Jobs in Telangana: ایس آئی امتحانات کے لیے یہ ہے نمونہ سوالات، اس سے مل سکتی ہے مدد

حیدرآباد: یہ مضمون سب انسپکٹر آف پولیس بھرتی امتحانات (Sub-Inspector of Police recruitment exams) کی تیاری سے متعلق ہے۔ یہاں کچھ موضوع کے لحاظ سے پہلے پوچھے گئے سوالات اور جوابات وضاحت کے ساتھ پیش کیے جارہا ہیں۔ تا کہ مذکورہ امتحان لکھنے والوں کو مدد مل سکے۔

اوسط (AVERAGE):

اوسط ایک سادہ سا موضوع ہے اور اس میں سادہ ریاضیاتی حسابات شامل ہیں۔ اس تصور کے مختلف اطلاقات ہیں۔ سب سے پہلے ہم موضوع کی بنیادی باتوں کو سمجھیں گے۔ اوسط تمام دیے گئے مشاہدات کی صرف ایک اوسط قدر ہے یا ہم کہہ سکتے ہیں کہ یہ مشاہدات کا ریاضی کا مطلب ہے۔

ذیل میں ضابطے، سوالات اور دیگر تفصیلات پیش کی جارہی ہیں:

Average =(Sum of all observations)/(Number of observations )
Example1: Find an average of following observations:
53, 54, 58, 62, 52, 55, 51
Solution: Average = (Sum of all observations)/(Number of observations )
Average = (53 54 58 62 52 55 51 )/7
So, Average = 55

Properties of Average:
i) Average lies between maximum and minimum observation.

ii) If value of each observation is multiplied by some value ‘N’, then
Average will also be multiplied by the same value i.e. N.
For example: Assume the previous set of observations. If 2 is multiplied with all observations, then new observations will be as follows:

6, 8, 16, 24, 4, 10, 2

New Average = 707 = 10 = 2(5) = 2 × Old Average

iii) If value of each observation is increased or decreased by some number, then average will also be increased or decreased by the same number.
For example: Continuing with the same example. If 2 is added to all observations, then new observations will be as follows:
5, 6, 10, 14, 4, 7, 3
New Average = 49/7 = 7 = 5 2 = 2 Old Average
iv) Similarly, if each observation is divided by some number, then average will also be divided by same number.

For example 1: If 2 is divided from all observations, then new observations will be as follows:

1.5, 2, 4, 6, 1, 2.5, 0.5

New Average = 17.57 = 2.5 = 52

Therefore, we can say any general operation applied on observations will have same effect on average.

مزید پڑھیں: EXPLAINED: پاکستان میں سیاسی ہلچل کا باقی دنیا کے لیے کیا ہےمطلب؟ کیاعالمی سیاست ہوگی متاثر؟

Formulae:
If the number of quantities in two groups be ‘m’ and ’n’, and their averages are x and y respectively. Then the average of all of them put together = mx ny /m n

If the average of m quantities is x and the average of n quantities out of them is y, then the average of remaining group = mx – ny/ m-n

The average of n quantities is equal to x. When a quantity is removed, the average becomes y. The value of the removed quantity is n(x – y) y
The average of n quantities is equal to y. When a quantity is added, the average becomes y. The value of the new quantity is n(y – x) y.
Questions

1 The average of 40 numbers is 35. If two numbers 44, 45 are discarded, then the average of the remaining numbers is (SI mains 2018)

a) 33.5 b) 34 c) 34.25 d) 34.5

Ans: d

According to the question

Average of 40 numbers is = 35

Sum of 40 numbers is = 40 × 35 = 1400

Two numbers discarded = 44 45 = 89

Sum of 38 numbers = 1400 – 89 = 1311

Average = 1311/38= 34.5

2 There are 4 numbers, the average of first 3 numbers is 56 and the average of last 3 numbers is 49. If the first number is 48, then the last number is (SI mains 2018)

a) 40 b) 55 c) 39 d) 27

Ans: d

Assume that the given four numbers are represented by a, b, c and d.

a b c = 56*3 = 168—- (1)

یہ بھی پڑھئے : کیا رمضان کے مہینہ میں میک اپ کرنے سے ٹوٹ جاتا ہے روزہ؟

b c d = 49*3 = 147— (2)

a = 48 substitute first number in the first equation then

b c = 168 – 48 = 120

Substitute this value in the second equation, then
120 d = 147 –>; d = 147 – 120 = 27

3 If the average age of three persons is 20 years and the ages are in the ratio 2:3:5, then the age (in years) of the youngest among them is (SI mains 2018)

(a) 12 (b) 18 (c) 10 (d) 8

Ans: a

Let the ages of three persons according to the question be 2x, 3x and 5x.

According to the question, (2x 3x 5x)/3 = 20
Hence 10x = 60
So x = 6