UP Police Constable Mock Test - 3 - UP Police Constable MCQ

Let the repayment annually be X. Then: 8000 + 3 years interest on 8000 (on compound interest of 5%) = X + 2 years interest on X + X + 1 years interest on X + X → X = 2937.67

Let us assume that the width of the lake = x. So, when one of the runners A covers 900 m, the other one B is covering (x - 900) m. To meet next time, A will be covering (x - 900 + 300) m whereas B will be covering (900 + X-300) m.
Now, 900/(x - 900) = (x - 900 + 300)/(x + 900 - 300)
Now use options to find the answer.

Hence, Option C is correct.

Hence, Option A is correct.

X × 32 + 8 – 40  = X × 30
2X = 32
X = 16
Hence, Option A is correct.

Volume of a cuboid = lbh
So the answer = 20 × 4 × 8 = 640 cm³
Hence, Option C is correct.

We know that: 
LCM is the least common multiple of the given numbers whereas HCF is the highest common factor of those numbers.
Then, LCM is the multiplication of one common factor of the numbers and the other different factors of the numbers.
Write the LCM = 120 into factored form, that is
120 = 2 × 2 × 2 × 3 × 5
= 4(2 × 3 × 5)
⇒ 4 is the common factor of the numbers.
So, the HCF of three numbers is a multiple of 4.
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...
Therefore, 35 is not the multiple of 4, then 35 cannot be their HCF.

Reqd. ratio = 40 : 20 = 2 : 1
Hence, Option B is correct.

Given

Approach

1. We can see that the terms on the left hand side of the equation are powers of 2.
   1. So, we will simplify the expression in powers of 2.
2. So, we will get 2^{expression in x} = 1. This is only possible if expression in x = 0 (as 2^∘ = 1)
3. We will equate the expression in x = 0 and use the constraint that x > 0, to find out the value of x.

Working Out

As x> 0, the only possible value of x = 2.

Answer: D

Let us assume the first installment is a and difference between two consecutive installments is d.
According to question,
Sum of 40 Installments = 3600
Apply the formula Sum of first n terms in an Arithmetic Progression = S_n = n/2[ 2a + (n?1)d ]
where a = the first term, d = common difference, n = number of terms.
n/2[ 2a + (n?1)d ] = 3600
Put the value of a, n and d from question,
40/2[ 2a + (40 ?1)d ] = 3600
20[ 2a + 39d ] = 3600
[ 2a + 39d ] = 3600/20 = 180
2a + 39d = 180...........................(1)
Again according to given question,
After paying the 30 installments the unpaid amount = 1/3(total unpaid amount) = 3600 x 1/3
After paying the 30 installments the unpaid amount = 1200
So After paying the 30 installments the paid amount = 3600 - 1200 = 2400
Sum of 30 installments = 2400
30/2[ 2a + (30 ?1)d ] = 2400
[ 2a + (30 ?1)d ] = 2400 x 2/30
2a + 29d = 80 x 2 = 160
2a + 29d = 160..........................(2)
Subtract the Eq. (2) from Eq. (1), we will get
2a + 39d - 2a - 29d = 180 - 160
10d = 20
d = 2
Put the value of d in Equation (1), we will get
2a + 39 x 2 = 180
2a = 180 - 78
a = 102/2
a = 51
The value of first installment = a = 51 

I. x² – 32x + 247 = 0
x² – 19x – 13x + 247 = 0
x = 19 and 13
II. y² – 24y + 143 = 0
y² – 13y – 11y + 143 = 0
y = 13 and 11
Answer: x ≥ y
Hence, Option C is correct.

d = -4, n = 7, a(n) = 4
a(n) = a + (n – 1) x d
a + (7 – 1) x (-4) = 4
a + 6 x (-4) = 4
a – 24 = 4
a = 4 + 24
a = 28

Concept:

The Harmonic Mean of a & b is

H = 2ab/a+b

Calculation:

let a = 1, b = 3,

H = 2ab/(a+b)

H = (2 × 1 × 3)/(1 + 3)

H = 6/4 = 3/2

Therefore,

Let the number of rows be x
Thus, the each row contains x plants.
The total number of plants in the garden = number of rows × number of plants in each rows
Thus,
   2025=x×x
=>x² =2025
=>x=  3×3×3×3×5×5
​       =3×3×5
        =45
Thus, there are 45 rows and each row contains 45 plants.

