Mathematics · Quantitative Aptitude

Algebraic Expressions and Polynomials

292 Questions

Algebraic expressions and polynomials form the foundation of algebra, involving variables, constants, and mathematical operations. This topic is heavily tested in the quantitative aptitude sections of SSC, banking, and state exams. Use these questions to practice expanding, factoring, and simplifying various polynomial expressions.

Expanding algebraic expressionsFactoring polynomialsAlgebraic identitiesFinding common factorsSimplifying numerical statements

Algebraic Expressions and Polynomials Questions

Multiple choice technology databases

What is filter factor?

  1. One divided by the number of distinct values of a column.

  2. Zero divided by the number of distinct values of a column.

  3. Zero divided by the number of distinct values of a row.

  4. One divided by the number of distinct values of a Rrow.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Filter factor (or selectivity) is a measure used by query optimizers to estimate the fraction of rows that satisfy a predicate. For an equality predicate on a column with a uniform distribution, it is calculated as 1 divided by the number of distinct values (NDV).

Multiple choice technology

FIELD ("+1+2+3ABAC","+", 2,2) =?

  1. 1

  2. 1+2

  3. 3ABAC

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

The FIELD function extracts a substring between two occurrences of a delimiter. FIELD("+1+2+3ABAC", "+", 2, 4) means: find the substring between the 2nd and 4th occurrences of "+". The delimiters are at positions: 1st at 0, 2nd at 2, 3rd at 4, 4th at 6. The substring between positions 2 and 4 is "1+2".

Multiple choice

The Boolean expression F(X, Y, Z) = $\bar{X}Y \bar{Z} + X\bar{Y}\bar{Z} + XY\bar{Z} + XYZ$ converted into the canonical product of sum (POS) form is
  1. (X + Y + Z) (X + Y + $\bar{Z}$) (X + Y + $\bar{Z}$) ($\bar{X}$ + Y + $\bar{Z}$)
  2. (X + $\bar{Y}$ + Z) ($\bar{X}$ + Y + $\bar{Z}$) ($\bar{X}$ + $\bar{Y}$ + Z) ($\bar{X}$ + $\bar{Y}$ + $\bar{Z}$)
  3. (X + Y + Z) ($\bar{X}$ + Y + $\bar{Z}$) (X + $\bar{Y}$ + Z) ($\bar{X}$ + $\bar{Y}$ + $\bar{Z}$)
  4. (X + $\bar{Y}$ + $\bar{Z}$) (X + Y + Z) (X + $\bar{Y}$ + Z) (X + Y + Z)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Multiple choice

Directions: Carry Two Marks Each.

A function of Boolean variables X, Y and Z is expressed in terms of the minterms as

$F(X, Y, Z) = \sum(1, 2, 5, 6, 7)$

Which of the following products of sums given below is equal to the function F(X, Y, Z)?
  1. $(\bar{X} + \bar{Y}+ \bar{Z}).(\bar{X} + Y + Z).(X + \bar{Y}+\bar{Z})$
  2. $(X + Y + Z).(X + \bar{Y} + \bar{Z}).(\bar{X} + Y + Z)$
  3. $(\bar{X} + \bar{Y} + Z).(\bar{X} + y + \bar{Z}). (X + \bar{Y}+ Z).(X + Y + \bar{Z}).(X + Y + Z)$
  4. $( X + y + \bar{Z}) . (\bar{X} + Y + Z). (\bar{X} + Y + \bar{Z}).(\bar{X} + \bar{Y}+ \bar{Z})$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Multiple choice

Find the sum of additive inverse and multiplicative inverse of the following expression? (abc/de)

  1. {(de)2 + (abc)2}/ abcde

  2. {(de)2 - (abc)2}/ abcde

  3. {(de)2 - (abc)2}/ abde

  4. {(de)2 - (abc)2}/ de

  5. {(de)2 - (abc)2}/ abc
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given expression is (abc/de). Additive inverse of the given expression is (- abc/de). Thus, abc/de - abc/de = 0 Multiplicative inverse of the given expression is (de/abc). Thus, abc/de x de/abc = 1 So, the required sum of additive inverse and multiplicative inverse = - abc/de + de/abc = {(de)2 - (abc)2}/ abcde

Multiple choice

What is (7x + 5) (4y + 5) in expanded form?

  1. 28xy + 26 + 37x + 21y

  2. 28xy + 26 + 37y + 21x

  3. 28xy + 25 + 35y + 20x

  4. 28xy + 25 + 35x + 20y
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

(7x + 5) (4y + 5) = 28xy + 35x + 20y + 25            (Using Foil)