-
question_answer1)
The roots of the equation \[a({{x}^{2}}+1)-({{a}^{2}}+1)x=0\] are
A)
\[a,\frac{1}{a}\] done
clear
B)
a, 2a done
clear
C)
\[a,\frac{1}{2a}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer2)
The roots of the equation \[{{x}^{4}}-8{{x}^{2}}-9=0\] are
A)
\[\pm 3,\ \pm 1\] done
clear
B)
\[\pm 3,\ \pm i\] done
clear
C)
\[\pm 2,\ \pm i\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer3)
The roots of the equation \[i{{x}^{2}}-4x-4i=0\] are
A)
\[-2i\] done
clear
B)
\[2i\] done
clear
C)
\[-2i,-2i\] done
clear
D)
\[2i,2i\] done
clear
View Solution play_arrow
-
question_answer4)
The roots of the equation \[{{x}^{2/3}}+{{x}^{1/3}}-2=0\] are [UPSEAT 2004]
A)
1, 4 done
clear
B)
\[1,-4\] done
clear
C)
\[1,-8\] done
clear
D)
1, 8 done
clear
View Solution play_arrow
-
question_answer5)
If \[x=2+{{2}^{2/3}}+{{2}^{1/3}},\]then \[{{x}^{3}}-6{{x}^{2}}+6x=\] [MNR 1985]
A)
3 done
clear
B)
2 done
clear
C)
1 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer6)
The number of roots of the quadratic equation \[8{{\sec }^{2}}\theta -6\sec \theta +1=0\] is [Pb. CET 1989, 94]
A)
Infinite done
clear
B)
1 done
clear
C)
2 done
clear
D)
0 done
clear
View Solution play_arrow
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question_answer7)
The roots of the equation \[\sqrt{3x+1}+1=\sqrt{x}\] are
A)
0 done
clear
B)
1 done
clear
C)
0, 1 done
clear
D)
None done
clear
View Solution play_arrow
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question_answer8)
The number which exceeds its positive square root by 12 is
A)
9 done
clear
B)
16 done
clear
C)
25 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer9)
The roots of the equation \[{{3}^{2x}}-{{10.3}^{x}}+9\]=0 are
A)
1, 2 done
clear
B)
0, 2 done
clear
C)
0, 1 done
clear
D)
1, 3 done
clear
View Solution play_arrow
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question_answer10)
If \[{{x}^{2/3}}-7{{x}^{1/3}}+10=0,\] then \[x=\] [BIT Ranchi 1992]
A)
{125} done
clear
B)
{8} done
clear
C)
\[\varphi \] done
clear
D)
{125, 8} done
clear
View Solution play_arrow
-
question_answer11)
If \[{{x}^{2}}+{{y}^{2}}=25,\ xy=12\], then \[x=\] [BIT Ranchi 1992]
A)
{3, 4} done
clear
B)
{3, -3} done
clear
C)
{3, 4, -3, -4} done
clear
D)
{-3, -3} done
clear
View Solution play_arrow
-
question_answer12)
The solution set of the equation \[{{x}^{{{\log }_{x}}{{(1-x)}^{2}}}}=9\] is [Pb. CET 2003]
A)
{- 2, 4} done
clear
B)
{4} done
clear
C)
{0, - 2, 4} done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer13)
Let one root of \[a{{x}^{2}}+bx+c=0\] where \[a,b,c\] are integers be \[3+\sqrt{5}\], then the other root is [MNR 1982]
A)
\[3-\sqrt{5}\] done
clear
B)
3 done
clear
C)
\[\sqrt{5}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer14)
The number of real solutions of the equation\[|x{{|}^{2}}\]- \[3|x|+2=0\] are [IIT 1982, 89; MP PET 1997; DCE 2002; AMU 2000; UPSEAT 1999; AIEEE 2003]
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
View Solution play_arrow
-
question_answer15)
The number of real roots of the equation \[{{e}^{\sin x}}-{{e}^{-\sin x}}-4\] \[=0\] are [IIT 1982; Pb. CET 2000]
A)
1 done
clear
B)
2 done
clear
C)
Infinite done
clear
D)
None done
