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

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31)The product of the zeroes of x + 2x² + 1 is

A) -1

B) 2

C) 1

D) ½

View Answer

D) ½
Explanation:We are given the quadratic polynomial:
$f(x) = x + 2x^2 + 1$

Rewriting it in standard form:
$f(x) = 2x^2 + x + 1$

Shortcut to find product of zeroes of a quadratic:
For a quadratic $ax^2 + bx + c$

,
Product of zeroes = $\frac{c}{a}$

Here:
$a = 2$

$c = 1$

$\text{Product} = \frac{1}{2}$

Final Answer: D. ½

32)The zeroes of the polynomial x³ – x² are

A) 0,0,1

B) 0,1,1

C) 1,1,1

D) 0,0,0

View Answer

A) 0,0,1
Explanation:We are given the cubic polynomial:
$f(x) = x^3 - x^2$

Step 1: Factor the polynomial
Factor out the common term:
$f(x) = x^2(x - 1)$

Step 2: Find the zeroes
Set $f(x) = 0$

:
$x^2(x - 1) = 0 \Rightarrow x = 0,\ 0,\ 1$

So the zeroes are 0, 0, and 1.
Final Answer: 0, 0, 1

33)The quadratic polynomial whose zeroes are α,β is

A) x²-(α+β)x+αβ

B) x²+(α+β)x

C) x²-α-βx+αβ²

D) None of these

View Answer

A) x²-(α+β)x+αβ
Explanation:To form a quadratic polynomial with given zeroes $\alpha$

and $\beta$

, use the standard form:
$\boxed{x^2 - (\alpha + \beta)x + \alpha\beta}$

Final Answer: $x^2 - (\alpha + \beta)x + \alpha\beta$

34)The equation x-4y=5 has

A) no solution

B) unique solution

C) two solution

D) infinitely many solutions

View Answer

D) infinitely many solutions
Explanation:To determine the nature of the solutions for the equation $x - 4y = 5$

, let's analyze it step-by-step.
Step 1: Understand the Equation
The given equation is:
x – 4y = 5
This is a linear equation in two variables ( $x$

and $y$

).
Step 2: Express in Slope-Intercept Form
Rewriting the equation to solve for $y$

:
x – 4y = 5
-4y = -x + 5
$y = \frac{1}{4}x - \frac{5}{4}$

This is now in the slope-intercept form y = mx + b , where:
– Slope (m): $\frac{1}{4}$

– Y-intercept (b): $-\frac{5}{4}$

Step 3: Analyze the Solutions
A linear equation in two variables represents a straight line on the Cartesian plane. For such equations:
– Every point (x, y) on the line is a solution to the equation.
– Since a line extends infinitely in both directions, there are infinitely many solutions.
Step 4: Verify with Examples
Let's find a few solutions to confirm:
→1. If $x = 1$

:
$y = \frac{1}{4}(1) - \frac{5}{4} = -1$

So, $(1, -1)$

is a solution.
→2. If $x = 5$

:
$y = \frac{1}{4}(5) - \frac{5}{4} = 0$

So, $(5, 0)$

is another solution.
→3. If $x = 9$

:
$y = \frac{1}{4}(9) - \frac{5}{4} = 1$

So, $(9, 1)$

is yet another solution.
This pattern continues infinitely, demonstrating that there are infinitely many solutions.
Step 5: Conclusion
The equation $x - 4y = 5$

represents a straight line with infinitely many points (solutions).
Final Answer: Infinitely many solutions

35)If ax+b=0, then x=

A) -a

B) a

C) b/a

D) -b/a

View Answer

D) -b/a
Explanation:We are given the equation:
ax + b = 0
To solve for $x$

:
$ax = -b \Rightarrow x = \frac{-b}{a}$

Final Answer: $-\frac{b}{a}$

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