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question_answer1)
The roots of \[a{{x}^{2}}+bx+c=0,\] \[a\ne 0\] are real and unequal, if \[{{b}^{2}}-4ac\]is _______.
A)
=0 done
clear
B)
> 0 done
clear
C)
<0 done
clear
D)
\[\ge 0\] done
clear
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question_answer2)
lf\[x=\sqrt{2+\sqrt{2+\sqrt{2+.........}}}\], then __________.
A)
\[x=1\] done
clear
B)
\[0<x<1\] done
clear
C)
x is infinite done
clear
D)
\[x=2\] done
clear
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question_answer3)
If 2 is a root of the equation \[{{x}^{2}}+bx+12=0\]and the equation \[{{x}^{2}}+bx+q=0\]has equal: roots, then q is equal to
A)
8 done
clear
B)
\[-8\] done
clear
C)
16 done
clear
D)
\[-16\] done
clear
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question_answer4)
If one root of the equation \[a(b-c){{x}^{2}}+b(c-a)x+c(a-b)=0\] is 1, then the other root is __.
A)
\[\frac{b(c-a)}{a(b-c)}\] done
clear
B)
\[\frac{a(b-c)}{c(a-b)}\] done
clear
C)
\[\frac{a(b-c)}{b(c-a)}\] done
clear
D)
\[\frac{c(a-b)}{a(b-c)}\] done
clear
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question_answer5)
If the roots of the equation \[(a-b){{x}^{2}}+(b-c)x+(c-a)=0\] are equal. Then _______.
A)
\[2b=a+c\] done
clear
B)
\[2a=b+c\] done
clear
C)
\[2c=a+b\] done
clear
D)
\[\frac{1}{b}=\frac{1}{a}+\frac{1}{c}\] done
clear
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question_answer6)
One of the two students, while solving a quadratic equation in x, copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of \[{{x}^{2}}\]correctly as \[-6\] and 1 respectively. The correct roots are ??.
A)
\[3,-2\] done
clear
B)
\[-3,2\] done
clear
C)
\[-6,-1\] done
clear
D)
\[6,-1\] done
clear
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question_answer7)
If \[\sqrt{x-1}-\sqrt{x+1}+1=0,\] then 4x is equal to_____.
A)
\[4\sqrt{-1}\] done
clear
B)
\[0\] done
clear
C)
5 done
clear
D)
\[1\frac{1}{4}\] done
clear
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question_answer8)
If one of roots of \[2{{x}^{2}}+ax+32=0\] is twice the other root, then the value of a is _____?
A)
\[-3\sqrt{2}\] done
clear
B)
\[8\sqrt{2}\] done
clear
C)
\[12\sqrt{2}\] done
clear
D)
\[-2\sqrt{2}\] done
clear
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question_answer9)
For what value of a, the roots of the equation \[2{{x}^{2}}+6x+a=0,\]satisfy the condition \[\left( \frac{\alpha }{\beta } \right)+\left( \frac{\beta }{\alpha } \right)<2\] (where \[\alpha \] and \[\beta \]are the roots of equation).
A)
\[a<0\] done
clear
B)
\[-1<a<0\] done
clear
C)
\[-1<a<1\] done
clear
D)
None of these done
clear
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question_answer10)
Roots of the quadratic equation \[{{x}^{2}}+x-(a+1)\,(a+2)=0\] are _____.
A)
\[-(a+1),\,(a+2)\] done
clear
B)
\[(a+1),\,-(a+2)\] done
clear
C)
\[(a+1),(a+2)\] done
clear
D)
\[-(a+1),-(a+2)\] done
clear
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question_answer11)
The roots of the equation \[3\sqrt{x}+5{{(x)}^{\frac{1}{2}}}=\sqrt{2}\]can be found by solving
A)
\[9{{x}^{2}}+28x+25=0\] done
clear
B)
\[9{{x}^{2}}+30x+25=0\] done
clear
C)
\[9{{x}^{2}}+28x-25=0\] done
clear
D)
\[16{{x}^{2}}+22x-30=0\] done
clear
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question_answer12)
If the roots of the equation \[({{a}^{2}}+{{b}^{2}}){{x}^{2}}-2b(a+c)x+({{b}^{2}}+{{c}^{2}})=0\] are equal, then _____.
A)
\[2b=a+c\] done
clear
B)
\[{{b}^{2}}=ac\] done
clear
C)
\[b=\frac{2ac}{a+c}\] done
clear
D)
\[b=ac\] done
clear
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question_answer13)
Two numbers whose sum is 12 and the absolute value of whose difference is 4 are the roots of the equation _____.
A)
\[{{x}^{2}}-12x+30=0\] done
clear
B)
\[{{x}^{2}}-12x+32=0\] done
clear
C)
\[2{{x}^{2}}-6x+7=0\] done
clear
D)
\[2{{x}^{2}}-24x+43=0\] done
clear
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question_answer14)
The roots of the equation \[{{x}^{2/3}}+{{x}^{1/3}}-2=0\]are _____.
