Algebra Questions and Answers

If $a=b^x, b=c^y text{ and } c = a^z,$, $b=c^y$  and $c=a^z$ then the value of $xyz$ is equal to

A bill for Rs. 40 is paid by means for Rs. 5 notes and Rs. 10 notes. Seven notes are used in all. If $x$ is the number of Rs. 5 notes and $y$ is the number of Rs 10 notes then

if $sqrt{1 + frac{55}{729}} = 1 + frac{x}{27}$,  then the value of $x$ is

If $5x^3 + 5x^2 - 6x + 9$ is divided by $(x + 3)$, then the remainder is:

If $x + y = 2$, then the value of $x^4 + y^4 - x^3y^2 - x^2y^3 + 16xy$ is equal to

If the roots of the equation $ax^2 + 2bx + c = 0$ are $alpha text{ and } beta$ is equal to 

If $2^x = 4^y = 8^z$ and $xyz = 288$, then $frac{1}{2x} + frac{1}{4y} + frac{1}{8z}$ is equal to 

if  $Big(frac{a}{b} Big)^{x-1} = Big(frac{b}{a}Big)^{x-3}$, then the value of $x$ is 

The solution of the equation $2^{x-7} = 256$ is

$x$ varies inversely as the square of $y$. Given that $y=2$ for $x=1$. The value of $x$ for $y=6$ will be equal to

$x^4 - mx^3 + 2x^2 - 5x + 8 = 0$, when divided by $x - 2$, gives remainder as $3m$. Then the value of $3m$ is equal to

If $x^m = y^n = z^p, xyz = 1 text{ and } m ne 0$, then $frac{1}{m} + frac{1}{n} + frac{1}{p}$ is equal to

The value of $k$, for which the system of equations $x + 2y + 7 = 0$ and $2x + ky + 14 = 0$ will have infinitely many solutions, is

Roots of the equation $x^2 + x(2 - p^2) - 2p^2 = 0$ are

If one root of the equation $ax^2 + bx + c = 0, a ne 0$, is reciprocal of the other, then

If $alpha$ and $beta$ are the roots of the equation $x^2 - px + q = 0$, then the equation whose roots are $alpha beta + alpha + beta$ and $alpha beta - alpha - beta$ is

Roots of the equation $frac{(x - b)(x -c)}{(a - b)(a - c)} a^2 + frac{(x - a)(x - c)}{(b - c)(b - a)}b^2 = x^2$ are

Solution of $4^{2x} = frac{1}{32}$ is

If $10^{2y} = 25$, then to $10^{-y}$ equals

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

If $a + b + c = 2s$, then the value of $(s - a)^2 + (s - b)^2 + (s - c)^2 + s2$ will be:

If $a^3 = 117 + b^3$ and $a = 3 + b$, then the value of $a + b$ is:

If $a^{m + 5} = 2^{2m + 10}$, then, using the law of indices, the value of $a$ is:

If $alpha, beta, gamma$ and $delta$ are the roots of the polynomial equation $(x^2 - 3x + 4)(x^2 + 2x + 5) = 0$ then quadratic equation whose roots are $alpha + beta + gamma + delta$ and $alpha beta gamma delta$ is:

The solution for real $x$ in equation $x^2 - 2x + 1 lt 0$ is:

If $x + y = 1$, then the largest value of $xy$ is

If $x - y = 1$ and $x^2 + y^2 = 41$, then the value of $x + y$ will be:

If $sqrt{dfrac{x}{y}} + sqrt{dfrac{y}{x}} = dfrac{10}{3}$ and $x + y =10$, then the value of $xy$ will be:

If $a = 3$ and $b * c = frac{sqrt{(b-c) + (b^2 - c^2)}}{2bc}$  then calculate $a times b * c$ for $b = 7, c = 3$—