The condition that the roots of the equation \[a{{x}^{2}}+bx\text{ +}c=0\]be such that one root times the other is
A)
\[n{{c}^{2}}=ab{{(n+1)}^{2}}\]
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B)
\[n{{a}^{2}}=bc{{(n+1)}^{2}}\]
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C)
\[n{{b}^{2}}=ca{{(n+1)}^{2}}\]
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D)
None of these
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The sum of \[(n-1)\] terms of\[1+\left( 1+3 \right)+\left( 1+3+5 \right)+\left( 1+3+5+7 \right)+\] ..... is
A)
\[\frac{n(n+1)(2n+1)}{6}\]
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B)
\[\frac{n(n-1)(2n-1)}{6}\]
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C)
\[{{\left( \frac{n{{(n+1)}^{{}}}}{2} \right)}^{2}}\]
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D)
\[\left( \frac{n{{(n+1)}^{{}}}}{2} \right)\]
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The general term in the expansion of \[{{\left( 1-2x \right)}^{3/4}}\]is
A)
\[\frac{-{{3}^{r}}}{{{2}^{r}}r!}{{x}^{r}}\]
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B)
\[\frac{-{{3}^{r}}}{{{2}^{r}}(2r)!}{{x}^{r}}\]
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C)
\[\frac{-{{3}^{r}}}{{{2}^{r}}2r!}{{x}^{2}}\]
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D)
None of these
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The value of \[\underset{x\to 0}{\mathop{\lim }}\,\,\,{{\left( \frac{1+5{{x}^{2}}}{1+3{{x}^{2}}} \right)}^{1/{{x}^{2}}}}\] is
A)
\[{{e}^{2}}\]
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B)
e
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C)
\[{{e}^{-1}}\]
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D)
None of these
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The slope of a non vertical line passing through the point (2, 3) and making intercept of length 2 units between the lines y + 2x = 3 and y + 2x = 5 must be
A)
\[3/2\]
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B)
\[-3/2\]
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C)
\[-3/4\]
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D)
None of these
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The area of the triangle formed by the lines joining the vertex of the parabola \[{{x}^{2}}=12y\] to the end of latus rectum is
A)
12
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B)
18
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C)
\[6\sqrt{3}\]
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D)
None of these
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A person can kill a bird with probability 3/4. He tries 5 times, what is the probability that he may not kill the bird?
A)
\[\frac{1023}{1024}\]
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B)
\[\frac{1}{1024}\]
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C)
\[\frac{781}{1024}\]
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D)
\[\frac{243}{1024}\]
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If the standard deviation of 0, 1, 2, 3,..., 9 is k, then the standard deviation of 10, 11,12, ...., 19 is_____.
A)
K
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B)
\[10+K\]
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C)
\[K+\sqrt{10}\]
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D)
10 K
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Which of the following is a statement?
A)
May you live long!
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B)
Hurrah! we have won the match
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C)
What a great fall it is !
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D)
The quadratic equation \[{{x}^{2}}-5x+6=0\]has two real roots.
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The function\[{{\log }_{10}}[(1-{{\log }_{10}}({{x}^{2}}-5x+16)]\], has domain
A)
\[(0,2)\cup (2,\infty )\]
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B)
\[(1,4)\]
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C)
\[(2,3)\]
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D)
all x
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A, B, C are angles of a triangle, such that \[{{\sin }^{2}}A+{{\sin }^{2}}B+{{\sin }^{2}}C=\] constant, find \[\frac{dA}{dB}\]
A)
\[\frac{\sin A}{\sin (2A+B)}\]
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B)
\[\frac{-\operatorname{sinB}}{\sin (2A+B)}\]
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C)
\[\frac{cosB}{\sin (2A+B)}\]
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D)
\[\frac{-cosB}{\sin (2A+B)}\]
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What is the locus of point of intersection of tangents of \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] drawn at the extremities of a chord subtending \[90{}^\circ \] at origin is
A)
\[\frac{{{x}^{2}}}{{{a}^{4}}}+\frac{{{y}^{2}}}{{{b}^{4}}}=\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}\]
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B)
\[\frac{{{x}^{2}}}{{{a}^{4}}}+\frac{{{y}^{2}}}{{{b}^{4}}}={{\left( \frac{1}{{{a}^{{}}}}+\frac{1}{b} \right)}^{2}}\]
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C)
\[{{a}^{2}}{{x}^{2}}+{{b}^{2}}{{y}^{2}}{{({{a}^{2}}+{{b}^{2}})}^{2}}\]
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D)
\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}+{{b}^{2}}\]
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The number of ways in which 6 different balls can be put in two boxes of different sizes so that no box remain empty is
A)
64
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B)
62
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C)
36
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D)
None of these
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What is the remainder when 496 is divided by 6?
A)
0
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B)
2
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C)
3
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D)
4
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Find the number of positive integers greater than 6000 and less than 7000 which are divisible by 5, provided that no digit is to be repeated.
A)
111
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B)
112
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C)
113
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D)
None of these
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Statement I : For every natural number \[n\ge 2,\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+.....+\frac{1}{\sqrt{n}}>\sqrt{n}\] Statement II: For every natural number \[n\ge 2,\sqrt{n(n+1)}<n+1\]
A)
Statement I is true, Statement II is true; Statement II is a correct explanation for Statement
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B)
Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement .I
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C)
Statement I is true; Statement II is false
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D)
Statement I is false; Statement II is true
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If the coefficients of \[{{2}^{nd}},\text{ }{{3}^{rd}}\]and \[{{4}^{th}}\] terms in the expansion of (1 + x)" are in A.P., then value of n is
A)
2
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B)
7
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C)
11
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D)
14
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The most general solutions of the equation secx \[x-1=\left( \sqrt{2-1} \right)\] tanx are given by
A)
\[n\pi +\frac{\pi }{8}\]
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B)
\[2n\pi ,2n\pi +\frac{\pi }{4}\]
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C)
\[2n\pi \]
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D)
None of these
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The domain of the function \[f(x)\frac{1}{\sqrt{{{[x]}^{2}}-[x]-6}}\]is
A)
\[(-\infty ,-2)\cup [4,\infty )\]
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B)
\[(-\infty ,-2)\cup [4,\infty )\]
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C)
\[(-\infty ,-2)\cup [4,\infty )\]
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D)
None of these
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A point equidistant from the lines 4x + 3y + 10 = 0, 5x - 12y + 26 = 0 and 7x + 24y - 50 = 0 is
A)
(1,-1)
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B)
(1, 1)
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C)
(0, 0)
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D)
(0,1)
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