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

21)The arithmetic mean of a-3d,a-d,a+d and a+3d

A) a

B) d

C) 2a

D) 2d

View Answer

A) a
Explanation:To find the arithmetic mean, use the formula:
$\text{Mean} = \frac{\text{Sum of terms}}{\text{Number of terms}}$

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)
$\frac{4a}{4} = a$
Final Answer: a

22)Which of the following is not a measure of central tendency

A) Mean

B) Median

C) Range

D) Mode

View Answer

C) Range

23)The product of two numbers is 30. If their HCF is 5, then LCM is

A) 5

B) 6

C) 4

D) 8

View Answer

B) 6
Explanation:Use the shortcut formula:
$\text{HCF} \times \text{LCM} = \text{Product of the numbers}$

Given:
Product = 30
HCF = 5
So:
$5 \times \text{LCM} = 30 \Rightarrow \text{LCM} = \frac{30}{5} = 6$

Final Answer: 6

24)The smallest odd composite number is

A) 3

B) 5

C) 7

D) 9

View Answer

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

25)√2 is

A) a rational number

B) an irrational number

C) a prime number

D) a composite number

View Answer

B) an irrational number

26)If log₂ x² = 2, then x=

A) 2

B) -2

C) 3

D) -3

View Answer

A) 2
Explanation:To solve the equation $\log_2 x^2 = 2$

, let's follow these steps:
Step 1: Rewrite the Logarithmic Equation in Exponential Form
Given:
$\log_2 x^2 = 2$

This means:
$2^2 = x^2$

$4 = x^2$

Step 2: Solve for x
Take the square root of both sides:
$x = \sqrt{4} \quad \text{or} \quad x = -\sqrt{4}$

$x = 2 \quad \text{or} \quad x = -2$

Step 3: Verify the Solutions
Both x = 2 and x = -2 satisfy the original equation because:
$\log_2 (2)^2 = \log_2 4 = 2 \quad \text{and} \quad \log_2 (-2)^2 = \log_2 4 = 2$

Final Answer
Both A. 2 and B. -2 are correct solutions. However, if the question expects a single answer, either $2$

or $-2$

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)

27)Set of even prime numbers is

A) {3,4}

B) {4,6,8}

C) {8,10}

D) {2}

View Answer

D) {2}

28)If A∩B = B, then the correct statement is

A) A⊆B

B) B⊂A

C) A≠Φ

D) B≠Φ

View Answer

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

29)Which of the following sets are finite

A) set of all natural numbers

B) set of all prime numbers

C) set of months in a year

D) none of these

View Answer

C) set of months in a year

30)The number of zeroes, a biquadratic polynomial can have at most is

A) 1

B) 2

C) 3

D) 4

View Answer

D) 4
Explanation:A biquadratic polynomial is a polynomial of degree 4, typically of the form:
$ax^4 + bx^2 + c$

Even though it's written in terms of $x^2$

, 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

Your Score: 0 / 0

Spread the love

Pages: 1 2 3 4 5 6 7 8 9 10 11 12

Leave a Comment Cancel Reply