A)
\[1,-8\] done
clear
B)
\[1,-2\] done
clear
C)
\[\frac{2}{3},\frac{1}{3}\] done
clear
D)
\[-2,-8\] done
clear
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question_answer15)
In the equation \[\frac{x(x-1)-(m+1)}{(x-1)\,(m-1)}=\frac{x}{m},\] the roots are equal when m = _____.
A)
\[\frac{1}{2}\] done
clear
B)
\[-\frac{1}{2}\] done
clear
C)
0 done
clear
D)
1 done
clear
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question_answer16)
In a bangle shop, if the shopkeeper displays; the bangles in the form of a square then he is left with 38 bangles. If he wanted to increase the size of square by one unit each side of the square he found that 25 bangles fall short of in completing the square. The actual number of bangles which he had with him in the shop was _____.
A)
1690 done
clear
B)
999 done
clear
C)
538 done
clear
D)
Can't be determined done
clear
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question_answer17)
A man walks a distance of 48 km in a given time. If he walks 2 km/hr faster, he will perform the journey 4 hrs before. His; normal rate of walking, is _____.
A)
3 km/hr done
clear
B)
4 km/hr done
clear
C)
- 6 km/hr or 4 km/hr done
clear
D)
5 km/hr done
clear
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question_answer18)
In the Maths Olympiad of 2020 at Animal Planet, two representatives from the donkey's side, while solving a quadratic equation, committed the following mistakes.
(i) One of them made a mistake in the constant term and got the roots as 5 I and 9. |
(ii) Another one committed an error in the coefficient of x and he got the roots as 12 and 4. |
But in the meantime, they realized that they are wrong and they managed to get it right jointly. Find the quadratic equation.
A)
\[{{x}^{2}}+4x+14=0\] done
clear
B)
\[2{{x}^{2}}+7x-24=0\] done
clear
C)
\[{{x}^{2}}\text{-}14x+48=0\] done
clear
D)
\[3{{x}^{2}}-17x+52=0\] done
clear
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question_answer19)
Rs.6500 were divided equally among a certain number of persons. If there had been 15 more persons, each would have got Rs. 30 less. Find the original number of persons.
A)
50 done
clear
B)
60 done
clear
C)
45 done
clear
D)
55 done
clear
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question_answer20)
Swati can row her boat at a speed of 5 km/hr in still water. If it takes her 1 hour more to row the Boat 5.25 km upstream than to return downstream, find the speed of the stream.
A)
5 km/hr done
clear
B)
2 km/hr done
clear
C)
3 km/hr done
clear
D)
4 km/hr done
clear
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question_answer21)
Which of the following equations has two distinct real roots?
A)
\[2{{x}^{2}}-3\sqrt{2}x+\frac{9}{4}=0\] done
clear
B)
\[{{x}^{2}}+x-5=0\] done
clear
C)
\[{{x}^{2}}+3x+2\sqrt{2}=0\] done
clear
D)
\[5{{x}^{2}}-3x+1=0\] done
clear
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question_answer22)
Read the statements carefully. .
Statement I: The quadratic equation \[a{{x}^{2}}+bx+c=0\] has two distinct real roots, if\[{{b}^{2}}-4ac>0\]. |
Statement II: The quadratic equation \[2({{a}^{2}}+{{b}^{2}}){{x}^{2}}+2(a+b)x+1=0\]has no real roots, when \[a\ne b\]. |
A)
Both Statement - I and Statement - II are true. done
clear
B)
Statement - I is true but Statement - II is false. done
clear
C)
Statement - I is false but Statement - II is true. done
clear
D)
Both Statement - I and Statement - II are false. done
clear
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question_answer23)
If the roots of the equation \[~{{x}^{2}}+2cx+ab=0\]are real and unequal, then the equation \[{{x}^{2}}-2(a+b)x+{{a}^{2}}+{{b}^{2}}+2{{c}^{2}}=0\] has _____ roots.
A)
Real done
clear
B)
Equal done
clear
C)
No real done
clear
D)
Can't be determined done
clear
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question_answer24)
Read the statement carefully and state 'T' for true and 'F' for false.
(i) The value of \[2+\frac{1}{2+\frac{1}{2+......\infty }}\] is \[\sqrt{2}\]. |
(ii) A line segment AB of length 2 m is divided at C into two parts such that\[A{{C}^{2}}=AB-CB\] The length of the part CB is\[3+\sqrt{5}\]. |
(iii) Every quadratic equation can have at most two real roots. |
(iv) A real number a is said to be root of the quadratic equation \[a{{x}^{2}}+bx+c=0,\] if\[a{{\alpha }^{2}}+b\alpha +c=0\]. |
A)
i-F ii-T iii-T iv-T done
clear
B)
i-F ii-T iii-T iv-F done
clear
C)
i-T ii-F iii-F iv-T done
clear
D)
i-F ii-F iii-T iv-T done
clear
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question_answer25)
The denominator of a fraction is one more than twice the numerator. If the sum of the A r. fraction and its reciprocal is \[2\frac{16}{21},\] find the fraction.
A)
\[\frac{3}{7}\] done
clear
B)
\[\frac{7}{3}\] done
clear
C)
\[\frac{4}{3}\] done
clear
D)
\[\frac{3}{4}\] done
clear
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