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

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.
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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:
$A = \frac{1}{2} \left| (-5)[-5 - 2] + 3[2 - (-1)] + 5[-1 - (-5)] \right|$
$A = \frac{1}{2} \left| (-5)(-7) + 3(3) + 5(4) \right|$
$A = \frac{1}{2} \left| 35 + 9 + 20 \right|$
$A = \frac{1}{2} \left| 64 \right|$
$A = \frac{64}{2} = 32$
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?