TS Polycet (Polytechnic) 2024 Previous Question Paper with Answers And Model Papers With Complete Analysis

TS Polycet (Polytechnic) 2024 Previous Question Paper with Answers And Model Papers With Complete Analysis
TS Polycet (Polytechnic) Previous Year Question Papers And Model Papers:
While preparing for TS Polycet (Polytechnic), candidates must also refer to the previous year question papers of the same. Scoring well in TS Polycet (Polytechnic) and understanding weaknesses and strengths in the respective sections.

TS Polycet (Polytechnic) Previous Year Question Papers can be found on this page in PDF format. Students taking the exam to get into some of the best Polytechnic colleges/institutes in the state of Andhra Pradesh may practice these papers to get a clear idea of the structure of the exam, marking scheme, important topics, etc.

TS Polycet Mock Test

Section — A
MATHEMATICS

1)The centroid of the triangle with vertices (1,-1), (0, 6) and (-3, 0) is
బిందువులు (1, −1), (0, 6) మరియు (-3, 0) లు శీర్షాలుగా గల త్రిభుజము యొక్క గురుత్వ కేంద్రము

A) $\left(\frac23,\frac53\right)$

B) $\left(\frac{-2}3,\frac{-5}3\right)$

C) $\left(\frac{-2}3,\frac53\right)$

D) $\left(\frac23,\frac{-5}3\right)$

View Answer

C) $\left(\frac{-2}3,\frac53\right)$

Explanation:Sure! Let’s find the **centroid** of the triangle with the given vertices:
Vertices:
– A = (1, -1)
– B = (0, 6)
– C = (-3, 0)
Centroid Formula:
The centroid $G$

of a triangle with vertices $(x_1, y_1), (x_2, y_2), (x_3, y_3)$

is:
$G = \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right)$

Applying the values:
x-coordinate:
$\frac{1 + 0 + (-3)}{3} = \frac{-2}{3}$

y-coordinate:
$\frac{-1 + 6 + 0}{3} = \frac{5}{3}$

Final Answer: $G = \left( \frac{-2}{3}, \frac{5}{3} \right)$

2)In ΔABC, if DE || BC, $\frac{AE}{CE}=\frac35$ and AB 5.6 cm, then AD = _________.
ΔABC లో DE || BC, $\frac{AE}{CE}=\frac35$ మరియు AB = 5.6 సెం.మీ. అయిన, AD = __________.

A) 2.8 cm

B) 2.1 cm

C) 3 cm

D) 2.4 cm

View Answer

B) 2.1 cm
Explanation:We are given:
– In triangle $\Delta ABC$

, line DE || BC
– $\frac{AE}{EC} = \frac{3}{5}$

– Total length AB = 5.6 cm
– We are to find AD
—
Since DE || BC, by Basic Proportionality Theorem (Thales’ Theorem), we know:
$\frac{AD}{DB} = \frac{AE}{EC} = \frac{3}{5}$

Let’s assume:
– $AD = 3x$

– $DB = 5x$

So total length of $AB = AD + DB = 3x + 5x = 8x$

Given: $AB = 5.6$

So: $8x = 5.6 \Rightarrow x = \frac{5.6}{8} = 0.7$

Now, $AD = 3x = 3 \times 0.7 = \boxed{2.1 \text{ cm}}$

3)A Kiddy bank contains hundred 50 paise coins, fifty ₹ 1 coins, twenty ₹ 2 coins and ten ₹ 5 coins. If one of the coins will fall out when the bank is turned upside down, what is the probability that the coin is ₹ 5 coin?
ఒక కిడ్డీ బ్యాంక్ డబ్బాలో వంద 50 పైసల నాణెములు, యాభై కౌ ₹ 1 నాణెములు, ఇరవై ₹ 2 నాణెములు మరియు పది ₹ 5 నాణెములు ఉన్నాయి. డబ్బాను తలక్రిందులు చేసినప్పుడల్లా యాదృచ్ఛికంగా ఒక నాణెం పడుతుంటే, అది ₹ 5 నాణెము కావడానికి సంభావ్యత ఎంత?

