UP Police Constable Mock Test - 2 - UP Police Constable MCQ

Let us assume 2∠A = 3∠B = 6∠C = K

Reqd. time with 100% efficiency 

Hence, Option D is correct.

So the answer = 100% – 96.875% = 3.125%
Hence, Option A is correct.

Let the number of students in Section C = X
The combined number of students in sections A and B = 200 – X
X × 104 + (200 – X) × 80 = 200 × 95
104X + 16000 – 80X = 19000
3000 = 24X
125 = X
Hence, Option D is correct.

Volume of the cylinder = πr²h = 1232


Hence, Option A is correct.

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
First number × second number = HCF × LCM
⇒ 84 × second number = 12 × 336

Hence, Option C is correct.

Step 1: Question statement and Inferences

Given that x is not a positive integer and we need to find the value of x from the given equation.

Step 2 & 3: Finding required values and calculating the final answer

Given equation is

Squaring on both sides

​Squaring on both sides

• 8x  =x²
• x² -8x=0
• x(x -8)=0

 Putting each factor to zero, we get:

x = 0 or x = 8

However, since it is already given that x is not a positive integer, x≠8.

Therefore x = 0.

 Answer: Option (A)

Let us assume the first Odd number is a.
then 2nd odd number = a + 2
and 3rd odd number = a + 4
According to question,
Sum of three consecutive odd numbers is 20 more than the first of these numbers;
a + (a + 2) + (a + 4) = a + 20
⇒ a + a + 2 + a + 4 - a = 20
⇒ 2a + 6 = 20
⇒ 2a + 6 = 20
⇒ 2a = 20 - 6
⇒ 2a = 14
⇒ a = 7
The First odd number a = 7
The second odd number = a + 2 = 7 + 2 = 9
Second odd number is middle number = 9

I. 4x + 6y = 82 
II. 21x + 4y = 183
→ 1.50 × II – I
31.50x – 4x = 274.50 – 82
27.50x = 192.50
x = 7
Put the value of x = 7 in I
4 × 7 + 6y = 82 
28 + 6y = 82
6y = 54
y = 9
Answer: x < y
Hence, Option D is correct.

 a = -3 and a(2) = 4
a = -3
d = 4 - a = 4 - (-3) = 7
a(21)=a + (21-1) x d
= -3 + (20) x 7
= -3 + 140
= 137

Concept:

If a, b, c are in HP then  

If a, b, c are in AP then 2b = a + c

A sequence of numbers is called a Harmonic progression if the reciprocal of the terms are in AP.

Calculation:

Given: 1 / 4, 1 / x, 1 / 10 are in HP

The sequence  1 / 4, 1 / x, 1 / 10 are in HP, so its reciprocals 4, x, 10 are in AP.

As we know, If a, b, c are in AP then 2b = a + c

⇒ 2x = 4 + 10

⇒ 2x = 14

∴ x = 7

Since we have 7²=49 and 8²=64. And both numbers lies outside 50 and 60 There is no perfect square between 50 and 60.

Salary Suman + Reena = 20,000
Using Statement I : We do not know whose salary is more.
So, statement I alone is not sufficient.

Using Statement II:
Savings of Reena = Salary of Suman
So, salary of Reena > Salary of Suman
But we cannot find the savings of Reena
So, statement I alone is not sufficient.

Using both Statement I and II:
Salary (Suman + Reena) = 20,000
Salary (Reena – Suman) = 4,000 (Salary of Reena > Salary of Suman)
Salary of Reena = 12,000 and Salary of Suman = 8,000
Savings of Reena = 8,000
Spent by Reena = 12,000 – 8,000 = 4,000
So, both the statements are together necessary.|
Hence, option D is correct.

The number of triangle can be formed by 10 points = ¹⁰C₃
Similarly, the number of triangle can be formed by 4 points when no one is collinear = ⁴C₃
In the question, given 4 points are collinear, Thus, required number of triangle can be formed,
= ¹⁰C₃ - ⁴C₃
= 120 - 4
= 116

After every 400 years, the same day occurs. Before 400 years if 27th February 2003 is Thursday then on 27th February 1603 has to be Thursday.
Option 2 is the correct answer.

1 hour 20 minutes = 80 minutes
Upstream time : Downstream time = 80 : 48 = 5 : 3
Upstrem speed : Downstream speed = 3 : 5
Hence, Option D is correct.

Time taken to cover the length of the train = 20 seconds
Time taken to cover the length of the train + bridge = 30
Length → Train : Bridge = 20 : (30 – 20) = 2 : 1

Hence, Option C is correct.

Let x be number of pumps
9 : 6 : : 12 : x = 12 : 15 : : 12 : x
9 × 12 × x = 6 × 12 × 15

A : B = 100 : 90.
A : C = 100 : 72.

When B runs 90 m, C runs 72 m.

When B runs 100 m, C runs 
∴ B can give C 20 m.

Let C subscribes = Rs x
Then, B subscribes = x + 5000
and A subscribes = x + 5000 + 4000 = x + 9000.
Hence, x + (x + 5000) + (x + 9000) = 50000
=> x = 12000
Therefore ratio of their investments i.e. A : B : C = (12000 + 9000) : (12000 + 5000) : 12000 = 21000 : 17000 : 12000 = 21 : 17 : 12.
Thus A’s share in the profit = 35000 x 21/50 = Rs 14,700 (option ‘D’)

Hence, Option D is correct.

There should be 123 in place of 121.
Hence, Option D is correct. 

Let AB be the tower and C and D be the positions of the boat.
Distance travelled by boat = CD
From the figure 75tan(60) = (75 + CD)tan(45)
=> 75√3 = 75 + CD
=> CD = 55 m
Speed = distance/time = 55/10
= 5.5 m/sec = 19.8 kmph

Total digits = 5
A 3-digit number is to be formed
So the answer = 5 × 5 × 5 = 125

Given in the question,
Price of 6 toys is Rs. 264.37.
∴ Price of 1 toys is Rs. 264.37/ 6 .
∴ Price of 5 toys is Rs. 264.37 x 5 / 6 .
∴ Price of 5 toys is Rs. 44 x 5 .
∴ Price of 5 toys is Rs. 220.

Complement of 30°20′ = 90° – ( 30°20′ ) = 90° – ( 30° + 20′ )
= (89° – 30°) + (1° – 20′)
= 59° + 60′ – 20′ [ ∴ 1° = 60°′]
= 59° + 40′ = 59°40′.

Since the two points A and B are on circle O, the distance between OA and OB will be equal.
Therefore, using the distance formula we get

Squaring both sides,
(x−2)² + 4 = 4 therefore x = 2
Hence, x = 2 is the correct answer.

The volume of cube = side3
So the answer = 16 × 16 × 16 = 4,096 m³
Hence, Option D is correct.