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question_answer1)
\[p{{x}^{3}}+q{{x}^{2}}+rx+s=0\] is said to be cubic polynomial, if _____.
A)
\[s\ne 0\] done
clear
B)
\[r\ne 0\] done
clear
C)
\[q\ne 0\] done
clear
D)
\[p\ne 0\] done
clear
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question_answer2)
If sum of all zeros of the polynomial \[5{{x}^{2}}-(3+k)x+7\] is zero, then zeroes of the polynomial \[2{{x}^{2}}-2(k+11)x+30\] are
A)
3, 5 done
clear
B)
7, 9 done
clear
C)
3, 6 done
clear
D)
2, 5 done
clear
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question_answer3)
If the sum of the product of the zeroes taken two at a time of the polynomial \[f(x)=2{{x}^{3}}-3{{x}^{2}}+4tx-5\] is \[-8,\] then the value of t is _____.
A)
2 done
clear
B)
4 done
clear
C)
\[-2\] done
clear
D)
\[-4\] done
clear
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question_answer4)
if a and b are the roots of the quadratic equation \[{{x}^{2}}+px+12=0\]with the condition \[a-b=1,\]then the value of 'p' is _____.
A)
1 done
clear
B)
7 done
clear
C)
\[-7\] done
clear
D)
7 or \[-7\] done
clear
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question_answer5)
What will be the value of p(3), if 3 is one I of zeroes of polynomial \[p(x)={{x}^{3}}+bx+D\]?
A)
3 done
clear
B)
D done
clear
C)
27 done
clear
D)
0 done
clear
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question_answer6)
A cubic polynomial with sum of its zeroes, sum of the product of its zeroes taken two at a time and the product of its zeroes as \[-3,\text{ }8,\text{ }4\] respectively, is _____.
A)
\[{{x}^{3}}-3{{x}^{2}}-8x-4\] done
clear
B)
\[{{x}^{3}}+3{{x}^{2}}-8x-4\] done
clear
C)
\[{{x}^{3}}+3{{x}^{2}}+8x-4\] done
clear
D)
\[{{x}^{3}}-3{{x}^{2}}-8x+4\] done
clear
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question_answer7)
If p, q are the zeroes of the polynomial \[f(x)={{x}^{2}}+k(x-1)-c,\] then \[(p-1)\,(q-1)\]is equal to _____.
A)
\[c-1\] done
clear
B)
\[1-c\] done
clear
C)
c done
clear
D)
\[1+c\] done
clear
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question_answer8)
When \[{{x}^{3}}-3{{x}^{2}}+3x+5\]is divided by \[{{x}^{2}}-\text{ }x+1,\]the quotient and remainder are
A)
\[x+2,\text{ }7\] done
clear
B)
\[x-2,-7\] done
clear
C)
\[x-2,\text{ }7\] done
clear
D)
\[~x+2,-7\] done
clear
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question_answer9)
What should be subtracted from \[f(x)=6{{x}^{3}}+11{{x}^{2}}-39x-65\] so that f(x) is exactly divisible by\[{{x}^{2}}+x-1\]?
A)
\[38x+60\] done
clear
B)
\[-38x-60\] done
clear
C)
\[-19x-30\] done
clear
D)
\[9x+10\] done
clear
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question_answer10)
Which of the following graph has more than three distinct real roots?
A)
B)
C)
D)
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question_answer11)
If one zero of the polynomial \[f(x)=({{k}^{2}}+4){{x}^{2}}+13x+4k\] is reciprocal of the other, then k is equal to ____.
A)
2 done
clear
B)
\[-2\] done
clear
C)
1 done
clear
D)
\[-1\] done
clear
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question_answer12)
A polynomial of the form \[a{{x}^{5}}+b{{x}^{3}}+c{{x}^{2}}+dx+e\] has atmost ____ zeroes.
A)
3 done
clear
B)
5 done
clear
C)
7 done
clear
D)
11 done
clear
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question_answer13)
If \[\alpha \] and \[\beta \] are the roots of the equation \[2{{x}^{2}}-7x+8=0,\]then the equation whose roots are \[(3\alpha -4\beta )\]and \[(3\beta -4\alpha )\] is____.
A)
\[2{{x}^{2}}+7x+98=0\] done
clear
B)
\[~{{x}^{2}}+7x+98=0\] done
clear
C)
\[2{{x}^{2}}-7x-98=0\] done
clear
D)
\[2{{x}^{2}}-7x+98=0\] done
clear
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question_answer14)
For \[{{x}^{2}}+2x+5\]to be a factor of\[{{x}^{4}}+\alpha {{x}^{2}}\text{+}\beta ,\] the values of \[\alpha \] and \[\beta \] should respectively be_____.
A)
2, 5 done
clear
B)
5, 25 done
clear
C)
6, 25 done
clear
D)
5, 2 done
clear
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question_answer15)
If \[\alpha ,\beta \] be two zeroes of the quadratic polynomial \[a{{x}^{2}}+bx-c=0,\] then find the value of \[\frac{{{\alpha }^{2}}}{\beta }+\frac{{{\beta }^{2}}}{\alpha }\].
A)
\[\frac{{{b}^{2}}-2ac}{{{a}^{2}}}\] done
clear
B)
\[\frac{3abc-{{b}^{3}}}{{{c}^{3}}}\] done
clear
C)
\[\frac{3abc-{{b}^{3}}}{{{a}^{2}}c}\] done
clear
D)
\[\frac{{{b}^{3}}+3abc}{{{a}^{2}}c}\] done
clear
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question_answer16)
Area of a triangular field is \[({{x}^{4}}-6{{x}^{3}}-26{{x}^{2}}+138x-35){{m}^{2}}\]and base of the triangular field is \[({{x}^{2}}-4x+1)m\]. Find the height of the triangular field.
