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

11) If the equation ax²-8x+4=0 has equal roots then a =

A) 2

B) 3

C) 4

D) 5

View Answer

C) 4
Explanation:If the equation ax² – 8x + 4 = 0 has equal roots, then a = ?
Solution:
For equal roots, discriminant (D) = 0.
Given:
$D = b^2 - 4ac = 0$
Here, b = -8, a = a, c = 4.
So,
$(-8)^2 - 4(a)(4) = 0$
64 – 16a = 0
16a = 64
a = 4

12) If $\frac{a_1}{a_2}$ = $\frac{b_1}{b_2}$ ≠ $\frac{c_1}{c_2}$ , then the lines are

A) Unique solution

B) Coincident

C) Infinitely many solutions

D) No solutions

View Answer

D) No solutions
Explanation:If $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$ , then the lines are:
Solution:
This condition implies that the lines are parallel but not coincident, so they have no solution.
Answer: No solutions

13) The number ‘π’ is a

A) Natural number

B) Rational number

C) Integer

D) Irrational number

View Answer

D) Irrational number
Explanation:The number ‘π’ is a:
Solution:
π (pi) is an irrational number because it cannot be expressed as a fraction of two integers.
Answer: Irrational number

14) If the H.C.F of any two numbers is equal to ‘1’ then those numbers are called as

A) Coprime numbers

B) Prime numbers

C) Irrational numbers

D) Rational numbers

View Answer

A) Coprime numbers
Explanation:If the HCF of any two numbers is equal to ‘1’, then those numbers are called:
Solution:
Numbers with HCF = 1 are called coprime numbers.
Answer: Coprime numbers

15) The value of log₁₂₅₀ 1250 is

A) 0

B) 1

C) 2

D) 3

View Answer

B) 1
Explanation:The value of log₁₂₅₀ 1250 is:
Solution:
By definition, $\log_b b = 1$ for any base b.
Answer: 1

16) How many two-digit numbers are divisible by 3?

A) 30

B) 35

C) 40

D) 45

View Answer

A) 30
Explanation:How many two-digit numbers are divisible by 3?
Solution:
The smallest two-digit number divisible by 3 is 12, and the largest is 99.
Number of terms:
$\frac{99 - 12}{3} + 1 = \frac{87}{3} + 1 = 29 + 1 = 30$ .
Answer: 30

17) In an A.P if the first term is 4 and 9th term is 20 then 15th term is

A) 16

B) 32

C) 18

D) 36

View Answer

B) 32
Explanation:In an A.P., if the first term is 4 and the 9th term is 20, then the 15th term is:
Solution:
Given:
First term ( $a_1$ ) = 4
9th term ( $a_9$ ) = 20
In an A.P.,
$a_n = a_1 + (n-1)d$
So,
$a_9 = 4 + 8d = 20$
8d = 16
d = 2
Now,
15th term ( $a_{15}$ )
= 4 + 14 × 2
= 4 + 28
= 32.
Answer: 32

18) The pair of equations x=0 and x=5 has

A) Unique solutions

B) Infinitely many solutions

C) Two solutions

D) No solutions

View Answer

D) No solutions
Explanation:The pair of equations x=0 and x=5 has:
Solution:
x = 0 and x = 5 are two parallel vertical lines, so they never intersect.
Answer: No solutions

19) The degree of a quadratic equation ax² + bx+c=0, a≠0 is

A) 2

B) √2

C) 3√2

D) 2√2

View Answer

A) 2
Explanation:The degree of a quadratic equation ax² + bx + c = 0, a≠0 is:
Solution:
The degree of a quadratic equation is 2 (highest power of x.
Answer: 2

20) The distance between the points (2,3) and (4,1) is

A) 2

B) √2

C) 3√2

D) 2√2

View Answer

D) 2√2
Explanation:The distance between the points (2,3) and (4,1) is:
Solution:
Using the distance formula:
$d = \sqrt{(4-2)^2 + (1-3)^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2}$ .
Answer: 2√2
Here are the correct answers with brief explanations for questions 21 to 40 from the TS POLYCET 2022 Mathematics section:

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