x 3 27 + x 2 y 15 + xy 2 25 + y 3 125

x 3 27 + x 2 y 25 + xy 2 25 + y 3 125

x 3 25 + x 2 y 15 + xy 2 25 + y 3 125

x 3 27 + xy 15 + xy 2 25 + y 3 125

The value of 27 a 3 - 2 2 b 3 is equal to:

3 a - 2 b 9 a 2 + 2 b 2 + 3 2 ab

3 a - 2 b 9 a 2 + 2 b 2 + 6 2 ab

3 a - 2 b 9 a 2 - 2 b 2 - 3 2 ab

3 a - 2 b 9 a 2 - 2 b 2 + 6 2 ab

MEDIUM

Earn 100

Consider the following statements:

$1 . x^{4} (y - z) + y^{4} (z - x) + z^{4} (x - y)$ is positive if $x > y > z$

$2 . x^{4} (y - z) + y^{4} (z - x) + z^{4} (x - y)$ is negative if $x < y < z$

Which of the following statements is/are correct?

50% studentsanswered this correctly

Important Questions on Complex Numbers

EASY

Mathematics>Algebra>Complex Numbers>Quadratic Equation with Complex Roots

2 x^{2} + y^{2} + 8 z^{2} - 2 \sqrt{2} xy + 4 \sqrt{2} yz - 8 zx = {(Ax + y + Bz)}^{2}

, then the value of

(A^{2} + B^{2} - AB)

is:

EASY

Mathematics>Algebra>Complex Numbers>Quadratic Equation with Complex Roots

The coefficient of

y

in the expansion

{(2 y - 5)}^{3}

, is:

EASY

Mathematics>Algebra>Complex Numbers>Quadratic Equation with Complex Roots

Expand

{(\frac{x}{3} + \frac{y}{5})}^{3}

MEDIUM

Mathematics>Algebra>Complex Numbers>Quadratic Equation with Complex Roots

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

Mathematics>Algebra>Complex Numbers>Quadratic Equation with Complex Roots

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

Mathematics>Algebra>Complex Numbers>Quadratic Equation with Complex Roots

If the

5

-digit number

538 x y

is divisible by

3, 7

and

11

, then the value of

(x^{2} + y^{2})

is _____.

EASY

Mathematics>Algebra>Complex Numbers>Quadratic Equation with Complex Roots

1 - 64 x^{3} - 12 x + {px}^{2} = {(1 - 4 x)}^{3}

, then the value of

p

is:

MEDIUM

Mathematics>Algebra>Complex Numbers>Quadratic Equation with Complex Roots

The product of the polynomials

(x + 2), (x - 2), (x^{3} - 2 x^{2} + 4 x - 8)

and

(x^{3} + 2 x^{2} + 4 x + 8)

MEDIUM

Mathematics>Algebra>Complex Numbers>Quadratic Equation with Complex Roots

The number of polynomials

p (x)

with integer coefficients such that curve

y = p (x)

passes through (

2, 2

) and (

4, 5

) is

EASY

Mathematics>Algebra>Complex Numbers>Quadratic Equation with Complex Roots

The value of

27 a^{3} - 2 \sqrt{2} b^{3}

is equal to:

MEDIUM

Mathematics>Algebra>Complex Numbers>Quadratic Equation with Complex Roots

what is the value of

α (α \neq 0)

for which

x^{2} - 5 x + α

and

x^{2} - 7 x + 2 α

have a common factor?

EASY

Mathematics>Algebra>Complex Numbers>Quadratic Equation with Complex Roots

Find the remainder in the expression

\frac{557 \times 653 \times 672}{9}

MEDIUM

Mathematics>Algebra>Complex Numbers>Quadratic Equation with Complex Roots

What are the factors of

x^{3} + 4 x^{2} - 11 x - 30

MEDIUM

Mathematics>Algebra>Complex Numbers>Quadratic Equation with Complex Roots

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

MEDIUM

Mathematics>Algebra>Complex Numbers>Quadratic Equation with Complex Roots

5 x^{3} + 5 x^{2} - 6 x + 9

is divided by

(x + 3)

, then the remainder is:

MEDIUM

Mathematics>Algebra>Complex Numbers>Quadratic Equation with Complex Roots

(x + 2)

is a common factor of

x^{2} + a x + b

and

x^{2} + b x + a

, then the ratio

a : b

is equal to

EASY

Mathematics>Algebra>Complex Numbers>Quadratic Equation with Complex Roots

Let

f (x)

and

g (x)

be two polynomials(with real coefficients) having degrees

3

and

4

respectively. What is the degree of

f (x) g (x)

MEDIUM

Mathematics>Algebra>Complex Numbers>Quadratic Equation with Complex Roots

30 x^{2} - 15 x + 1 = 0

, then what is the value of

25 x^{2} + {(36 x^{2})}^{- 1}

EASY

Mathematics>Algebra>Complex Numbers>Quadratic Equation with Complex Roots

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

Mathematics>Algebra>Complex Numbers>Quadratic Equation with Complex Roots

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 _____.

Consider the following statements: 1.x4y-z+y4z-x+z4x-y is positive if x>y>z 2.x4y-z+y4z-x+z4x-y is negative if x<y<z Which of the following statements is/are correct?

Important Questions on Complex Numbers

Learn and Prepare for any exam you want !

Consider the following statements:

$1 . x^{4} (y - z) + y^{4} (z - x) + z^{4} (x - y)$ is positive if $x > y > z$

$2 . x^{4} (y - z) + y^{4} (z - x) + z^{4} (x - y)$ is negative if $x < y < z$

Which of the following statements is/are correct?