Ratio of efficiency of A : B : C = 3 : 1 : 2
Let the efficiency of A = 9x, B = 3x and C = 6x

Using Statement I :
When all three pipes are opened
Water level decrease = 6x – 3x – 9x = – 6x
6x = 30 liters per min
x = 5 liters per min
But we cannot find the capacity of the tank.
So, statement I alone is not sufficient.

Using Statement II :
Ratio of efficiency of B : C = 1 : 2
Ratio of time taken by B : C = 2 : 1

But we cannot find the capacity of the tank.
So, statement II alone is not sufficient.

Using both Statement I and II :
Efficiency of A = 9x, B = 3x and C = 6x
x = 5 litres per min
Time taken by C to fill the tank

Tank capacity = 60 × 5 × 6 = 1800 liters
So, both the statements are together necessary.
Hence, option D is correct.

One digit positive numbers = 5
Two digit positive numbers = 25
Three digit positive numbers = 100
4 digit positive numbers = 300
5 digit positive numbers = 600
Six digit positive numbers = 600
Total positive numbers,
= 5 + 25 + 100 + 300 + 600 + 600
= 1630

2/7 in a leap year there are 366 days means 52 weeks and 2days. So already we have 52 Fridays. Now the rest two days can be (Sunday, Monday), (Monday, Tuesday), (Tuesday, wed), (Wednesday, Thursdays), (Thursday, Friday), (Friday, sat), (sat, sun) so, the probability of 53 Fridays= 2/7
Option 3 is the correct answer

1 hour 45 minutes = 1.75 hours

Speed of stream = 30 – 16 = 14 km/hr
So the answer = 30 + 14 = 44 km/hr
Hence, Option D is correct.

Hence, Option C is correct.

Using Rule 1,
Part of tank filled by pipes A and B in 2 hours

Remaining part = 
This part is filled by pipe B.

A : C = 200 : 182.


When C covers 182 m, B covers 169 m.
When C covers 350 m,         

Therefore, C beats B by (350 - 325) m = 25 m.            

Old ratio of A & B 20,000 : 30,000 = 2 : 3 (They share profit in the ratio of their capitals)
So A’s share is 2/5 and B’s share is 3/5
New Share of A will be in the ratio of 3 : 4 : 3 i.e. A = 3/10; B = 4/10 = 2/5
Now we have to find their sacrificing shares and then the ratio.
Now A’s sacrifice = Old share – New share =>>> 2/5 – 3/10 = 1/10, and B’s sacrifice = 3/5 – 2/5 = 1/5
Hence the ratio in which the premium is be divided between A and B is 1/10 : 1/5 = 1 : 2 (option ‘A’)

Profit = 6 – 5 = 1

Hence, Option C is correct.

There should be 24 in place of 36.
Hence, Option C is correct. 

Let AB be the kite and AC be the level ground
So that BC - AC.
At that point, ∠BAC = 60°and BC = 75m. Let AB = x meters.
Presently AB/BC = coses60° = 2/ √3
=> x/75 = 2/√3 => x = 150/√3 = 150 * √3/3 = 50 √3m.
∴ Length of the string = 50 √3m.

Total balls = 6 + 4 = 10
Total white balls = 4
Selecting 2 white balls from four

Selecting 2 white balls from ten

According to question,
A shadow of length 40.25 meters is build for a height of 17.5 meters.
A shadow of length 1 meters is build for a height of 17.5 /40.25 meters.
A shadow of length 28.75 meters is build for a height of 17.5 x 28.75 /40.25 meters.
A shadow of length 28.75 meters is build for a height of 17.5 x 2875 /4025 meters.
A shadow of length 28.75 meters is build for a height of 17.5 x 575 /805 meters.
A shadow of length 28.75 meters is build for a height of 17.5 x 115/161 meters.
A shadow of length 28.75 meters is build for a height of 12.5 meters.

The figure is as follows:

Assuming, the radius of circle be r.
Then,
AB = BC = CA = 2r
So, all the three sides are equal of the triangle.
△ABC is an equilateral triangle.
Hence, the required answer is equilateral triangleequilateral triangle.

We assume that,

x₁ = 2, y₁ = 5, x₂ = 5 & y₂ = 2 Point C: (x,y)
Line divides the line segment in the ratio m₁ : m₂  
This is known as internal division.

Point C satisfies the equation of line.