clear
View Solution play_arrow
-
question_answer16)
The number of real solutions of the equation |\[{{x}^{2}}\] + 4x + 3| + 2x + 5 = 0 are [IIT 1988]
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
View Solution play_arrow
-
question_answer17)
The roots of the given equation \[(p-q){{x}^{2}}+(q-r)x+(r-p)=0\] are [RPET 1986; MP PET 1999; Pb. CET 2004]
A)
\[\frac{p-q}{r-p},1\] done
clear
B)
\[\frac{q-r}{p-q},1\] done
clear
C)
\[\frac{r-p}{p-q},1\] done
clear
D)
\[1,\frac{q-r}{p-q}\] done
clear
View Solution play_arrow
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question_answer18)
If a root of the equation \[{{x}^{2}}+px+12=0\] is 4, while the roots of the equation \[{{x}^{2}}+px+q=0\] are same, then the value of \[q\]will be [RPET 1991; AIEEE 2004]
A)
4 done
clear
B)
4/49 done
clear
C)
49/4 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer19)
How many roots the equation \[x-\frac{2}{x-1}=1-\frac{2}{x-1}\]have [IIT 1984; UPSEAT 1999; Pb. CET 2003]
A)
One done
clear
B)
Two done
clear
C)
Infinite done
clear
D)
None done
clear
View Solution play_arrow
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question_answer20)
The solution of the equation \[x+\frac{1}{x}=2\] will be [MNR 1983]
A)
2, -1 done
clear
B)
0, -1, \[-\frac{1}{5}\] done
clear
C)
\[-1,-\frac{1}{5}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer21)
If the product of the roots of the equation \[2{{x}^{2}}+6x+\] \[{{\alpha }^{2}}+1=0\] is \[-\alpha \], then the value of \[\alpha \] will be
A)
-1 done
clear
B)
1 done
clear
C)
2 done
clear
D)
-2 done
clear
View Solution play_arrow
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question_answer22)
If \[\sqrt{3{{x}^{2}}-7x-30}+\sqrt{2{{x}^{2}}-7x-5}=x+5\],then x is equal to
A)
2 done
clear
B)
3 done
clear
C)
6 done
clear
D)
5 done
clear
View Solution play_arrow
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question_answer23)
The value of \[2+\frac{1}{2+\frac{1}{2+...........\infty }}\] is
A)
\[1-\sqrt{2}\] done
clear
B)
\[1+\sqrt{2}\] done
clear
C)
\[1\pm \sqrt{2}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer24)
The roots of the equation \[{{2}^{x+2}}{{27}^{x/(x-1)}}=9\] are given by
A)
\[1-{{\log }_{2}}3,\,2\] done
clear
B)
\[{{\log }_{2}}\left( \frac{2}{3} \right)\,,\,\ 1\] done
clear
C)
\[2,-2\] done
clear
D)
\[-2,\ 1-\frac{\log 3}{\log 2}\] done
clear
View Solution play_arrow
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question_answer25)
Let \[\alpha \]and \[\beta \] be the roots of the equation \[{{x}^{2}}+x+1=0\] The equation whose roots are \[{{\alpha }^{19}},{{\beta }^{7}}\] is [IIT Screening 1994]
A)
\[{{x}^{2}}-x-1=0\] done
clear
B)
\[{{x}^{2}}-x+1=0\] done
clear
C)
\[{{x}^{2}}+x-1=0\] done
clear
D)
\[{{x}^{2}}+x+1=0\] done
clear
View Solution play_arrow
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question_answer26)
If \[|x-2|+|x-3|=7\], then x =
A)
6 done
clear
B)
-1 done
clear
C)
6 or -1 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer27)
If \[{{x}_{1}},{{x}_{2}},{{x}_{3}}\] are distinct roots of the equation \[a{{x}^{2}}+bx+c=0\] then
A)
\[a=b=0,c\in R\] done
clear
B)
\[a=c=0,b\in R\] done
clear
C)
\[{{b}^{2}}-4ac\ge 0\] done
