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

21) Which of the following equation is not a linear equation

A) 2+3x=y-5
B) 3-x=y²+7
C) x+3y=2y-x
D) 5x+2y=0

View Answer

B) 3-x=y²+7

Explanation:Which of the following equations is not a linear equation?
(2 + 3x = y – 5) → Linear(Degree 1)
(3 – x = y² + 7) → Not linear(Degree 2 in (y))
(x + 3y = 2y – x) → Linear(Degree 1)
(5x + 2y = 0) → Linear(Degree 1)

22) If x²+kx+1=0 has a root x=1 then k =

A) 1
B) 2
C) 3
D) -2

View Answer

D) -2

Explanation:If (x² + kx + 1 = 0) has a root (x = 1), then (k = ?)
Substitute (x = 1):
1² + k(1) + 1 = 0 ⇒ 1 + k + 1 = 0 ⇒ k = -2

23) If the roots of the quadratic equation ax² + bx+c=0 are sinα and cosα, then $1+2\frac ca$ = …….

A) $\frac{a^2}{b^2}$
B) $\frac{b^2}{a^2}$
C) a²
D) b²

View Answer

B) $\frac{b^2}{a^2}$

Explanation:If the roots of (ax^2 + bx + c = 0) are (sin α) and (cos α), then (1 + 2 $\frac{c}{a}$ = ?)
Given roots: (sin α + cos α = – $\frac{b}{a}$ ) and (sin α cos α = $\frac{c}{a}). Using the identity: sin2 α + cos2 α = 1 ⇒ (sin α + cos α)2 - 2 sin α cos α = 1 Substitute:$ \left(-\frac{b}{a}\right)^2 – 2\left(\frac{c}{a}\right) = 1 ⇒ \frac{b^2}{a^2} – \frac{2c}{a} = 1 $Rearrange:$ 1 + 2\frac{c}{a} = \frac{b^2}{a^2} \]

24) If the system of equation 3x-2y-7=0 and kx+2y+11=0 has unique solution then …….

A) k≠3
B) k≠-3
C) k=3
D) k=-3

View Answer

B) k≠-3

Explanation:If the system (3x – 2y – 7 = 0) and (kx + 2y + 11 = 0) has a unique solution, then:
For a unique solution, the lines must not be parallel:
$\frac{a_1}{a_2} ≠q \frac{b_1}{b_2} ⇒ \frac{3}{k} ≠q \frac{-2}{2} ⇒ \frac{3}{k} ≠q -1 ⇒ k ≠q -3$

25) If 7x-5y=2 and 3x+y=4, then x=

A) 3
B) -3
C) 1
D) 2

View Answer

C) 1

Explanation:If (7x – 5y = 2) and (3x + y = 4), then (x = ?)
From the second equation: (y = 4 – 3x).
Substitute into the first equation:
7x – 5(4 – 3x) = 2
⇒ 7x – 20 + 15x = 2
⇒ 22x = 22
⇒ x = 1

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