AP Polycet (Polytechnic) 2022 Previous Question Paper with Answers And Model Papers With Complete Analysis

Polycet Mock Test

26) If the slope of the line joining the two points P(2,5) and Q(x,3) is 2, then the value of x is

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

View Answer

A) 1

Explanation:Slope = (3 − 5)/(x − 2) = −2/(x − 2) = 2
Solve: -2 = 2(x – 2) ⇒ x = 1

27) If the points P(2,3),Q(5,k) and R(6,7) are collinear, then the value of k is

A) 4
B) $\frac14$
C) $-\frac34$
D) 6

View Answer

D) 6

Explanation:Points collinear → slopes equal
Slope PQ = $\frac{k - 3}{5 - 2} = \frac{k - 3}{3}$
Slope QR = $\frac{7 - k}{6 - 5} = 7 - k$
Set equal: $\frac{k - 3}{3} = 7 - k$
→k – 3 = 21 – 3k ⇒ 4k = 24 ⇒ k = 6

28) In the given △ABC, if DE||BC, $\frac{AD}{DB}$ = $\frac35$ and AC 5.6cm, then AE=

A) 2.1cm
B) 2cm
C) 2.2cm
D) 4.2cm

View Answer

A) 2.1cm

Explanation:Given: $\frac{AD}{DB} = \frac{3}{5}$ , so total AB = 3 + 5 = 8 parts
Then AE = $\frac{3}{8} × AC = \frac{3}{8} × 5.6 = 2.1$

29) If the lengths of the diagonals of a rhombus are 30cm and 40cm, then the side of the rhombus is

A) 15cm
B) 20cm
C) 25cm
D) 30cm

View Answer

C) 25cm

Explanation:Rhombus diagonals are perpendicular and bisect each other.
Half diagonals: 15cm and 20cm
Side = $\sqrt{15^2 + 20^2} = \sqrt{225 + 400} = \sqrt{625} = 25$

30) In the given figure, O is the centre of the circle and ∠AOC=110°, then ∠ADC is equal to

A) 110°
B) 55°
C) 70°
D) 125°

View Answer

B) 55°

Explanation:∠AOC = 110°, ∠ADC = ½ ∠AOC (angle at center is twice the angle at circumference subtending same arc)
→ ∠ADC = 55°

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