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

Polycet Mock Test

11) The distance between the points $\left(x_1,\;y_1\right)$ and $\left(x_2,\;y_2\right)$ is $\left(x_1,\;y_1\right)$ మరియు $\left(x_2,\;y_2\right)$ బిందువుల మధ్య దూరము కనుగొనుటకు సూత్రము

A) $\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$
B) $\sqrt{\left(x_2+x_1\right)^2+\left(y_2+y_1\right)^2}$
C) $\sqrt{\left(x_2-x_1\right)^2-\left(y_2-y_1\right)^2}$
D) $\sqrt{\left(x_2+x_1\right)^2-\left(y_2+y_1\right)^2}$

View Answer

A) $\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

Explanation:🎯 Shortcut Method to Find the Distance Between Two Points
The distance formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a plane is:
$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
Explanation:
– The difference between the x-coordinates is $(x_2 - x_1)$ .
– The difference between the y-coordinates is $(y_2 - y_1)$ .
– Then, apply the Pythagorean theorem to find the distance.
Final Answer:
$\boxed{\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}$

12) The coordinates of the point which divides the line segment joining the points (4,-3) and (8, 5) in the ratio 3:1 internally is బిందువులు (4, −3) మరియు (8, 5) లచే ఏర్పడు రేఖాఖండమును 3:1 నిష్పత్తిలో అంతరంగా విభజించు బిందువు నిరూపకాలు

A) (3,7)
B) (7,3)
C) (-7,-3)
D) (-3,-7)

View Answer

B) (7,3)

Explanation:🎯 Shortcut Method: Finding Coordinates of a Point Dividing a Line Segment in a Given Ratio
To find the coordinates of a point that divides a line segment joining two points $(x_1, y_1)$ and $(x_2, y_2)$ in the ratio m : n, use the section formula:
$\left( x, y \right) = \left( \frac{m x_2 + n x_1}{m + n}, \frac{m y_2 + n y_1}{m + n} \right)$
Given:
– Point 1: (4, -3)
– Point 2: (8, 5)
– Ratio: 3 : 1
Step 1: Apply the Section Formula
$x = \frac{3(8) + 1(4)}{3 + 1} = \frac{24 + 4}{4} = \frac{28}{4} = 7$
$y = \frac{3(5) + 1(-3)}{3 + 1} = \frac{15 - 3}{4} = \frac{12}{4} = 3$
Final Answer:
The coordinates of the point are (7, 3).
$\boxed{(7, 3)}$

13) Which of the following is not a formula for arithmetic mean? ఈ క్రింది వానిలో అంకగణిత సగటునకు సూత్రము కానిది ఏది?

A) $\frac{\Sigma f_ix_i}{\Sigma f_i}$
B) $a+\frac{\Sigma f_id_i}{\Sigma f_i}$
C) $a+\left[\frac{\Sigma f_i\mu_i}{\Sigma f_i}\right]\times h$
D) $l+\left[\frac{f_1-f_0}{2f_1\;-\;f_0\;-\;f_2}\right]\times h$

View Answer

D) $l+\left[\frac{f_1-f_0}{2f_1\;-\;f_0\;-\;f_2}\right]\times h$

Explanation:🎯 Shortcut Method for Identifying the Formula for Arithmetic Mean
We are asked to identify which of the following is NOT a formula for the arithmetic mean.
Let’s quickly review each option:
– 1. $\frac{\Sigma f_i x_i}{\Sigma f_i}$
This is the weighted mean formula. It is a standard formula for the arithmetic mean when you have data with frequencies. Correct formula.
– 2. $a + \frac{\Sigma f_i d_i}{\Sigma f_i}$
This formula is used for grouped data where $a$ is the assumed mean, and $d_i$ is the deviation of values from the assumed mean. Correct formula.
– 3. $a + \left[ \frac{\Sigma f_i \mu_i}{\Sigma f_i} \right] \times h$
This is another formula for grouped data. Here, $\mu_i$ is the deviation from the actual mean, and $h$ is the class width. Correct formula.
– 4. $l + \left[ \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right] \times h$
This formula is used to calculate the mode in grouped data, not the mean. Incorrect formula for arithmetic mean.
Conclusion:
The formula for the mode is in Option 4. Therefore, the correct answer is:
$\boxed{4. \, l + \left[\frac{f_1 - f_0}{2f_1 - f_0 - f_2}\right] \times h}$
This is NOT a formula for the arithmetic mean; it is for the mode.

14) Rain fall of a town in a week is 4 cm, 5 cm, 12 cm, 3 cm, 6 cm, 8 cm and 4 cm, then the average rainfall per day is ఒక వారములో ఒక పట్టణపు వర్షపాతం 4 సెం.మీ., 5 సెం.మీ., 12 సెం.మీ., 3 సెం.మీ., 6 సెం.మీ., 8 సెం.మీ. మరియు 4 సెం.మీ. అయిన, ఒక రోజులో సరాసరి వర్షపాతము

A) 4 cm
B) 5 cm
C) 6 cm
D) 7 cm

View Answer

C) 6 cm

Explanation:🎯 Shortcut Method for Finding the Average Rainfall per Day
To find the average rainfall per day, we use the formula for the arithmetic mean:
$\text{Average Rainfall} = \frac{\text{Total Rainfall}}{\text{Number of Days}}$
Given rainfall for the week:
– 4 cm, 5 cm, 12 cm, 3 cm, 6 cm, 8 cm, and 4 cm.
Step 1: Calculate the total rainfall
$\text{Total Rainfall} = 4 + 5 + 12 + 3 + 6 + 8 + 4 = 42 \, \text{cm}$
Step 2: Divide the total rainfall by the number of days (7 days in a week)
$\text{Average Rainfall} = \frac{42}{7} = 6 \, \text{cm}$
Final Answer: $\boxed{6 \, \text{cm}}$

15) Mode of the data 9, 10, 19, 7, 11, 5, 6, 7, 8, 14, 10, 7, 6 is 9, 10, 19, 7, 11, 5, 6, 7, 8, 14, 10, 7, 6 అనే దత్తాంశం యొక్క బాహుళకము

A) 6
B) 7
C) 10
D) 19

View Answer

B) 7

Explanation:🎯 Shortcut Method for Finding the Mode
The mode of a dataset is the value that appears most frequently. Let’s go through the steps to find the mode.
Given data:
9, 10, 19, 7, 11, 5, 6, 7, 8, 14, 10, 7, 6
Step 1: Count the frequency of each number
– 9 appears 1 time
– 10 appears 2 times
– 19 appears 1 time
– 7 appears 3 times
– 11 appears 1 time
– 5 appears 1 time
– 6 appears 2 times
– 8 appears 1 time
– 14 appears 1 time
Step 2: Identify the number with the highest frequency
– The number 7 appears 3 times, which is the highest frequency.
Final Answer: $\boxed{7}$

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