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Answers posted by sreemathi.v

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Triangles ABC and DEF are similar as shown in the figure.The area of $\Delta ABC$ is $16$ sq.cm and that of $\Delta DEF$ is $25$ sq.cm.If $BC=2.3$ cm then $EF$ is _______
answered Dec 31, 2014
Answer : $2.9$ cm(approx)
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In the given figure AD is the bisector of $\angle BAC, AB=6$ cm,$AC=5$ cm and $BD=3$ cm then $DC$=_______
answered Dec 31, 2014
Solution : $\large\frac{AB}{AC} =\frac{BD}{DC}$=> $\large\frac{6}{5} =\frac{3}{x}$=> $x =\larg...
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Two triangles ABC and DEF are similar to each other in which $AB=10$ cm and $DE=8$ cm,then the ratio of the areas of $\Delta ABC$ and $\Delta DEF$ is ________
answered Dec 31, 2014
Solution : Change the tagging$\Large\frac{area\; of\;\Delta\;ABC}{area\; of\;\Delta\;DEF}=\frac{AB^2...
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If $(a+b)=13,(a-b)=11$ then $a^2+b^2$=_____
answered Dec 31, 2014
Answer : $145$If $(a+b)=13,(a-b)=11$ then $a^2+b^2=145$
0 votes
The value of $(996)^2$ is ______
answered Dec 31, 2014
Answer : $992016$The value of $(996)^2$ is $992016$
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If $2x+y=3$ and $xy=1$,then the value of $8x^3+y^3$ is ______
answered Dec 31, 2014
Answer : $9$The value of $8x^3+y^3$ is $9$
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If $(x-\large\frac{1}{x})$$=5$,then $x^3-\large\frac{1}{x^3}$=_____
answered Dec 31, 2014
Solution : $(x -\large\frac{1}{x}) $$=5$$x^3-\large\frac{1}{x^3}=(x-\large\frac{1}{x})^3+$$3(x- \lar...
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If $x^4+\large\frac{1}{x^4}$$=119$,then $x^3-\large\frac{1}{x^3}$ is _______
answered Dec 31, 2014
Solution : $\bigg(x^2+\large\frac{1}{x^2})^2=x^4+\large\frac{1}{x^4} $$+2$$\qquad= 119+2 =121$$x^2+\...
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If $4x^2+\large\frac{1}{x^2}$$=12$ ,then $8x^3+\large\frac{1}{x^3}$ is ______
answered Dec 31, 2014
$4x^2 + \frac{1}{x^2} = 12$$\begin{align*}\implies (2x + \frac{1}{x})^2 - 4 & = 12 \\ \implies (...
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The value of $\large\frac{(0.013)^3+(0.007)^3}{(0.013)^2-0.013\times 0.007+(0.007)^2}$ is ________
answered Dec 31, 2014
$\frac{(0.013)^2 + (0.007)^3 }{(0.013)^2 - 0.013 \times 0.007 + (0.007)^2}$$a^3 + b^3 = (a+b) (a^2 -...
0 votes
The value of $\large\frac{(2.3)^3-0.027}{(2.3)^2+0.69+0.09}$ is
answered Dec 31, 2014
$\frac{(2.3)^2 - (0.027) }{(2.3)^2 + (0.69) + 0.09}$$a^3 - b^3 = (a-b) (a^2+ab+b^2)$a = 2.3 and b = ...