clear
D)
\[a=b=c=0\] done
clear
View Solution play_arrow
-
question_answer28)
The number of roots of the equation \[|x{{|}^{2}}-7|x|+12=0\] is [MNR 1995]
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
View Solution play_arrow
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question_answer29)
The number of solutions of \[\frac{\log 5+\log ({{x}^{2}}+1)}{\log (x-2)}=2\] is
A)
2 done
clear
B)
3 done
clear
C)
1 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer30)
If \[x=\sqrt{7+4\sqrt{3}},\] then \[x+\frac{1}{x}=\] [EAMCET 1994]
A)
4 done
clear
B)
6 done
clear
C)
3 done
clear
D)
2 done
clear
View Solution play_arrow
-
question_answer31)
If \[{{\log }_{2}}x+{{\log }_{x}}2=\frac{10}{3}={{\log }_{2}}y+{{\log }_{y}}2\] and \[x\ne y,\] then \[x+y=\] [EAMCET 1994]
A)
2 done
clear
B)
65/8 done
clear
C)
37/6 done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer32)
The value of \[x=\sqrt{2+\sqrt{2+\sqrt{2+.....}}}\]is [Karnataka CET 2001]
A)
-1 done
clear
B)
1 done
clear
C)
2 done
clear
D)
3 done
clear
View Solution play_arrow
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question_answer33)
The value of x in the given equation\[{{4}^{x}}-{{3}^{x\,\ -\ \frac{1}{2}}}={{3}^{x+\frac{1}{2}}}-{{2}^{2x-1}}\]is
A)
\[\frac{4}{3}\] done
clear
B)
\[\frac{3}{2}\] done
clear
C)
\[\frac{2}{1}\] done
clear
D)
\[\frac{5}{3}\] done
clear
View Solution play_arrow
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question_answer34)
The equation\[{{e}^{x}}-x-1=0\] has [Kurukshetra CEE 1998]
A)
Only one real root \[x=0\] done
clear
B)
At least two real roots done
clear
C)
Exactly two real roots done
clear
D)
Infinitely many real roots done
clear
View Solution play_arrow
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question_answer35)
The equation \[{{x}^{2}}+qx+rp=0,\] has [IIT 1997 Cancelled]
A)
No solution done
clear
B)
One solution done
clear
C)
Two solutions done
clear
D)
More than two solutions done
clear
View Solution play_arrow
-
question_answer36)
The equation \[{{\log }_{e}}x+{{\log }_{e}}(1+x)=0\] can be written as [Kurukshetra CEE 1998; MP PET 1989]
A)
\[{{x}^{2}}+x-e=0\] done
clear
B)
\[{{x}^{2}}+x-1=0\] done
clear
C)
\[{{x}^{2}}+x+1=0\] done
clear
D)
\[{{x}^{2}}+xe-e=0\] done
clear
View Solution play_arrow
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question_answer37)
If \[x=\sqrt{6+\sqrt{6+\sqrt{6+....\text{to}\,\,\infty }},}\] then [Pb. CET 1999]
A)
x is an irrational number done
clear
B)
\[2<x<3\] done
clear
C)
\[x=3\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer38)
The real roots of the equation \[{{x}^{2}}+5|x|+\,\,4=0\] are [UPSEAT 1993, 99; Orissa JEE 2004]
A)
- 1, 4 done
clear
B)
1, 4 done
clear
C)
- 4, 4 done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer39)
A real root of the equation \[{{\log }_{4}}\{{{\log }_{2}}(\sqrt{x+8}-\sqrt{x})\}=0\] is [AMU 1999]
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
View Solution play_arrow
-
question_answer40)
\[\{x\in R:|x-2|\,\,={{x}^{2}}\}=\] [EAMCET 2000]
A)
{ - 1, 2} done
clear
B)
{1, 2} done
clear
C)
{ - 1, - 2} done
clear
D)
{1, - 2} done
clear
View Solution play_arrow
