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

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