clear
D)
\[\pm 1\]
done
clear
View Answer play_arrow
\[\underset{x\to \infty }{\mathop{\lim }}\,\frac{\mathbf{2}{{\mathbf{x}}^{\mathbf{3}}}-\mathbf{4x}+\mathbf{7}}{3{{x}^{3}}+5{{x}^{2}}-4}\]Is equal to
A)
\[\frac{3}{2}\]
done
clear
B)
\[\frac{2}{3}\]
done
clear
C)
0
done
clear
D)
¥
done
clear
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If\[{{x}^{2}}+{{y}^{2}}=1\], then
A)
\[y.y''-2{{\left( y' \right)}^{2}}+1=0\]
done
clear
B)
\[y.y''+{{(y')}^{2}}+1=0\]
done
clear
C)
\[y.y''+{{\left( y' \right)}^{2}}-1=0\]
done
clear
D)
\[y.y''+2{{\left( y' \right)}^{2}}+1=0\]
done
clear
View Answer play_arrow
The straight line \[\mathbf{x}+\mathbf{y}=\mathbf{0},\mathbf{3x}+\mathbf{y}-\mathbf{4i}=\mathbf{0}\]and \[\mathbf{x}+\mathbf{3y}-\mathbf{4}=\mathbf{0}\]form a triangle which is:
A)
Right angled triangle
done
clear
B)
equilateral triangle
done
clear
C)
Isosceles triangle
done
clear
D)
scalene triangle
done
clear
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The centroid of a triangle ABC is at the point\[\left( \mathbf{1},\mathbf{2},\mathbf{3} \right)\].If the coordinate of A and B are\[\left( \mathbf{3},-\mathbf{5},-\mathbf{7} \right)\]and\[\left( \mathbf{1},\mathbf{7},\mathbf{6} \right)\], respectively then co-ordinate of C.
A)
\[(-1,4,10)\]
done
clear
B)
\[\left( 4,-1,10 \right)\]
done
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C)
\[\left( 10,-1,4 \right)\]
done
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D)
\[\left( 1,4,10 \right)\]
done
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View Answer play_arrow
The vertices of triangle ABC be \[\mathbf{A}\left( \mathbf{0},\mathbf{0},\mathbf{6} \right),\mathbf{B}\left( \mathbf{0},\mathbf{4},\mathbf{0} \right)\]and \[\left( \mathbf{6},\mathbf{0},\mathbf{9} \right)\] then length of medians of triangles be:
A)
\[6,6,6\]
done
clear
B)
\[6,\sqrt{34},6\]
done
clear
C)
\[7,\sqrt{34},7\]
done
clear
D)
None of these
done
clear
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The centre of the circle passing through the point \[\left( \mathbf{0},\mathbf{1} \right)\] and touching the curve \[\mathbf{y}={{\mathbf{x}}^{\mathbf{2}}}\] at \[\left( \mathbf{2},\mathbf{4} \right)\]is:
A)
\[\left( \frac{-16}{5},\frac{27}{10} \right)\]
done
clear
B)
\[\left( \frac{-16}{7},\frac{53}{10} \right)\]
done
clear
C)
\[\left( \frac{-16}{5},\frac{53}{10} \right)\]
done
clear
D)
\[\left( \frac{16}{5},\frac{-53}{10} \right)\]
done
clear
View Answer play_arrow
The point of intersection of the tangents at the ends of the latus rectum of the parabola \[{{\mathbf{y}}^{\mathbf{2}}}=\mathbf{4x}\] is
A)
\[\left( 1,0 \right)\]
done
clear
B)
\[\left( 0,1 \right)\]
done
clear
C)
\[\left( 0,-1 \right)\]
done
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D)
\[\left( -1,0 \right)\]
done
clear
View Answer play_arrow
If \[\mathbf{tanA}=\left( \frac{1-\mathbf{cosB}}{\sin B} \right)\]then tan2A is equal to:
A)
\[tanB\]
done
clear
B)
\[tan\frac{B}{2}\]
done
clear
C)
\[\frac{\tan B}{2}\]
done
clear
D)
None of these
done
clear
View Answer play_arrow
If one root of a quadratic equation is \[\frac{-1+\sqrt{3}}{2}\] then the sum of the roots is:
A)
\[-i\]
done
clear
B)
\[i\]
done
clear
C)
\[\sqrt{3}\]
done
clear
D)
\[\frac{\sqrt{3}}{2}\]
done
clear
View Answer play_arrow
The variance of n natural is
A)
\[\frac{{{n}^{2}}+1}{12}\]
done
clear
B)
\[\frac{\left( n+1 \right)\left( 2n+1 \right)}{6}\]
done
clear
C)
\[\frac{{{n}^{2}}-1}{12}\]
done
clear
D)
None of these
done
clear
View Answer play_arrow
The A.M. of the series \[\mathbf{1},\mathbf{2},\mathbf{4},\mathbf{8},\mathbf{16}....{{\mathbf{2}}^{\mathbf{4}}}\]is
A)
\[\frac{{{2}^{n}}-1}{n}\]
done
clear
B)
\[\frac{{{2}^{n+1}}-1}{n+1}\]
done
clear
C)
\[\frac{{{2}^{n}}+1}{n}\]
done
clear
D)
\[\frac{{{2}^{n}}-1}{n+1}\]
done
clear
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The equation of straight Sine which makes an angle of \[\mathbf{1}{{\mathbf{5}}^{{}^\circ }}\] with the positive direction of x-axis, cuts an intercept of the length 4 on the negative.
A)
\[\left( 2-\sqrt{3} \right)x-y+4=0\]
done
clear
B)
\[(2-\sqrt{3})x+y-4=0\]
done
clear
C)
\[\left( 2-\sqrt{3} \right)x+y+4=0\]
done
clear
D)
\[(2-\sqrt{3})x-y-4=0\]
done
clear
View Answer play_arrow
If tan \[\theta =\frac{b}{a}\]then the value of \[a.cos2\theta +b.sin2\theta \] is
A)
a
done
clear
B)
b
done
clear
C)
\[a-b\]
done
clear
D)
\[a+b\]
done
clear
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