AP Polycet (Polytechnic) 2025 Previous Question Paper with Answers And Model Papers With Complete Analysis

37) The solution of x – 2y = 0 and 3x + 4y – 20 = 0 is:

A) x = 2, y = 4
B) x = 4, y = 2
C) x = -2, y = 4
D) x = 2, y = -4

View Answer

B) x = 4, y = 2

Explanation:Solve:
From $x = 2y$ , substitute in 2nd equation:
$3(2y) + 4y = 20 \Rightarrow 6y + 4y = 20 \Rightarrow y = 2$ , then $x = 4$
→ x = 4, y = 2

38) The product of Karan’s age five years ago and his age after 9 years from now is 32. This is represented by the quadratic equation:

A) x² + 4x + 77 = 0
B) x² – 4x + 77 = 0
C) x² + 4x – 77 = 0
D) x² – 4x – 77 = 0

View Answer

C) x² + 4x – 77 = 0

Explanation:Let present age = x
Then (x – 5)(x + 9) = 32 →
$x^2 + 4x - 45 = 32 \Rightarrow x^2 + 4x - 77 = 0$
→ x² + 4x – 77 = 0

39) The roots of the equation 6x² – x – 2 = 0 are

A) $\frac{2}{3}, -\frac{1}{2}$
B) $-\frac{2}{3}, \frac{1}{2}$
C) $-\frac{2}{3}, -\frac{1}{2}$
D) $\frac{2}{3}, \frac{1}{2}$

View Answer

B) $-\frac{2}{3}, \frac{1}{2}$

Explanation: $6x^2 - x - 2 = 0$ → Factor:
$(3x + 2)(2x - 1) = 0 \Rightarrow x = -2/3, 1/2$
→ $-\frac{2}{3}, \frac{1}{2}$

40) The equation 3x² – 5x + 2 = 0 has

A) two real and unequal roots
B) two real and equal roots
C) no real roots
D) None of these

View Answer

A) two real and unequal roots

Explanation:Discriminant $D = 25 - 24 = 1 > 0$
→ two real and unequal roots

41) Find two numbers whose sum is 27 and product is 182.

A) 13, 12
B) 13, 14
C) 15, 12
D) 11, 16

View Answer

B) 13, 14

Explanation:x + y = 27, xy = 182 → try 13, 14 → 13 + 14 = 27 and 13×14 = 182
→ 13, 14

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