Mathematics · Quantitative Aptitude

Algebra and Arithmetic

333 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

The H.C.F of (x3 + x2 + x + 1) and (x4 - 1) is

  1. (x2 - 1) (x2 + 1)

  2. (x + 1) (x2 + 1)

  3. (x + 1 ) (x2 - 1)

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

x3 + x2 + x + 1 = (x2 + 1) (x + 1) and x4 - 1 = (x - 1) (x + 1) (x2 + 1) H.C.F. = (x + 1) (x2 + 1)

Multiple choice

A batsman in his 18th inning makes a score of 95 and thereby increases his average by 2. What is his average after 18th inning?

  1. 41

  2. 51

  3. 61

  4. 38

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let his original average of 17 innings = x So, the some of his runs of 17 innings = 17x Now his new average = x + 2 So, the new sum of his runs of 18 innings = 18(x + 2) Therefore difference of his 17 and 18 innings = 95 So, 18(x + 2) - 17x = 95 x = 59 So, his original average is 59 and his average after 18th innings = 59 + 2 => 61 Therefore, 61 is correct answer.

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. 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.