AP Polycet (Polytechnic) 2022 Previous Question Paper with Answers And Model Papers With Complete Analysis

6) If log $\frac ab$ +log $\frac ba$ = log(a+b), then

A) a+b=1
B) a=b
C) a-b=1
D) None of these

View Answer

A) a+b=1

Explanation:Use log laws:
$\log\frac{a}{b} + \log\frac{b}{a} = \log(a+b)$ $\log\left(\frac{a}{b} × \frac{b}{a}\right) = \log(1) = 0$
So, log(a+b) = 0 ⇒ a+b = 1

7) Which of the following collections is not a set?

A) The collection of all boys in a class
B) The collection of all even integers
C) The collection of ten most talented writers of India
D) None of the above

View Answer

C) The collection of ten most talented writers of India

Explanation:”A collection of ten most talented writers of India” is not well-defined (subjective) → not a set

8) Match the following:

a) Null set	(i) {x:x is a real number}
b) singleton set	(ii) (x:x is a whole number and x<0}
c) Infinite set	(iii) {x:x is an even prime number}

A) A-(i),B-(ii),C-(iii)
B) A-(iii),B-(ii),C-(i)
C) A-(ii),B-(i),C-(iii)
D) A-(ii),B-(iii),C-(i)

View Answer

D) A-(ii),B-(iii),C-(i)

Explanation:a) Null set → (ii) {x: x is a whole number and x < 0} = Ø
b) Singleton set → (iii) {x: x is an even prime number} = {2}
c) Infinite set → (i) {x: x is a real number}
Answer:A-(ii), B-(iii), C-(i)

9) If A and B are disjoint sets, then

A) AUB=A
B) A∩B=A
C) A∩B={0}
D) A∩B=Φ

View Answer

D) A∩B=Φ

Explanation:Disjoint sets → no common elements → intersection = empty set
Answer:A ∩ B = Φ

10) In a class of 60 students, 45 students like music, 50 students like dance and 5 students like neither. Then the number of students in the class who like both music and dance is

A) 35
B) 40
C) 50
D) 55

View Answer

B) 40

Explanation:Let M = students liking music = 45
D = dance = 50
Total = 60, 5 like neither → 55 like music or dance
Use:
n(M ∪ D) = n(M) + n(D) – n(M ∩ D)
→ 55 = 45 + 50 – x → x
= 40

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