A) 5/9

B) 5/18

C) 1/9

D) 1/18

View Answer

D) 1/18
Explanation:We are given the number of each type of coin:
– 50 paise coins = 100
– ₹1 coins = 50
– ₹2 coins = 20
– ₹5 coins = 10
Let’s find the total number of coins:
$100 + 50 + 20 + 10 = 180$

We are asked to find the probability that the coin falling out is a ₹5 coin.
There are 10 ₹5 coins, and total coins are 180.
So, the probability is:
$\frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{10}{180} = \frac{1}{18}$

4)In a grouped frequency distribution, the formula to find median is
వర్గీకృత పౌనఃపున్య విభాజనానికి, మధ్యగతము సూత్రము

A) $l+\left(\frac{{\displaystyle\frac n2}+cf}f\right)\times h$

B) $l-\left(\frac{{\displaystyle\frac n2}+cf}f\right)\times h$

C) $l+\left(\frac{{\displaystyle\frac n2}-cf}f\right)\times h$

D) $l-\left(\frac{{\displaystyle\frac n2}-cf}f\right)\times h$

View Answer

C) $l+\left(\frac{{\displaystyle\frac n2}-cf}f\right)\times h$

Explanation:To find the median in a grouped frequency distribution, we use the following formula:
$\text{Median} = l + \left( \frac{\frac{n}{2} - cf}{f} \right) \times h$

Where:
– l = lower boundary of the median class
– n = total frequency
– cf = cumulative frequency before the median class
– f = frequency of the median class
– h = class width
—

5)In a G. P. the 3rd term is 24 and 6th is 192, then the 10th term is
ఒక గుణశ్రేఢిలో 3 వ పదము ’24’ మరియు 6 వ పదము ‘192’ అయిన, 10 వ పదము

A) 2072

B) 3072

C) 1072

D) 1672

View Answer

B) 3072
Explanation:Sure! Here’s a shortcut method using the property of G.P. terms:
—
We are given:
– $T_3 = 24$

– $T_6 = 192$

We are asked to find: $T_{10} = ?$

—
Shortcut Idea:
In G.P., $T_n = T_m \cdot r^{n - m}$

So we use: $T_{10} = T_6 \cdot r^{10 - 6} = T_6 \cdot r^4$

First, find $r$

from: $T_6 = T_3 \cdot r^{6-3} = 24 \cdot r^3 = 192 \Rightarrow r^3 = \frac{192}{24} = 8 \Rightarrow r = 2$

Now: $T_{10} = 192 \cdot 2^4 = 192 \cdot 16 = \boxed{3072}$

6)(6+5√3)-(4-3√3) is
(6+5√3)-(4-3√3) అనునది

A) Rational number
అకరణీయ సంఖ్య

B) Irrational number
కరణీయ సంఖ్య

C) Natural number
సహజ సంఖ్య

D) None of the above
పైవేవి కావు

View Answer

B) Irrational number
కరణీయ సంఖ్య
Explanation:We are given the expression: $(6 + 5\sqrt{3}) - (4 - 3\sqrt{3})$

Step-by-step simplification:
$= 6 + 5\sqrt{3} - 4 + 3\sqrt{3} = (6 - 4) + (5\sqrt{3} + 3\sqrt{3}) = 2 + 8\sqrt{3}$

This result contains a surd (irrational part: $\sqrt{3}$

), so the entire expression is irrational.
—

7)One card is selected from a well-shuffled deck of 52 cards, the probability of getting the queen of diamond is
బాగుగా కలిపిన 52 పేక ముక్కల కట్టనుండి యాదృచ్ఛికంగా ఒక కార్డును తీస్తే, అది డైమండు రాణి కావడానికి సంభావ్యత

A) 1/52

B) 3/26

C) 1/26

D) 1/13

View Answer

A) 1/52
Explanation:🎯 Shortcut Method:
A standard deck has 52 cards, with exactly 1 Queen of Diamonds.
So, probability = $\frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{1}{52}$

📝 Shortcut Tip: When asked for the probability of a specific card, it’s always 1/52.

