Value of $p^2-3q+7$ is when $p=3$ and $q=2$.

Important Questions on Introduction to Algebra

MEDIUM

Mathematics>Algebra>Introduction to Algebra>Variables

what is the value of $\alpha (\alpha \ne 0)$ for which $x^2-5x+\alpha$ and $x^2-7x+2\alpha$ have a common factor?

MEDIUM

Mathematics>Algebra>Introduction to Algebra>Variables

If $4x^4-37x^2+9=0$, $x>\sqrt{\frac{3}{2}}$, then what is the value of $8x^3-\frac{27}{x^3}$?

MEDIUM

Mathematics>Algebra>Introduction to Algebra>Variables

If $a^2+c^2+17=2(a-8b-2b^2)$, then what is the value of $(a^3+b^3+c^3)$?

MEDIUM

Mathematics>Algebra>Introduction to Algebra>Variables

If $ab+bc+ca=0$, then what is the value of $\frac{a^2}{a^2-bc}+\frac{b^2}{b^2-ca}+\frac{c^2}{c^2-ab}$?

MEDIUM

Mathematics>Algebra>Introduction to Algebra>Variables

If $b+c=ax$, $c+a=by$, $a+b=cz$ then the value of $\frac{1}{9}\left[\frac{1}{x+1}+\frac{1}{y+1}+\frac{1}{z+1}\right]$ is :

MEDIUM

Mathematics>Algebra>Introduction to Algebra>Variables

If $\left(x+2\right)$ is a common factor of $x^2+ax+b$ and $x^2+bx+a$, then the ratio $a:b$ is equal to

MEDIUM

Mathematics>Algebra>Introduction to Algebra>Variables

If $a-\frac{12}{a}=1$, where $a>0$, then find the value of $a^2+\frac{16}{a^2}$.

MEDIUM

Mathematics>Algebra>Introduction to Algebra>Variables

If $\frac{\mathrm{b}}{\mathrm{y}}+\frac{\mathrm{z}}{\mathrm{c}}=1$ and $\frac{\mathrm{c}}{\mathrm{z}}+\frac{\mathrm{x}}{\mathrm{a}}=1$, then what is $\frac{\mathrm{ab}+\mathrm{xy}}{\mathrm{bx}}$ equal to?

EASY

Mathematics>Algebra>Introduction to Algebra>Variables

If $\mathrm{a}=2\mathrm{b}=8\mathrm{c}$ and $\mathrm{a}+\mathrm{b}+\mathrm{c}=13$ then the value of $\frac{\sqrt{{\mathrm{a}}^2+{\mathrm{b}}^2+{\mathrm{c}}^2}}{2\mathrm{c}}$ is:

HARD

Mathematics>Algebra>Introduction to Algebra>Variables

$ab(a-b)+bc(b-c)+ca(c-a)$ is equal to:

MEDIUM

Mathematics>Algebra>Introduction to Algebra>Variables

If the sum of the squares of three consecutive natural numbers $110$, then the sum of their cubes is:

MEDIUM

Mathematics>Algebra>Introduction to Algebra>Variables

If the value of ${(a+b-2)}^2+{(b+c-5)}^2+{(c+a-5)}^2=0$, then the value of $\sqrt{{(b+c)}^a+{(c+a)}^b-1}$ is:

MEDIUM

Mathematics>Algebra>Introduction to Algebra>Variables

If $x=2+2^{\frac{2}{3}}+2^{\frac{1}{3}}$, then the value of the expression $x^3-6x^2+6x$ will be:

MEDIUM

Mathematics>Algebra>Introduction to Algebra>Variables

If$𝑥 = 111\dots \dots 1 (20 digits),$ $𝑦 = 333\dots .3 (10 digits)$and$𝑧 = 222\dots \dots .2 (10 digits),$ then what is $\frac{𝑥-{𝑦}^2}{z}$ equal to?

MEDIUM

Mathematics>Algebra>Introduction to Algebra>Variables

If $\alpha$ and $\beta$ are two real numbers such that $\alpha +\beta =-qp$ and $\alpha \beta =rp$, where $1 < p < q < r$, then which one of the following is the greatest?

MEDIUM

Mathematics>Algebra>Introduction to Algebra>Variables

If $2b=a+c$ and $y^2=xz$, then what is $x^{b-c}{y}^{c-a}{z}^{a-b}$ equal to?

EASY

Mathematics>Algebra>Introduction to Algebra>Variables

If $a+b=2c$ , then what is the value of$\frac{a}{a-c}+\frac{c}{b-c}$  ?

EASY

Mathematics>Algebra>Introduction to Algebra>Variables

A sum of $₹8200$ was divided among $A,B$ and $C$ in such a way that $A$ has $₹500$ more than $B$, and $C$ has $₹300$ more than $A$. How much was $A\text{'}s$ share (in $₹$)?

EASY

Mathematics>Algebra>Introduction to Algebra>Variables

If $3^a={27}^b={81}^c$ and $abc=144$, then the value of $12\left(\frac{1}{a}+\frac{1}{2b}+\frac{1}{5c}\right)$ is:

MEDIUM

Mathematics>Algebra>Introduction to Algebra>Variables

For $\frac{1}{5+2\sqrt{3}}$, find the rational value of denominator in vehicles.