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

A) a
Explanation:To find the arithmetic mean, use the formula:

Given terms:a – 3d, a – d, a + d, a + 3d
Step 1: Add them all
(a – 3d) + (a – d) + (a + d) + (a + 3d) = 4a
Step 2: Divide by number of terms (4)

Final Answer: a

C) Range

B) 6
Explanation:Use the shortcut formula:

Given:
Product = 30
HCF = 5
So:

Final Answer: 6

D) 9
Explanation:A composite number has more than two factors (not prime), and an odd number is not divisible by 2.
Check options:
3 → Prime
5 → Prime
7 → Prime
9 → 3 × 3 → More than 2 factors → Composite and odd
Final Answer: 9

B) an irrational number

A) 2
Explanation:To solve the equation , let’s follow these steps:
Step 1: Rewrite the Logarithmic Equation in Exponential Form
Given:

This means:


Step 2: Solve for x
Take the square root of both sides:


Step 3: Verify the Solutions
Both x = 2 and x = -2 satisfy the original equation because:

Final Answer
Both A. 2 and B. -2 are correct solutions. However, if the question expects a single answer, either or is acceptable.
If the options are to be interpreted as allowing multiple correct answers, both A and B are correct.
But typically, such questions expect one correct choice, so you can select either A. 2 or B. -2 based on the context.
However, looking at the options, both A and B are correct. If only one option is to be selected, the primary answer is: A. 2
(and B. -2 is also correct)
If the question implies selecting all correct options, then both A and B are correct.
But in most standard cases, the simplest answer is:
A. 2
*(Note: Since logarithms of squared numbers are defined for both positive and negative values, both solutions are valid.)
Conclusion
The correct options are A and B, but if only one answer is expected, A. 2 is the standard choice.
Final Answer: A. 2 (and B. -2 is also correct)

D) {2}

B) B⊂A
Explanation:We are given:
A ∩ B = B
This means:
All elements of B are also in A, because the intersection gives back B itself.
So, B is a subset of A, i.e.,B ⊆ A
Which matches Option B: B ⊂ A
(Note: In some contexts, ⊂ is used to mean ⊆ — subset. If strict subset is intended, the wording would be different.)
Final Answer: B ⊂ A

C) set of months in a year

D) 4
Explanation:A biquadratic polynomial is a polynomial of degree 4, typically of the form:

Even though it’s written in terms of , its highest power is 4.
Shortcut:
A polynomial of degree n can have at most n real or complex zeroes.
So, a biquadratic polynomial (degree 4) can have:
At most 4 zeroes
Final Answer: 4