8)Area of the triangle formed by the points (-5, -1), (3, −5) and (5, 2) is
(−5, −1), (3, −5) మరియు (5, 2) అనే బిందువులతో ఏర్పడు త్రిభుజ వైశాల్యము

A) 32

B) 22

C) 42

D) 52

View Answer

A) 32
Explanation:🎯 Shortcut Method: Area of Triangle using Coordinates
For a triangle with vertices $(x_1, y_1)$

, $(x_2, y_2)$

, and $(x_3, y_3)$

, the area $A$

is given by the formula:
$A = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|$

Given points:
$(x_1, y_1) = (-5, -1)$

,
$(x_2, y_2) = (3, -5)$

,
$(x_3, y_3) = (5, 2)$

Apply the formula:

$A = \frac{1}{2} \left| (-5)[-5 - 2] + 3[2 - (-1)] + 5[-1 - (-5)] \right| <img src="https://www.mcqbits.com/wp-content/ql-cache/quicklatex.com-7116a89cf631202603d4e7567db7aa8a_l3.png" height="36" width="240" class="ql-img-displayed-equation quicklatex-auto-format" alt="\[A = \frac{1}{2} \left| (-5)(-7) + 3(3) + 5(4) \right|\]" title="Rendered by QuickLaTeX.com"/>A = \frac{1}{2} \left| 35 + 9 + 20 \right| <img src="https://www.mcqbits.com/wp-content/ql-cache/quicklatex.com-5ab7ebe38429be4a3bb40fcc7b92fa07_l3.png" height="36" width="78" class="ql-img-displayed-equation quicklatex-auto-format" alt="\[A = \frac{1}{2} \left| 64 \right|\]" title="Rendered by QuickLaTeX.com"/>A = \frac{64}{2} = 32$

Final Answer: $\boxed{32}$

9)The median of 75, 21, 56, 36, 81, 05 and 42 is
75, 21, 56, 36, 81, 05 మరియు 42 ల మధ్యగతము

A) 36

B) 42

C) 56

D) 21

View Answer

B) 42
Explanation:To find the median of a set of numbers, follow these steps:
– 1. Arrange the numbers in ascending order.
– 2. If the number of terms is odd, the median is the middle number.
– 3. If the number of terms is even, the median is the average of the two middle numbers.
Given numbers:
75, 21, 56, 36, 81, 05, 42
Step 1: Arrange the numbers in ascending order:
5, 21, 36, 42, 56, 75, 81
Step 2: Find the middle number.
There are 7 numbers (an odd count), so the median is the 4th number.
The 4th number in the ordered list is 42.
Final Answer: $\boxed{42}$

10)The common ratio of G. P.: 25, -5, 1, $\frac{-1}5$ , ……..is
25, -5, 1, $\frac{-1}5$ ,…… అను గుణశ్రేఢి యొక్క సామాన్య నిష్పత్తి

A) -1/5

B) 1/5

C) 2/5

D) 3/5

View Answer

A) -1/5
Explanation:🎯 Shortcut Method for Finding the Common Ratio of a G.P.
In a Geometric Progression (G.P.), the common ratio $r$

is the ratio of any term to its previous term.
So, for the given G.P.:
$25, -5, 1, \frac{-1}{5}, \dots$

Step 1: Find the common ratio r
The common ratio is calculated by dividing any term by its preceding term:
$r = \frac{\text{Second term}}{\text{First term}} = \frac{-5}{25} = -\frac{1}{5}$

Step 2: Verify with the next terms
Check the ratio between the next terms to confirm:
$r = \frac{\text{Third term}}{\text{Second term}} = \frac{1}{-5} = -\frac{1}{5}$

Since the ratio is consistent, the common ratio $r = -\frac{1}{5}$

.
Final Answer: $\boxed{-\frac{1}{5}}$

This is the fastest way to find the common ratio of a G.P. when the terms are given! Would you like more examples?

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Section — A MATHEMATICS

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Section — A
MATHEMATICS