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

If (126)x = (56)y , find x and y

  1. 8, 16

  2. 16, 10

  3. 2, 8

  4. 16, 8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

1*x^2 + 2*x + 6 = 5*y + 6. If x=8, 64+16+6 = 86. If y=16, 5*16+6 = 86. The equation holds for x=8 and y=16.

Multiple choice

How many Boolean functions of three variables f (x, y, z) have the property f (x, y, z) = (f (x' , y' , z' ))?

  1. 8

  2. 16

  3. 64

  4. 256
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The condition f(x, y, z) = f(x', y', z') means the function is invariant under complementation of all inputs. There are 2^3 = 8 possible input combinations, which can be grouped into 4 pairs of (x, y, z) and (x', y', z'). For each pair, the function can take 2 values (0 or 1), leading to 2^4 = 16 possible functions.

Multiple choice

if x, y, z are Boolean variables, then

  1. x.x = 1

  2. x (y + z) = (x + y) (x + z)

  3. x + xz = x

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

Option D represents the Commutative Law of Boolean algebra, which states that x + y = y + x. Option A is incorrect (x.x = x), Option B is incorrect (distributive law is x + yz = (x + y)(x + z)), and Option C is incorrect (x + xz = x is actually the Absorption Law, but the question asks for a general identity).

Multiple choice

Find the values of x and y from the equations – = 1 and + = 3.5.

  1. x = 2, y = 3

  2. x = 4, y = 3

  3. x = 4, y = 9

  4. x = 2, y = 9

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

Take = a, = b. Then, the equations will become 4a – 3b = 1 ……..(1) And a + ab = 3.5 ………(2) (1) × 3 + (2)⇒ a = and by substituting a in either (1) and (2), we can get b = . a = = ⇒ x = 4 and b = = ⇒ y = 9 Option 3 is correct.

Multiple choice

Find the respective values of x and y.

37x + 29y = 53 29x + 37y = 13

  1. 3 and - 2

  2. 2 and - 3

  3. 3 and 2

  4. -3 and - 2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

37x + 29y = 53...(i)29x + 37y =13...(ii) Adding (i) and (ii), we get66x + 66y = 66$\Rightarrow$ x + y = 1 ... (iii) Subtracting (ii) from (i), we get 8x - 8y = 40$\Rightarrow$ x- y = 5 ...(iv) Adding (iii) and (iv), we get 2x = 6$\Rightarrow$x = 3. Subtracting (iv) from (iii), we get 2y = -4$\Rightarrow$ y = - 2 Hence, the solution is x = 3 and y = -2.