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question_answer41)
The number of solutions of \[{{\log }_{4}}(x-1)={{\log }_{2}}(x-3)\] [IIT Screening 2001]
A)
3 done
clear
B)
1 done
clear
C)
2 done
clear
D)
0 done
clear
View Solution play_arrow
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question_answer42)
The roots of \[|x-2{{|}^{2}}+|x-2|-6=0\]are [UPSEAT 2003]
A)
0, 4 done
clear
B)
-1, 3 done
clear
C)
4, 2 done
clear
D)
5, 1 done
clear
View Solution play_arrow
-
question_answer43)
The solution of equation\[\frac{p+q-x}{r}+\frac{q+r-x}{p}\]+\[\frac{r+p-x}{q}\]+\[\frac{4x}{p+q+r}=0\] is [MP PET 2004]
A)
\[x=p+q+r\] done
clear
B)
\[x=p-q+r\] done
clear
C)
\[x=\frac{p+q}{q+r}\] done
clear
D)
\[x=\frac{p}{q}+r\] done
clear
View Solution play_arrow
-
question_answer44)
The number of solutions for the equation \[{{x}^{2}}-5|x|+\,6=0\] is [Karnataka CET 2004]
A)
4 done
clear
B)
3 done
clear
C)
2 done
clear
D)
1 done
clear
View Solution play_arrow
-
question_answer45)
If the roots of the given equation \[({{m}^{2}}+1){{x}^{2}}+2amx+{{a}^{2}}-{{b}^{2}}=0\] be equal, then
A)
\[{{a}^{2}}+{{b}^{2}}({{m}^{2}}+1)=0\] done
clear
B)
\[{{b}^{2}}+{{a}^{2}}({{m}^{2}}+1)=0\] done
clear
C)
\[{{a}^{2}}-{{b}^{2}}({{m}^{2}}+1)=0\] done
clear
D)
\[{{b}^{2}}-{{a}^{2}}({{m}^{2}}+1)=0\] done
clear
View Solution play_arrow
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question_answer46)
If \[P(x)=a{{x}^{2}}+bx+c\] and \[Q(x)=-a{{x}^{2}}+dx+c\]where \[ac\ne 0\], then \[P(x).Q(x)=0\]has at least [IIT 1985; Pb. CET 2003; AMU 2005]
A)
Four real roots done
clear
B)
Two real roots done
clear
C)
Four imaginary roots done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer47)
Both the roots of the given equation\[(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0\] are always [MNR 1986; IIT 1980; Kurukshetra CEE 1998; RPET 2002]
A)
Positive done
clear
B)
Negative done
clear
C)
Real done
clear
D)
Imaginary done
clear
View Solution play_arrow
-
question_answer48)
If the roots of the given equation \[2{{x}^{2}}+3(\lambda -2)x+\lambda +4=0\] be equal in magnitude but opposite in sign, then \[\lambda \]=
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
2/3 done
clear
View Solution play_arrow
-
question_answer49)
If the roots of the equation \[({{p}^{2}}+{{q}^{2}}){{x}^{2}}\]\[-2q(p+r)x\]+ \[({{q}^{2}}+{{r}^{2}})=0\] be real and equal, then \[p,q,r\]will be in
A)
A.P. done
clear
B)
G.P. done
clear
C)
H.P. done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer50)
If \[a+b+c=0\], then the roots of the equation \[4a{{x}^{2}}+3bx+2c=0\] are
A)
Equal done
clear
B)
Imaginary done
clear
C)
Real done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer51)
The roots of the given equation \[2({{a}^{2}}+{{b}^{2}}){{x}^{2}}+2(a+b)x+1=0\] are
A)
Rational done
clear
B)
Irrational done
clear
C)
Real done
clear
D)
Imaginary done
clear
View Solution play_arrow
-
question_answer52)
If the roots of the equations \[p{{x}^{2}}+2qx+r=0\]and \[q{{x}^{2}}-2\sqrt{pr}x+q=0\] be real, then
A)
\[p=q\] done
clear
B)
\[{{q}^{2}}=pr\] done
clear
C)
\[{{p}^{2}}=qr\] done
clear
D)
\[{{r}^{2}}=pq\] done
clear
View Solution play_arrow
-
question_answer53)