0 votes
$(x+1)^3-(x-1)^3$=________
answered Dec 31, 2014
Answer : $2(3x^2+1)$$(x+1)^3-(x-1)^3=2(3x^2+1)$
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Given that $(x+9)$ is a factor of $x^3+13x^2+31x-45$,then the other factors are _______
answered Dec 31, 2014
Answer : $(x-1)(x+5)$
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If $x=\large\frac{1}{2}$ is a zero of the polynomial $f(x)=8x^3+ax^2-4x+2$ ,then the value of $'a'$ is ______
answered Dec 31, 2014
Answer : $-2$
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When $x^3+4x^2+4x-3$ is divided by $x$,then the remainder is ______
answered Dec 31, 2014
Answer : $-3$
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If $f(x)=x^4-2x^3+3x^2-ax-b$ when divided by $x-1$,the remainder is $6$,then the value of $a+b$ is _______
answered Dec 31, 2014
Answer : $-4$The value of $a+b$ is $-4$
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If $(x+2)$ and $(x+1)$ are the factors of $x^3+13x^2+32x+20$,then the other factor is
answered Dec 31, 2014
Answer : $(x+10)$If $(x+2)$ and $(x+1)$ are the factors of $x^3+13x^2+32x+20$,then the other factor ...
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Let $f(x)$ be a polynomial such that $f(-\large\frac{1}{2})$$=0$,then the factor of $f(x)$ is _____
answered Dec 31, 2014
Answer : $2x+1$
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If $(x+2)$ is a factor of $x^4+mx+14$,then $m$=
answered Dec 31, 2014
Answer : $9$$m=9$
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If $(x-a)$ is a factor of $x^4-a^2x^2+3x-6a$,then $a$=______
answered Dec 31, 2014
Answer : $0$
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If $x^{140}+2x^{151}+k$ is divisible by $x+1$,then the value of $k$ is
answered Dec 31, 2014
Answer : $1$
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When $x^3-2x^2+ax-b$ is divided by $x^2-2x-3$,the remainder is $x-6$,the values of $a$ and $b$ are _____
answered Dec 31, 2014
Answer : $-2,6$The values of $a$ and $b$ are $-2,6$
0 votes
If $x^2+x+1$ is a factor of the polynomial $3x^3+8x^2+8x+3+5k$,then the value of $k$ is ______
answered Dec 31, 2014
Answer : $\large\frac{2}{5}$
0 votes
If $x^{51}+51$ is divided by $(x+1)$,then the remainder is
answered Dec 31, 2014
Answer : $50$If $x^{51}+51$ is divided by $(x+1)$,then the remainder is $50$
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If $x+a$ is a factor of $x^4-a^2x^2+3x-6a$ then $a$=_____
answered Dec 31, 2014
Answer : $0$
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If $x+1$ is a factor of the polynomial $2x^2+4x+k$,then $k$=_____
answered Dec 31, 2014
Answer : $-2$$k=-2$
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If both $x-2$ and $x-\large\frac{1}{2}$ are factors of $px^2+5x+r$,then
answered Dec 31, 2014
Answer : $p=r$
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If $x-3$ is a factor of $x^2-ax-15$,then $a$=_____
answered Dec 31, 2014
Answer : $-2$
0 votes
One factor of $x^4+x^2-20$ is $x^2+5$,then the other factor is ______
answered Dec 31, 2014
Answer : $x^2-4$One factor of $x^4+x^2-20$ is $x^2+5$,then the other factor is $x^2-4$
0 votes
A polynomial of degree $'n'$ has ______ roots.
answered Dec 31, 2014
Answer : $n$A polynomial of degree $'n'$ has $n$ roots.
