Mathematics · Quantitative Aptitude

Algebra and Arithmetic

406 Questions

Algebra and arithmetic questions cover fundamental mathematical operations, inequalities, and binomial products. They assess core quantitative reasoning skills required for various aptitude tests. Solving these problems strengthens the understanding of number systems and algebraic identities.

Binomial productsLinear inequalitiesLeast common multipleQuadratic equationsInteger properties

Algebra and Arithmetic Questions

Multiple choice

Which of the following is correct?

  1. (a-b)2 = a2 + 2ab – b2

  2. (a-b)2 = a2 -2ab + b2

  3. (a-b)2 = a2 – b2

  4. (a+b)2 = a2 + 2ab –b2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

(a-b)2 = a2 – 2ab + b2

Multiple choice

A2 – B2 is equal to

  1. (a –b)2

  2. (a –b) (a –b)

  3. (a +b) (a-b)

  4. (a +b) (a+ b)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

a2 – b2 = (a+b ) (a- b )

Multiple choice

In boolean algebra, x + 0 = _____

  1. 0

  2. 1

  3. x

  4. y
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In Boolean algebra, the identity law states that any variable ORed with 0 remains unchanged (x + 0 = x).

Multiple choice

In boolean algebra, x + 1 = _____

  1. 0

  2. 1

  3. x

  4. y
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In Boolean algebra, the null element law states that any variable ORed with 1 results in 1 (x + 1 = 1).

Multiple choice

In boolean algebra, x + x = _____

  1. 0

  2. 1

  3. x

  4. y
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to the idempotent law for OR, any variable ORed with itself results in the same variable. Therefore, x + x equals x.

Multiple choice

In boolean algebra, x + x' = _____

  1. 0

  2. 1

  3. x

  4. y
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

According to the complement law, a variable ORed with its complement always results in 1, because one of the two must be true.

Multiple choice

In boolean algebra, x. x' = _____

  1. 0

  2. 1

  3. x

  4. y
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

According to the complement law, a variable ANDed with its complement always results in 0, because it is impossible for both to be true simultaneously.

Multiple choice

In boolean algebra, (x')' = _____

  1. x

  2. y

  3. 0

  4. 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The involution law states that the double complement of a variable returns the original variable. Therefore, (x')' equals x.

Multiple choice

If (2a + 3b)(2c - 3d)=(2a - 3b)(2c + 3d)Then

  1. a/b = c/d

  2. a/d = c/b

  3. a/b = d/c

  4. b/a = c/d

  5. none of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

(2a + 3b)(2c - 3d)=(2a - 3b)(2c + 3d)(2a + 3b) / (2a - 3b) = (2c + 3d) / (2c - 3d)4ac -6ad +6bc -9bd = 4ac + 6ad - 6bc - 9bd12bc = 12 adbc = ada/b = c/dHence the option is correct