If the roots of the equation \[a{{x}^{2}}+x+b=0\] be real, then the roots of the equation \[{{x}^{2}}-4\sqrt{ab}x+1=0\] will be
A)
Rational done
clear
B)
Irrational done
clear
C)
Real done
clear
D)
Imaginary done
clear
View Solution play_arrow
-
question_answer54)
If one of the roots of the equation \[{{x}^{2}}+ax+b=0\] and \[{{x}^{2}}+bx+a=0\] is coincident, then the numerical value of \[(a+b)\] is [IIT 1986; RPET 1992; EAMCET 2002]
A)
0 done
clear
B)
- 1 done
clear
C)
2 done
clear
D)
5 done
clear
View Solution play_arrow
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question_answer55)
The equation \[{{x}^{(3/4){{({{\log }_{2}}x)}^{2}}+({{\log }_{2}}x)-5/4}}=\sqrt{2}\] has [IIT 1989]
A)
At least one real solution done
clear
B)
Exactly three real solutions done
clear
C)
Exactly one irrational solution done
clear
D)
All the above done
clear
View Solution play_arrow
-
question_answer56)
If \[a>0,b>0,c>0\] then both the roots of the equation \[a{{x}^{2}}+bx+c=0\]
A)
Are real and negative done
clear
B)
Have negative real parts done
clear
C)
Are rational numbers done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer57)
The value of \[k\]for which \[2{{x}^{2}}-kx+x+8=0\]has equal and real roots are [BIT Ranchi 1990]
A)
-9 and -7 done
clear
B)
9 and 7 done
clear
C)
-9 and 7 done
clear
D)
9 and -7 done
clear
View Solution play_arrow
-
question_answer58)
The roots of the quadratic equation \[2{{x}^{2}}+3x+1=0\], are [IIT 1983]
A)
Irrational done
clear
B)
Rational done
clear
C)
Imaginary done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer59)
If \[l,m,n\] are real and \[l\ne m\], then the roots of the equation \[(l-m){{x}^{2}}-5(l+m)x-2(l-m)=0\]are [IIT 1979; RPET 1983]
A)
Complex done
clear
B)
Real and distinct done
clear
C)
Real and equal done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer60)
If the roots of the equation \[{{x}^{2}}-8x+({{a}^{2}}-6a)=0\] are real, then [RPET 1987, 97; MP PET 1999]
A)
\[-2<a<8\] done
clear
B)
\[2<a<8\] done
clear
C)
\[-2\le a\le 8\] done
clear
D)
\[2\le a\le 8\] done
clear
View Solution play_arrow
-
question_answer61)
The roots of the equation \[{{x}^{2}}+2\sqrt{3}x+3=0\]are [RPET 1986]
A)
Real and unequal done
clear
B)
Rational and equal done
clear
C)
Irrational and equal done
clear
D)
Irrational and unequal done
clear
View Solution play_arrow
-
question_answer62)
If the roots of the given equation \[(\cos p-1){{x}^{2}}+(\cos p)x+\sin p=0\] are real, then [IIT 1990; RPET 1995]
A)
\[p\in (-\pi ,0)\] done
clear
B)
\[p\in \left( -\frac{\pi }{2},\frac{\pi }{2} \right)\] done
clear
C)
\[p\in (0,\pi )\] done
clear
D)
\[p\in (0,2\pi )\] done
clear
View Solution play_arrow
-
question_answer63)
If \[{{x}^{2}}+2x+2xy+my-3\] has two rational factors, then the value of m will be [RPET 1990]
A)
\[-6,-2\] done
clear
B)
\[-6,2\] done
clear
C)
\[6,-2\] done
clear
D)
6, 2 done
clear
View Solution play_arrow
-
question_answer64)
If a and b are the odd integers, then the roots of the equation \[2a{{x}^{2}}+(2a+b)x+b=0,\ a\ne 0,\] will be [Pb. CET 1988]
A)
Rational done
clear
B)
Irrational done
clear
C)
Non-real done
clear
D)
Equal done
clear
View Solution play_arrow
-
question_answer65)
