Mathematics · Reasoning

Algebraic Expressions

183 Questions

Algebraic expressions form the foundation of mathematics, involving variables, constants, and arithmetic operations. This topic includes evaluating coefficients, solving proportional relationships, and understanding boolean logic. It is widely tested across various competitive exams to assess analytical skills.

Variable evaluationExpression coefficientsBoolean logic variablesDirect proportionalityProgramming expressions

Algebraic Expressions Questions

Multiple choice

In the circuit shown

  1. Y = $\bar A\bar B + \bar C$

  2. Y = (A +B)
  3. Y = $(\bar A + \bar B) \bar C$

  4. Y = AB + C

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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Multiple choice

If x=5 and y=++x, what are the values of x and y?

  1. x=5, y=5

  2. x=5, y=6

  3. x=6, y=6

  4. x=6, y=5

  5. x=5, y=7
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is the correct answer. Here student uses Pre increment operator of C programming language and increases the value of x by 1. After that he assigns the value of x to y and he also assigns new value to x, which is 6. So, both x and y contain 6.

Multiple choice

If x = 9.3, y = x - 5.1, z = x - 0.2, k = y + 1.5, a = k + 2.2, b = a - 1.6, h = z + 2.8, u = 625 / 25 and t = 7, then solve the following expression according to the precedence. P = (x - y + z / k - a / b - h + u % t).

  1. P = - 2.54768

  2. P = - 2.45748

  3. P = - 2.54678

  4. P = - 2.54878

  5. P = - 2.45768
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This option is correct. First z / k will be solved which comes out to be 1.59649. Then a / b will be solved which comes out to be 1.25397. Then u % t will be solved which comes out to be 4. So, the last expression will be: 5.1 + 1.59649 - 1.25397 - 11.9 + 4. Solving it, the result will be -2.45748.

Multiple choice

In Boolean algebra, x (y + z) is equal to

  1. x

  2. y

  3. x.y

  4. x.y + x.z
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

This demonstrates the distributive property in Boolean algebra: x AND (y OR z) = (x AND y) OR (x AND z). The operation distributes over OR just like in regular algebra.

Multiple choice

In Boolean algebra, (xy)' is equal to

  1. x'

  2. y'

  3. x' + y'

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

By De Morgan's theorem, the complement of an AND operation equals the OR of the complements. Thus (x · y)' = x' + y'.

Multiple choice

If (123) base 5 = (x3) y, then the number of possible values of x is

  1. 4

  2. 1

  3. 3

  4. 2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

(123)_5 = 1×25 + 2×5 + 3 = 38 in decimal. For (x3)_y = 38, we need x×y + 3 = 38, so x×y = 35. Factor pairs of 35 with x < y (required for valid digit in base y) are (1,35) and (5,7), giving x = 1 or 5. The base y must exceed the highest digit (3), so y = 35 or 7 are both valid.