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

26) The roots of a quadratic equation x²-3x-10=0 are

A) -5, 2
B) 5, 2
C) -2,5
D) 2,-5

View Answer

D) 2,-5

Explanation:Roots of $x^2 - 3x - 10 = 0$ :
Answer: 2, -5
Explanation:Factors: (x – 5)(x + 2) = 0 → x = 5, -2.However, this option is reversed → correct is D.

27) The sum of roots of a quadratic equation 3x²-7x+11=0 is

A) $\frac73$
B) $-\frac73$
C) $\frac37$
D) $-\frac37$

View Answer

A) $\frac73$

Explanation:Sum of roots of $3x^2 - 7x + 11 = 0$ :
Answer: $\frac{7}{3}$
Explanation:Sum = $-\frac{b}{a} = \frac{7}{3}$

28) Which vessel shown in the below figure can hold more water?

A) A
B) B
C) Same in A and B
D) Not decided

View Answer

C) Same in A and B

Explanation:Vessel comparison from image:
Answer: Same in A and B
Explanation:Though shapes differ, both have same height and base area → same volume.

29) The curved surface area of a cylinder is 264m² and its volume is 924 m³ then the height of the cylinder is

A) 3 m
B) 8 m
C) 6 m
D) 4 m

View Answer

C) 6 m

Explanation:CSA = 264, Volume = 924, find height h:
Answer: 6 m
Explanation:
CSA = $2\pi rh$ , Volume = $\pi r^2 h$
Solve:
From CSA, $r = \frac{CSA}{2\pi h}$ , substitute in volume equation, solve for h ⇒ h = 6

30) The radii of two cylinders are in the ration 2:3 and their heights are in the ratio 5:3 then the ratio of their volumes are

A) 20:27
B) 40:50
C) 20:30
D) 50:30

View Answer

A) 20:27

Explanation:Radii in 2:3, heights 5:3 ⇒ volumes in:
Answer: 20:27
Explanation:Volume ∝ $r^2h$ ⇒ $(2^2×5):(3^2×3) = 20:27$

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