Roots of \[a{{x}^{2}}+b=0\] are real and distinct if
A)
\[ab>0\] done
clear
B)
\[ab<0\] done
clear
C)
\[a,b>0\] done
clear
D)
\[a,b<0\] done
clear
View Solution play_arrow
-
question_answer66)
Roots of the equations \[2{{x}^{2}}-5x+1=0\], \[{{x}^{2}}+5x+2=0\] are
A)
Reciprocal and of same sign done
clear
B)
Reciprocal and of opposite sign done
clear
C)
Equal in product done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer67)
If \[a+b+c=0,\]\[a\ne 0,a,b,c\in Q\], then both the roots of the equation \[a{{x}^{2}}+bx+c=0\] are
A)
Rational done
clear
B)
Non-real done
clear
C)
Irrational done
clear
D)
Zero done
clear
View Solution play_arrow
-
question_answer68)
If \[a,b,c\in Q\], then roots of the equation\[(b+c-2a){{x}^{2}}+\] \[(c+a-2b)x+(a+b-2c)=0\] are
A)
Rational done
clear
B)
Non-real done
clear
C)
Irrational done
clear
D)
Equal done
clear
View Solution play_arrow
-
question_answer69)
The expression \[{{x}^{2}}+2bx+c\] has the positive value if [Roorkee 1995]
A)
\[{{b}^{2}}-4c>0\] done
clear
B)
\[{{b}^{2}}-4c<0\] done
clear
C)
\[{{c}^{2}}<b\] done
clear
D)
\[{{b}^{2}}<c\] done
clear
View Solution play_arrow
-
question_answer70)
If the roots of \[4{{x}^{2}}+px+9=0\] are equal, then absolute value of p is [MP PET 1995]
A)
144 done
clear
B)
12 done
clear
C)
\[-12\] done
clear
D)
\[\pm 12\] done
clear
View Solution play_arrow
-
question_answer71)
The condition for the roots of the equation,\[({{c}^{2}}-ab){{x}^{2}}-\]\[2({{a}^{2}}-bc)x+({{b}^{2}}-ac)=0\] to be equal is [TS Rajendra 1982]
A)
\[a=0\] done
clear
B)
\[b=0\] done
clear
C)
\[c=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer72)
If \[{{b}_{1}}{{b}_{2}}=2\]\[({{c}_{1}}+{{c}_{2}})\], then at least one of the equations \[{{x}^{2}}+{{b}_{1}}x+{{c}_{1}}=0\] and \[{{x}^{2}}+{{b}_{2}}x+{{c}_{2}}=0\] has
A)
Real roots done
clear
B)
Purely imaginary roots done
clear
C)
Imaginary roots done
clear
D)
None of these done
clear
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question_answer73)
The value of \[k\] for which the quadratic equation,\[k{{x}^{2}}+1=\]\[kx+3x-11{{x}^{2}}\] has real and equal roots are [BIT Ranchi 1993]
A)
\[-11,-3\] done
clear
B)
\[5,\,7\] done
clear
C)
\[5,-7\] done
clear
D)
None of these done
clear
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question_answer74)
The expression \[y=a{{x}^{2}}+bx+c\] has always the same sign as c if
A)
\[4ac<{{b}^{2}}\] done
clear
B)
\[4ac>{{b}^{2}}\] done
clear
C)
\[ac<{{b}^{2}}\] done
clear
D)
\[ac>{{b}^{2}}\] done
clear
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question_answer75)
The value of m for which the equation\[\frac{a}{x+a+m}+\frac{b}{x+b+m}=1\]has roots equal in magnitude but opposite in sign is
A)
\[\frac{a+b}{a-b}\] done
clear
B)
0 done
clear
C)
\[\frac{a-b}{a+b}\] done
clear
D)
\[\frac{2(a-b)}{a+b}\] done
clear
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question_answer76)
The roots of the equation\[({{a}^{2}}+{{b}^{2}}){{t}^{2}}-2(ac+bd)t+({{c}^{2}}+{{d}^{2}})=0\] are equal, then [MP PET 1996]
A)
\[ab=dc\] done
clear
B)
\[ac=bd\] done
clear
C)
\[ad+bc=0\] done
clear
D)
\[\frac{a}{b}=\frac{c}{d}\] done
clear
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question_answer77)
