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

31) If the graph of y = p(x) does not intersect the X-axis at all, then the zeroes of p(x) are:

A) are equal

B) are unequal

C) don’t exist

D) All of these

View Answer

C) don’t exist
Explanation:If the graph of $y = p(x)$ does not intersect the X-axis
→ don’t exist

32) The number of zeroes of a polynomial y = p(x) as shown below is:

A) ‘0’

B) 1

C) 2

D) 3

View Answer

C) 2
Explanation:The number of zeroes of the polynomial from the graph is
→ 2

33) A pair of linear equations $a_1 x + b_1 y + c_1 = 0$ and $a_2 x + b_2 y + c_2 = 0$ is such that $\frac{a_1}{a_2} ≠ \frac{b_1}{b_2}$ , then they are:

A) consistent

B) inconsistent

C) dependent and consistent

D) None of these

View Answer

A) consistent
Explanation:If $\frac{a_1}{a_2} \ne \frac{b_1}{b_2}$ , the lines intersect
→ consistent

34) The lines 2x + 3y – 9 = 0 and 4x + 6y – 18 = 0 are:

A) intersecting lines

B) coinciding lines

C) parallel lines

D) All of these

View Answer

B) coinciding lines
Explanation: $4x + 6y - 18 = 2(2x + 3y - 9)$ , so they are same line
→ coinciding lines

35) If x – 4y – 14 = 0 and 5x – y – 13 = 0 will have:

A) unique solution

B) no solution

C) infinite number of solutions

D) None of these

View Answer

A) unique solution
Explanation:Lines intersect → unique solution
→ unique solution

36) 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

37) 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

38) 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:
$(3x + 2)(2x - 1) = 0 \Rightarrow x = -2/3, 1/2$
→ $-\frac{2}{3}, \frac{1}{2}$

39) 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

40) 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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