0 votes
The factors of $x^3-8x^2+17x-10$ is ________
answered Dec 31, 2014
Answer : $(x-1)(x-2)(x-5)$
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If $(x-3)$ is a factor of $x^2+4x+k$ then the value of $k$ is _______
answered Dec 31, 2014
Answer : $-6$
0 votes
The factors of $3x^2-x-4$ are ______
answered Dec 31, 2014
Answer : $(x+1)(3x-4)$
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If $(x+a)$ is the HCF of $x^2+px+q$ and $x^2+lx+m$ then the value of $'a'$ is given by
answered Dec 30, 2014
Answer : $\large\frac{q-m}{p-l}$
0 votes
If $(x^{11}+1)$ is divided by $(x+1)$,then the remainder is _____
answered Dec 30, 2014
Answer : $1$
0 votes
The polynomials $kx^3+4x^2+3x-4$ and $x^3-4x+k$ leave the same remainder when divided by $(x-3)$ then the value of $k$ is
answered Dec 30, 2014
Answer : $k=-1$
0 votes
If $Ax^3+31x^2-Bx-10$ is exactly divisible by $2x^2+9x-5$,then the values of $A$ and $B$ are _______
answered Dec 30, 2014
Answer : $6,-3$The values of $A$ and $B$ are $6,-3$
0 votes
$6x^2+ax+7$ when divided by $x-2$ gives the remainder $13$.The value of $a$ is ______
answered Dec 30, 2014
Answer : $-9$The value of $a$ is $-9$
0 votes
If $(x-a)$ is a factor of $x^3-mx^2-2anx+na^2$ then $a$=___ and $a\neq 0$.
answered Dec 30, 2014
Answer : $m+n$
0 votes
If both $(x-2)$ and $\big(x-\large\frac{1}{2}\big)$ are factors of $px^2+5x+r$,then $p$=_____$r$
answered Dec 30, 2014
Solution : $P(x) =Px^2+5x+r$$P(2) =P(2)^2+5(2) +r=0$=> $4p+r=-10$ --------(1)$P(1/2) =P(1/2)^2 +5...
0 votes
The value of $k$ if $(x-1)$ is a factor of $P(x)=kx^2-\sqrt 2x+1$ is ______
answered Dec 30, 2014
Solution : $P(x) =kx^2- \sqrt 2 x +1$$P(1) =k(1)^2-\sqrt 2(1) +1=0$=> $k= \sqrt 2 -1$
0 votes
If $(x-2)$ is a factor of $x^5-3x^4-ax^3+3ax^2+2ax+4$ is _____
answered Dec 30, 2014
Answer : $\large\frac{3}{2}$
0 votes
The value of $k$ if $P(x)=x^3-kx^2+11x-6$ and $(x-1)$ is a factor of $P(x)$ is _____
answered Dec 30, 2014
Solution : $P(x) =x^3-kx^2+11x-6$$P(1) =1^3-k(1)^2 +11(1)-6=0$=> $1-k+11-6 =0$$-k+6 =0$$k=6$
0 votes
The value of $k$ when $(x+3)$ is a factor of $P(x)=kx^3+x^2-22x-21$ is ________
answered Dec 30, 2014
Solution : $P(x) =kx^3+x^2-22x-21$$P(-3) =k(-3)^3+(-3)^2-22(-3) -21 =0$=> $-27k +9+66 -21 =0$=>...
0 votes
The expression $2x^3+ax^2+bx-2$ leaves remainder $7$ and $10$ when divided by $2x-3$ and $x+2$ respectively.The values of $a$ and $b$ are
answered Dec 30, 2014
Answer : $3,-3$The values of $a$ and $b$ are $3,-3$
0 votes
Find the remainder when $x^3-ax^2+6x-a$ is divided by $x-a$.
answered Dec 30, 2014
Answer : $5a$
0 votes
When $x^3+2x^2+4x+b$ is divided by $x+1$ the quotient is $x^2+ax+3$ and remainder is $-3+2b$.The values of $a$ and $b$ are
answered Dec 30, 2014
Answer : $1,0$The values of $a$ and $b$ are $1,0$
0 votes
$p(x)=kx^3+3x^2-3$ and $q(x)=2x^3-5x+k$ when divided by $x-4$ leaves the same remainder in each case,the value of $k$ is
answered Dec 30, 2014
Answer : $1$
0 votes
$6x^2+ax+7$ when divided by $x-2$ gives remainder $13$.The value of $a$ is
answered Dec 30, 2014
Answer : $-9$
0 votes
The remainder when $P(x)=x^3+3x^2+3x+1$ is divided by $x-\large\frac{1}{2}$ is _____
answered Dec 30, 2014
Answer : $\large\frac{27}{8}$
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