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

Polycet Mock Test

46) The centroid divides each median in the ratio of

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

View Answer

B) 2:1

47) If the centroid of the triangle formed with (a, b), (b, c) and (c, a) is O(0, 0) then a³+b³+c³=

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

View Answer

D) 3abc

Explanation:We are given:
Vertices of triangle:
A(a, b), B(b, c), C(c, a)
Centroid is O(0, 0)
Step 1: Use centroid formula
The coordinates of the centroid of triangle with vertices $(x_1, y_1), (x_2, y_2), (x_3, y_3)$ is:
$\left( \frac{x_1 + x_2 + x_3}{3},\ \frac{y_1 + y_2 + y_3}{3} \right)$
Plug in:
$x_1 = a,\ x_2 = b,\ x_3 = c$
$y_1 = b,\ y_2 = c,\ y_3 = a$
$\text{Centroid} = \left( \frac{a + b + c}{3},\ \frac{b + c + a}{3} \right)$
Given centroid is (0, 0), so:
$a + b + c = 0 \tag{1}$
Step 2: Use identity
We want to find:
$a^3 + b^3 + c^3 = ?$
Use identity:
$a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)$
From (1), a + b + c = 0, so:
$a^3 + b^3 + c^3 - 3abc = 0 \Rightarrow a^3 + b^3 + c^3 = 3abc$
Final Answer: 3abc

48) The vertices of a parallelogram are (2,-3),(6,5),(-2,1), (-6,-7) in this order. The point of intersection of the diagonals is

A) (0,-1)
B) (0,0)
C) (-1,0)
D) (4,1)

View Answer

A) (0,-1)

Explanation:We are given the vertices of a parallelogram in order:
A(2, -3) B(6, 5) C(-2, 1) D(-6, -7)
Step 1: Diagonals intersect at their midpoint
We can pick opposite vertices (diagonal endpoints):
Diagonal AC: Points A(2, -3) and C(-2, 1)
Find midpoint of AC:
$\left( \frac{2 + (-2)}{2}, \frac{-3 + 1}{2} \right) = (0, -1)$
Check diagonal BD just to verify:
Points B(6, 5) and D(-6, -7)
Midpoint:
$\left( \frac{6 + (-6)}{2}, \frac{5 + (-7)}{2} \right) = (0, -1)$
Same point! So diagonals intersect at (0, -1)
Final Answer: (0, -1)

49) Distance between the points (0,a) and (0,-a) is

A) a²
B) 2a²
C) 4a²
D) 2a

View Answer

D) 2a

Explanation:We are given two points:
(0, a) (0, -a)
Step-by-step shortcut:
These two points lie on the y-axis, so the distance between them is just the difference in y-coordinates.
Distance = |a – (-a)| = |a + a| = 2a
Final Answer: 2a

50) Two poles of height 6 m and 11 m stand on a plain ground and the distance between their feet is 12 m, then the distance between their tops is

A) 11
B) 12
C) 13
D) 14

View Answer

C) 13

Explanation:We are given:
Height of first pole = 6 m
Height of second pole = 11 m
Distance between their feet = 12 m
Step-by-step shortcut (Apply Pythagoras theorem):
Difference in height = 11 – 6 = 5 m
This forms a right triangle with:
vertical side = 5 m
horizontal side = 12 m
hypotenuse (distance between tops) = ?
$\text{Distance}^2 = 12^2 + 5^2 = 144 + 25 = 169 \Rightarrow \text{Distance} = \sqrt{169} = 13$
Final Answer: 13

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