Which of the following is incorrect?

Important Questions on Algebraic Expressions

EASY

Aptitude>Algebra>Algebraic Expressions>Polynomials

If $2{\mathrm{x}}^2+{\mathrm{y}}^2+8{\mathrm{z}}^2-2\sqrt{2}\mathrm{xy}+4\sqrt{2}\mathrm{yz}-8\mathrm{zx}={\left(\mathrm{Ax}+\mathrm{y}+\mathrm{Bz}\right)}^2$, then the value of $\left({\mathrm{A}}^2+{\mathrm{B}}^2-\mathrm{AB}\right)$ is:

HARD

Aptitude>Algebra>Algebraic Expressions>Polynomials

If $\mathrm{x}+\mathrm{y}+\mathrm{z}=3$, and ${\mathrm{x}}^2+{\mathrm{y}}^2+{\mathrm{z}}^2=101$, then what is the value of $\sqrt{{\mathrm{x}}^3+{\mathrm{y}}^3+{\mathrm{z}}^3-3xyz}$?

EASY

Aptitude>Algebra>Algebraic Expressions>Polynomials

Expand ${\left(\frac{\mathrm{x}}{3}+\frac{\mathrm{y}}{5}\right)}^3$

EASY

Aptitude>Algebra>Algebraic Expressions>Polynomials

Which is the largest six-digit number, which when divided by $12, 15, 20, 24$ and $30$, leaves the remainders $8, 11, 16, 20$ and $26$ respectively.

MEDIUM

Aptitude>Algebra>Algebraic Expressions>Polynomials

Two positive numbers differ by $2001$. When the larger number is divided by the smaller number, the quotient is $9$ and the remainder is $41$. The sum of the digits of the larger number is:

EASY

Aptitude>Algebra>Algebraic Expressions>Polynomials

If $\left(x^3-y^3\right):\left(x^2+xy+y^2\right)=5:1$ and $\left(x^2-\right.\left.y^2\right):(x-y)=7:1$, then the ratio $2 x: 3 y$ equals

EASY

Aptitude>Algebra>Algebraic Expressions>Polynomials

If $1-64{\mathrm{x}}^3-12\mathrm{x}+{\mathrm{px}}^2={\left(1-4\mathrm{x}\right)}^3$, then the value of $\mathrm{p}$ is:

MEDIUM

Aptitude>Algebra>Algebraic Expressions>Polynomials

Let $x$ be the least number divisible by $13$, such that when $x$ is divided by$4, 5, 6, 7, 8$and $12$, the remainder in each case is $2$. The sum of the digits of $x$ is _____.

MEDIUM

Aptitude>Algebra>Algebraic Expressions>Polynomials

The number of polynomials $p\left(x\right)$ with integer coefficients such that curve $y=p\left(x\right)$ passes through ($2,2$) and ($4,5$) is

EASY

Aptitude>Algebra>Algebraic Expressions>Polynomials

The value of $27{\mathrm{a}}^3-2\sqrt{2}{\mathrm{b}}^3$ is equal to:

MEDIUM

Aptitude>Algebra>Algebraic Expressions>Polynomials

When $3738, 5659$ and$9501$ are divided by the greatest possible number $x$, the remainder in each case is $y$. what is the sum of $x$ and $y$?

EASY

Aptitude>Algebra>Algebraic Expressions>Polynomials

Find the remainder in the expression $\frac{557\times 653\times 672}{9}$.

EASY

Aptitude>Algebra>Algebraic Expressions>Polynomials

If $1433\times 1433\times 1422\times 1425$ is divided by $12$, then what is the remainder?

MEDIUM

Aptitude>Algebra>Algebraic Expressions>Polynomials

The ratio of the divisor to the remainder is $3 : 2$ and the ratio of the divisor to quotient is $7 : 12$. If the remainder is $14$, then the remainder when the dividend is divided by $9$ is:

EASY

Aptitude>Algebra>Algebraic Expressions>Polynomials

If the $5$-digit number $538xy$ is divisible by$3, 7$and $11$, then the value of $(x^2+y^2)$ is _____.

EASY

Aptitude>Algebra>Algebraic Expressions>Polynomials

A number when divided by $6$ leaves remainder $3$ . When the square of the same number is divided by $6$ , the remainder is

MEDIUM

Aptitude>Algebra>Algebraic Expressions>Polynomials

When a number is successively divided by $3, 4$ and $7$, the remainder obtained are $2, 3$ and $5$ respectively. What will be the remainder when $84$ divided the same number?

MEDIUM

Aptitude>Algebra>Algebraic Expressions>Polynomials

If $30x^2-15x+1=0$, then what is the value of $25x^2+{\left(36x^2\right)}^{-1}$?

EASY

Aptitude>Algebra>Algebraic Expressions>Polynomials

In a division sum, the divisor is $10$ times the quotient and $5$ times the remainder. If the remainder is $46$, the dividend is:

MEDIUM

Aptitude>Algebra>Algebraic Expressions>Polynomials

A student was asked to divide a number by $6$ and add $12$ to the quotient. He, however, first added $12$ to the number and then divided it by $6$, getting $112$ as the answer. The correct answer should have been _____.