For what values of k will the equation\[{{x}^{2}}-2(1+3k)x+\]\[7(3+2k)=0\] have equal roots [MP PET 1997]
A)
\[1,-\frac{10}{9}\] done
clear
B)
\[2,-\frac{10}{9}\] done
clear
C)
\[3,-\frac{10}{9}\] done
clear
D)
\[4,-\frac{10}{9}\] done
clear
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-
question_answer78)
If the roots of equation \[{{x}^{2}}+{{a}^{2}}=8x+6a\] are real, then [MP PET 1999]
A)
\[a\in [2,\,8]\] done
clear
B)
\[a\in [-2,\,8]\] done
clear
C)
\[a\in (2,\,8)\] done
clear
D)
\[a\in (-2,\,8)\] done
clear
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question_answer79)
Let\[p,q\in \{1,\,2,\,3,\,4\}\]. The number of equations of the form \[p{{x}^{2}}+qx+1=0\] having real roots is [IIT Screening 1994]
A)
15 done
clear
B)
9 done
clear
C)
7 done
clear
D)
8 done
clear
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-
question_answer80)
For what value of k will the equation\[{{x}^{2}}-(3k-1)x+\]\[2{{k}^{2}}+2k\] have equal roots [Karnataka CET 1998]
A)
5 done
clear
B)
9 done
clear
C)
Both (a) and (b) done
clear
D)
0 done
clear
View Solution play_arrow
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question_answer81)
The value of k for which the equation\[(k-2){{x}^{2}}+8x+k+4=0\] has both real, distinct and negative is[Orissa JEE 2002]
A)
0 done
clear
B)
2 done
clear
C)
3 done
clear
D)
- 4 done
clear
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question_answer82)
If \[k\in (-\infty ,\,-2)\cup (2,\infty ),\] then the roots of the equation \[{{x}^{2}}+2kx+4=0\] are [DCE 2002]
A)
Complex done
clear
B)
Real and unequal done
clear
C)
Real and equal done
clear
D)
One real and one imaginary done
clear
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-
question_answer83)
If the equation \[(m-n){{x}^{2}}+(n-l)x+l-m=0\] has equal roots, then l, m and n satisfy [DCE 2002]
A)
\[2l=m+n\] done
clear
B)
\[2m=n+l\] done
clear
C)
\[m=n+l\] done
clear
D)
\[l=m+n\] done
clear
View Solution play_arrow
-
question_answer84)
The least integer k which makes the roots of the equation \[{{x}^{2}}+5x+k=0\] imaginary is [Kerala (Engg.) 2002]
A)
4 done
clear
B)
5 done
clear
C)
6 done
clear
D)
7 done
clear
View Solution play_arrow
-
question_answer85)
The roots of \[4{{x}^{2}}+6px+1=0\] are equal, then the value of p is [MP PET 2003]
A)
\[\frac{4}{5}\] done
clear
B)
\[\frac{1}{3}\] done
clear
C)
\[\frac{2}{3}\] done
clear
D)
\[\frac{4}{3}\] done
clear
View Solution play_arrow
-
question_answer86)
\[{{x}^{2}}+x+1+2k\,({{x}^{2}}-x-1)=0\]is a perfect square for how many values of k [Orissa JEE 2004]
A)
2 done
clear
B)
0 done
clear
C)
1 done
clear
D)
3 done
clear
View Solution play_arrow
-
question_answer87)
If \[\sin A,\sin B,\cos A\] are in G.P., then roots of \[{{x}^{2}}+2x\cot B+1=0\] are always [Orissa JEE 2005]
A)
Real done
clear
B)
Imaginary done
clear
C)
Greater than 1 done
clear
D)
Equal done
clear
View Solution play_arrow
-
question_answer88)
The values of 'a' and 'b' for which equation \[{{x}^{4}}-4{{x}^{3}}+a{{x}^{2}}+bx+1=0\] have four real roots [DCE 2005]
A)
- 6, - 4 done
clear
B)
- 6, 5 done
clear
C)
- 6, 4 done
clear
D)
6, - 4 done
clear
View Solution play_arrow