A)
\[2({{x}^{2}}-2x-35)m\] done
clear
B)
\[\frac{1}{2}({{x}^{2}}-2x-35)m\] done
clear
C)
\[2(3{{x}^{2}}-x-4)m\] done
clear
D)
\[\frac{1}{2}(3{{x}^{2}}-x-4)m\] done
clear
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question_answer17)
A rectangular garden of length \[(2{{x}^{3}}+5{{x}^{2}}-7)m\]has the perimeter \[(4{{x}^{3}}-2{{x}^{2}}+4)m.\]. Find the breadth of the garden.
A)
\[(6{{x}^{2}}-9)m\] done
clear
B)
\[(-6{{x}^{2}}+9)m\] done
clear
C)
\[(2{{x}^{3}}-7{{x}^{2}}+11)m\] done
clear
D)
\[(6{{x}^{3}}+7{{x}^{2}}+9)m\] done
clear
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question_answer18)
Raghav had \[Rs.(6{{x}^{3}}+2{{x}^{2}}+3x)\] and he bought \[(4{{x}^{2}}+3)\]shirts. The price of each shirt is \[Rs.(x+5)\]. How much money is left with Raghav?
A)
\[Rs.(2{{x}^{3}}-18{{x}^{2}}-15)\] done
clear
B)
\[Rs.(4{{x}^{2}}+2x+3)\] done
clear
C)
\[Rs.({{x}^{3}}-3x)\] done
clear
D)
\[Rs.(2{{x}^{3}}+2{{x}^{2}}-15)\] done
clear
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question_answer19)
Two different container contains \[(2{{x}^{3}}+2{{x}^{2}}+3x+3)L\] and \[(4{{x}^{3}}-2{{x}^{2}}+6x-3)L\] water. What is biggest measure that can measure both quantities exactly?
A)
\[({{x}^{2}}+2x)L\] done
clear
B)
\[(2{{x}^{2}}+3)L\] done
clear
C)
\[(2x-1)L\] done
clear
D)
\[(x+1)L\] done
clear
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question_answer20)
Length and breadth of a rectangular park are \[(3{{x}^{2}}+2x)m\] and \[(2{{x}^{3}}-3)m\]respectively. Find the area of the park, when\[x=3\].
A)
\[1924{{m}^{2}}\] done
clear
B)
\[1492{{m}^{2}}\] done
clear
C)
\[1881\text{ }{{m}^{2}}\] done
clear
D)
\[1683{{m}^{2}}\] done
clear
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question_answer21)
Find the roots of \[a{{x}^{2}}+bx+6,\]if the polynomial \[{{x}^{4}}+{{x}^{3}}+8{{x}^{2}}+ax+b\]is exactly divisible by\[{{x}^{2}}+1\].
A)
\[-1,3\] done
clear
B)
\[2,5\] done
clear
C)
\[-1,-6\] done
clear
D)
\[-3,2\] done
clear
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question_answer22)
Which of the following options hold?
Statement - I: If p(x) and g(x) are two polynomials with \[g(x)\ne 0,\] then we can find polynomials q(x) and r(x) such that \[p(x)=g(x)\times q(x)+r(x),\] where degree of r(x) is greater than degree of g(x). |
Statement - II: When \[4{{x}^{5}}+3{{x}^{3}}+2{{x}^{2}}+8\] is divided by \[4{{x}^{2}}+2x+1,\] then degree of remainder is 1. |
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)
Obtain all the zeroes of the polynomial \[f(x)=3{{x}^{4}}+6{{x}^{3}}-2{{x}^{2}}-10x-5,\]if two of its zeros are \[\sqrt{\frac{5}{3}}\] and \[-\sqrt{\frac{5}{3}}\].
A)
\[1,-1\] done
clear
B)
\[1,\,\,1\] done
clear
C)
\[-1,-1\] done
clear
D)
\[1,0\] done
clear
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question_answer24)
Match the following.
Column-I | Column - II |
(P) If one of the zero of the polynomial \[f(x)=({{k}^{2}}+4){{x}^{2}}\] \[+13x+4\] is reciprocal of the other, then k is equal to | (i) 1 |
(Q) Sum of the zeroes of the polynomial \[f(x)=2{{x}^{3}}+k{{x}^{2}}+4x+5\]is 3, then A-is equal to | (ii) 0 |
(R) If the polynomial \[f(x)=a{{x}^{3}}+bx+c\]is exactly divisible by \[g(x)={{x}^{2}}+bx+c,\]then \[ab\] is equal to | (iii) \[-6\] |
A)
(P) \[\to \] (iii); (Q) \[\to \] (i); (R) \[\to \] (ii) done
clear
B)
(P) \[\to \](ii); (Q)\[\to \] (iii); (R)\[\to \] (i) done
clear
C)
(P) \[\to \] (i); (Q) \[\to \] (iii); (R)\[\to \] (ii) done
clear
D)
(P) \[\to \] (ii); (Q)\[\to \] (i); (R)\[\to \] (iii) done
clear
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question_answer25)
If 1 and \[-1\] are zeroes of polynomial \[L{{x}^{4}}+M{{x}^{3}}+N{{x}^{2}}+Rx+P,\]then Find:
(i) \[L+N+P\] |
(ii) \[M+R\] |
(iii) \[{{M}^{3}}+{{R}^{3}}\] |
A)
i-1 ii-1 iii-\[-1\] done
clear
B)
i-0 ii-\[-1\] iii-0 done
clear
C)
i-0 ii-0 iii-0 done
clear
D)
i\[-1\] ii-1 iii-1 done
clear
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