AP Polycet (Polytechnic) 2021 Previous Question Paper with Answers And Model Papers With Complete Analysis

36) Which of the following in not a linear equation

A) 3x-2y = y+x
B) x+y = 1
C) 1+2x = y-5
D) 3-y = x²+4

View Answer

D) 3-y = x²+4

Explanation:To determine which is not a linear equation, we check for variables raised to powers other than 1 (i.e., squares, roots, etc.).
Definitions:
A linear equation is an equation in which each term is either a constant or the product of a constant and a single variable, and no variable is raised to a power other than 1.
Options:
A. 3x – 2y = y + x
Simplifies to 2x – 3y = 0 — Linear
B. x + y = 1
Already linear
C. 1 + 2x = y – 5
Simplifies to $2x - y = -6$ — Linear
D. $3 - y = x^2 + 4$
Has $x^2$ , which is non-linear
Correct Answer: $3 - y = x^2 + 4$

37) Which of the following represents the situation where Siri bought 5 apples and 6 oranges and Laxmi bought 2 apples and 15 oranges for same amount of total money

A) 5x+6y=2x+15y
B) 5x+15y=6x+2y
C) 5x-6y=2x-15y
D) 5x-15y=6x-2y

View Answer

A) 5x+6y=2x+15y

Explanation:We are given:
Siri bought 5 apples and 6 oranges → Cost: 5x + 6y
Laxmi bought 2 apples and 15 oranges → Cost: 2x + 15y
Total cost is same for both → So, equate both expressions:
5x + 6y = 2x + 15y
Correct Answer: 5x + 6y = 2x + 15y

38) Which of the following is a quadratic equation

A) x(x+4)=12
B) x(x+4)=x²+2x+1
C) x(x+4)-x(x-2)=0
D) x(x+4)=x(x+5)-x

View Answer

A) x(x+4)=12

Explanation:Let’s check each option to see which represents a quadratic equation (i.e., an equation of the form $ax^2 + bx + c = 0$ ):
A. x(x + 4) = 12
→ Expand LHS: $x^2 + 4x = 12$
→ Rearranged: $x^2 + 4x - 12 = 0$ Quadratic!
B. $x(x + 4) = x^2 + 2x + 1$
→ LHS: $x^2 + 4x$ , RHS: $x^2 + 2x + 1$
→ Subtract RHS: $x^2 + 4x - x^2 - 2x -1 = 0 \Rightarrow 2x - 1 = 0$
Linear, not quadratic
C. x(x + 4) – x(x – 2) = 0
→ Expand: $x^2 + 4x - (x^2 - 2x) = 0$
→ Simplify: $x^2 + 4x - x^2 + 2x = 0 \Rightarrow 6x = 0$
Linear
D. x(x + 4) = x(x + 5) – x
→ LHS: $x^2 + 4x$ , RHS: $x^2 + 5x - x = x^2 + 4x$
→ Both sides equal ⇒ 0 = 0
Identically true, not a quadratic equation
Correct Answer: $x(x+4) = 12$

39) Any equation of the form p(x)=0, where p(x) is a polynomial of degree 2 is called

A) linear equation in one variable
B) linear equation in two variables
C) quadratic equation
D) none of these

View Answer

C) quadratic equation

40) The equation x²+x-306 = 0 represents that the

A) sum of two consecutive positive integers is 306
B) product of two consecutive positive integers is 306
C) sum of squares of two consecutive positive integers is 306
D) product of squares of two consecutive positive integers is 306

View Answer

B) product of two consecutive positive integers is 306

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