UP Police Constable Mock Test - 8 - UP Police Constable MCQ

Hence, Option B is correct.

Initial area = L × B

New area = (100 + 20)% of L × (100 – 12.50)% of B = 1.05L × B

Hence, Option A is correct.

Prime numbers between 1 and 30 →13, 17, 19, 23 and 29 (5)
Rest are prime numbers.
Total numbers 12 to 29 = 18
Total composite numbers = 13

Hence, Option A is correct.

25 = √(15² + L²)
625 = 225 + L²
400 = L²
20 = L
So the answer = 20 cm
Hence, Option D is correct.

HCF = 12
Numbers = 12x and 12y
where x and y are prime to each other.
∴ 12x × 12y = 2160

= 15 = 3 × 5, 1 × 15
Possible pairs = (36, 60) and (12, 180)
Hence , Number of such possible pairs is 2.

Initial solution : Added Alcohol = 65% : 10% = 13 : 2

Hence, Option C is correct.

Here,
3x – 4y + 5 = 0
⇒  –4y = – 3x – 5

Compare it with, y = mx + c we get

Let us assume father age is F and his son age is S.
According to question,
The sum of the ages of father and his son is 4 times the age of the son,
F + S = 4S
F = 3S.............. (1)
Average age of father and son is 28.
(F + S)/2 = 28
F + S = 56
Put the value of F from equation from (1),
3S + S = 56
4S = 56
S = 14 years
Age of Son = 14 years.

I. 7x + 12y = 13 
II. 12x + 17y = 8
→ I × 12 – II × 7
12y × 12 – 17y × 7 = 13 × 12 – 8 × 7
25y = 100
y = 4
7x + 12 × 4 = 13 
x = – 5 
Answer: x < y
Hence, Option D is correct.

Formula used:
S_n = n/2(a + l)
l = a + (n − 1)d, where,
S_n = Sum of elements,
n  = number of elements.
a = First element,
n  = number of elements.
d  = difference between two consecutive elements.

Calculation:
Even numbers between 1 to 100 = 2, 4, 6, 8,....98, 100.
l = 100, a = 2, n = ?
According to the question,
l = a + (n − 1)d
⇒ 100 = 2 + (n - 1)2
⇒ n = 50
Now,
Sn = n/2(a + l)
⇒ Sn = 50/2(2 + 100) = 102 × 25 = 2,550
∴ The sum of all even numbers between 1 to 100 is 2550.

Concept:

Calculation:

From (1), 

∴ a, b and c are in H.P.

Let one number = a
∴ Second number = 4a
⇒ 4a × a = 1936
⇒ a² = 1936/4 = 484
⇒ a² = 484
⇒ a = 2 × 11 = 22
and 4a = 4 × 22 = 88
∴ Numbers are 22 and 88.

Cost prices and selling prices are less than Rs. 100
CP of A : B : C = 6 : 5 : 4
Possible combinations of CP are (30, 25, 20), (60, 50, 40), (90, 75, 60)

Using Statement I :
Profit on A is Rs. 12
So, the CP of A cannot be 90
As SP will be 102 and it cannot be more than 100
Possible combinations of CP of (A, B, C) are (30, 25, 20) and (60, 50, 40)
But, we cannot find a single value of CP
So, statement I alone is not sufficient.

Using Statement II :
B and A are sold at the same price and profit on B is Rs. 10 more than profit on A.
Only possible when cost price of A is Rs. 10 more than that of B
Possible combination of CP of (A, B, C) is (60, 50, 40)
So, cost price of C is Rs. 40
So, statement II is alone sufficient.
Hence, option B is correct.

Given:
The number of ways of arrangements of 10 persons in four chairs  

Formula used:
ⁿP_r = n!/(n – r)!
Where, n = Number of persons
r = Number of chairs

Calculation:
According to the question
ⁿP_r = n!/(n – r)!
⇒ 10!/(10 – 4)!
⇒ 10!/6!
⇒ (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)/(6 × 5 × 4 × 3 × 2 × 1)
⇒ (10 × 9 × 8 × 7)
⇒ 5040
∴ The required value is 5040

1076 → 1076 is completely divisible by 4.
1675 → 1675 is not completely divisible by 4.
1354 → 1354 is not completely divisible by 4.
1998 → 1998 is not completely divisible by 4.

Therefore, 1076 is a leap year.
Hence, ‘1076’ is the correct answer.

Upstream speed = 20 – 5 × 2 = 10 km/hr

Hence, Option D is correct.

200 meters
The train can cover 800 – 500 meters in 60 – 40 seconds.

Length of the train = 15 × 40 – 500 = 100 meters
Hence, Option A is correct.

Using Rule 1,
Part of the cistern filled by both pipes in 1 hour

The cistern will be filled in 6 hours.

A : B = 100 : 75
B : C = 100 : 96.

= 100 : 72.
∴ A beats C by (100 - 72) m = 28 m.

You have to remember here that the profit given is for 8 months, so we’ll find the one month equivalent investments for 8 months, not for 12 months.
So, Arun’s 1 month equivalent investment = 8000*6
Kamal’s 1 month equivalent investment = 4000*8
Vinay’s 1 month equivalent investment = 8000*8
Hence the ratio of investments = 8,000*6 : 4,000*8 : 8,000*8 = 3 : 2 : 4.
Therefore Kamal’s share in the profit = Rs. 4005 x 2/9 = Rs 890 (option ‘A)

Let CP = 100
MP = 180

So the answer = 100 – 94.50 = 5.50%
Hence, Option D is correct.

There should be 4 in place of 3.
Hence, Option D is correct. 

Let the distance between the towers be X 
From the right angled triangle CFD 
Tan(45) =  (90 - 45)/X   
=> x = 45 meters

Using BODMAS, we get 2.79 after simplifying

Total numbers on a dice = 6
Prime numbers on a dice = 3 (2, 3 and 5)

Given in the question,
M₁ = 7 spiders , D₁ = 7 days , W₁ = 7 webs
M₂ = 1 spider , D₂ = ? , W₂ = 1 web
We know that ,

⇒ D₂ = 7 x 1 = 7 days .
Hence , 1 spider will make 1 web in 7 days.

From the given question, by using Pythagoras theorem, we get,

We need to find 
⇒AB² + BC² + CD² + DE²  
By putting the value from the equation (1), we get,
⇒ AC² + CD² + DE²
⇒ By putting the value from the equation (2), we get,
⇒ AD2 + DE²
By putting the value from the equation (3), we get,
⇒ AE²
Hence, the correct answer is AE².

Calculations
We can choose 6 people from a Volleyball team.
The no. of ways of choosing  6 Players from among 12 players is = ¹²C₆   

∴ Option (2) is the correct answer.

Key Points

• The concept of days succeeding each other is based on a seven-day cycle in which each day follows the next in a fixed order.
• If today is Wednesday, tomorrow would be Thursday.
• Thus, the day after tomorrow would be Friday, a day not listed among the options.
• Therefore, given the context and the understanding of the sequence of days in a week, 'none of the above' is the correct answer.

Therefore, the correct answer is Option 4, 'None of the above'.