Algebra Review Test - 1

Directions for Questions 1 to 3: These are based on the functions defined below

Q(a, b) = Quotient when a is divided by b
R²(a, b) = Remainder when a is divided by b
R(a, b) = a²/b²
SQ(a, b) = √(a – 1)/√(b – 1)

Q. SQ (5, 10) – ? > 0

Directions for Questions 1 to 3: These are based on the functions defined below

Q(a, b) = Quotient when a is divided by b
R²(a, b) = Remainder when a is divided by b
R(a, b) = a²/b²
SQ(a, b) = √(a – 1)/√(b – 1)

Q. SQ (a, b) is same as

Directions for Questions 1 to 3: These are based on the functions defined below

Q(a, b) = Quotient when a is divided by b
R²(a, b) = Remainder when a is divided by b
R(a, b) = a²/b²
SQ(a, b) = √(a – 1)/√(b – 1)

Q. Which of the following relations cannot be false?

Directions for Questions 4 to 7: Answer the questions based on the following information:

W(a, b) = least of a and b
M(a, b) = greatest of a and b
N(a) = absolute value of a

Q. Find the value of 1 + M [y + N {– W (x, y)}, N {y + W (M (x, y), N (y))}] given that x = 2 and y = – 3.

Directions for Questions 4 to 7: Answer the questions based on the following information:

W(a, b) = least of a and b
M(a, b) = greatest of a and b
N(a) = absolute value of a

Q. Given that a > b, then the relation M {N (x), W (x, y)} = W [x, N {M (x, y)}] does not hold if
(a) x > 0, y < 0, |x| > |y|

Directions for Questions 4 to 7: Answer the questions based on the following information:

W(a, b) = least of a and b
M(a, b) = greatest of a and b
N(a) = absolute value of a

Q. Which of the following must be correct for x, y < 0

Directions for Questions 4 to 7: Answer the questions based on the following information:

W(a, b) = least of a and b
M(a, b) = greatest of a and b
N(a) = absolute value of a

Q. For what value of x is W (x² + 2x, x + 2) < 0?

It is given that \( (a^{n-3}+a^{n-5}b^{2}+\cdots+b^{n-3})pq=0 \), where \( p \) and \( q\neq0 \) and \( n \) is odd, then

\( \dfrac{a^n-b^n}{a^n+b^n}\cdot\dfrac{a+b}{a-b}= \ ? \)

If \( f=\dfrac{1}{\log_{2}\pi}+\dfrac{1}{\log_{4.5}\pi} \),

which of the following is true?

If px + qy > rx + sy, and y, x, p, q, r, s > 0 and if x < y, then which of the following must be true?