Consider the relation \[R=\left\{ \left( a,b \right),\left( a,c \right),\left( a,a \right),\left( c,c \right) \right\}\]on the set \[A=\left\{ a,\text{ }b,\text{ }c,\text{ }d \right\}\]Minimum number of elements of A x A which must be adjoined to R in order to make R an equivalence relation is
A)
4
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B)
5
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C)
6
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D)
7
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For any complex number z, the minimum value of \[\left| z \right|+\left| z-1 \right|\]is
A)
0
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B)
\[1/2\]
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C)
\[3/2~\]
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D)
\[1\]
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Two opposite vertices of a square are A(0, 4) and C(2, 8), then the other vertex may be
A)
\[\left( 3,5 \right)\]
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B)
\[\left( 1,7 \right)\]
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C)
\[\left( -3,5 \right)\]
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D)
None of these
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The probability of drawing a white ball from a bag containing 3 black balls and 4 white balls, is
A)
\[1/7~\]
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B)
\[3/7~\]
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C)
\[4/7~\]
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D)
None of these
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The solution set of \[\xrightarrow[X+1]{{{X}^{2}}-3x+4}1,X\in R\]
A)
\[(-1,1)\cup (3,+\infty )\]
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B)
\[(3,+\infty )\]
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C)
\[[-1,1]\cup (3,+\infty )\]
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D)
None of these
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The ratio between the sum of n terms of two A.P.'s is (3n + 8) : (7n +15) then the ratio between their 12th terms is
A)
5:7
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B)
12 : 11
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C)
11 : 12
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D)
7 16
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\[{{(r+1)}^{th}}\]term in the expansion of \[{{(1-x)}^{-4}}\] will be
A)
\[\frac{\left( r+1 \right)\left( r+2 \right)\left( r+3 \right)}{6}{{x}^{r}}\]
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B)
\[\frac{\left( r+2 \right)\left( r+3 \right)}{2}{{x}^{r}}\]
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C)
\[\frac{{{x}^{r}}}{r!}\]
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D)
None of these
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The directrix of the parabola \[{{y}^{2}}+4y+8x=0\]is
A)
x = 2
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B)
x = 3/2
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C)
x = 5/2
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D)
None of these
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The variance of 6, 8, 10, 12, 14 is
A)
16
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B)
8
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C)
12
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D)
1
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Let \[f(x)=\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{x}^{2n}}-1}{{{x}^{2n}}+1},then\]
A)
\[f(x)=1,for|X|\,\,\,>1\]
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B)
\[f(x)=-2,for|X|\,\,\,<1\]
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C)
f (x) is not defined for any value of x
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D)
\[f(x)=1,for|X|=1\]
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Negation of the Proposition: If we control population growth, we prosper is ______.
A)
We control population but we do not prosper
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B)
We do not control population, but we prosper
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C)
If we do not control population growth, we prosper
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D)
If we do not 'control population, we do not prosper
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Total number of positive integral solutions of \[15<{{x}_{1}}+{{x}_{2}}+{{x}_{3}}\le 20,\] is equal to
A)
1245
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B)
685
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C)
1025
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D)
None of these
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The expression \[\frac{\cos 6x+6\cos 4x+15\cos 2x+10}{\cos 5x+5\cos 3x+10\cos x}\]
A)
\[\cos 2x\]
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B)
\[2\cos x\]
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C)
\[{{\cos }^{2}}x\]
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D)
\[\cos x\]
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The owner of a local jewellery store hired 3 watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave 1/2 of the diamonds he had then, and more besides. He escaped with one diamond. How many did he steel originally?
A)
40
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B)
36
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C)
25
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D)
None of these
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If A = {2, 3, 4, 8, 10), B = {3, 4, 5, 10, 12}, C = {4, 5, 6, 12, 14}, then \[\left( A\cap B \right)\cup (A\cap C)\]is equal to,
A)
{3, 4, 10}
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B)
{2, 8, 10}
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C)
{4, 5, 6}
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D)
{3, 5, 14}
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The domain for which the functions defined by \[\operatorname{f}\left( x \right) = 3{{x}^{2}} -1\]Band g(x) = 3 + x ar equal is
A)
\[\left\{ -1,\frac{4}{3} \right\}\]
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B)
\[\left\{ -1,-\frac{4}{3} \right\}\]
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C)
\[\left\{ 1,\frac{4}{3} \right\}\]
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D)
\[\left\{ 1,-\frac{4}{3} \right\}\]
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The point represented by the complex number 2 - i is rotated about origin through an angle \[\frac{\pi }{2}\] in the clockwise direction, the new position of point is
A)
\[1+2i~\]
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B)
\[-1-\text{ }2i~\]
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C)
\[2+\text{i}~\]
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D)
\[-1+2i\]
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150 workers were engaged to finish a piece of work in a certain number of day; 4 workers dropped the second day, 4 more workers dropped the third day and on. It takes eight more days to finish the work now. The number of days in which the work was completed is
A)
15
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B)
20
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C)
25
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D)
30
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If the equations \[3{{x}^{2}}-2x+p=0\,\,and\,\,6{{x}^{2}}-17x+12=0\] have a common root, then the value of p is
A)
\[\frac{15}{3},\frac{8}{3}\]
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B)
\[-\frac{15}{4},-\frac{8}{3}\]
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C)
\[\frac{15}{7},\frac{8}{3}\]
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D)
\[-\frac{15}{4},\frac{8}{3}\]
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There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which hall can be illuminated.
A)
\[{{2}^{10}}-2\]
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B)
\[{{2}^{10}}-1~\]
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C)
\[{{2}^{10}}\text{+ }1~\]
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D)
None of these
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