UP Police Constable Mock Test - 10 - UP Police Constable MCQ

The value would increase by 4% per year. To go to 5 times it’s original value, it would require an increment of 400%. At 4% SI it would take 100 years.

By travelling at 10 kmph higher than the original speed, the train is able to make up 16 minutes
while traveling 80 km.
This condition is only satisfied at an initial speed of 50 (and a new speed of 60 kmph).

Hence, Option B is correct.

Let the first part = x
Second part = y
30% of y – 75% of x = 12 ----(1)
50% of y – 80% of x = 56 ----(2)
0.60 × Eq₂ – Eq₁
75% of x – 48% of x = 0.60 × 56 – 12
27% of x = 21.60

30% of y – 75% of 80 = 12
30% of y = 72
y = 240
so number is there sum ie. x + y
So the answer = 80 + 240 = 320
Hence, Option B is correct.

Reqd. weight = 50 × 3 – 59 × 2 = 32 kg

Hence, Option D is correct.

πr² = 154

r = 7
Perimeter = 2πr

Hence, Option B is correct.

The HCF and LCM of two numbers are 12 and 924.
Let the numbers be 12p and 12q where p and q are prime to each other.
∴ LCM = 12pq
∴ 12pq = 924
⇒ pq = 77
∴ Possible pairs are (1 , 77) and (7 ,11)
Hence , required answer is 2.

Cost price of resultant rice = 50/1.25 = 40

5 : 10 = 1 : 2

Hence, Option C is correct.

m³ + n³ + 3mn
= m³ + n³ + 3mn(m + n) [∵  m + n =1]
= (m + n)³ = 1

Let the number of rice bowls be a, the number of juice bowls be b, and the number of meat bowls be c.
According to question,
a + b + c = 65........................(1)
The total number of guests = 2a
The total number of guests = 3b
The total number of guests = 4c
So the total number of guests will be same in the party.
2a = 3b = 4c..........................(2)
As per Equation (2)
b = 2a/3................................(3)
c = 2a/4 = a/2......................(4)
Now put the value of b and c from Equation (3), (4) in Equation (1),
a + 2a/3 + a/2 = 65
(6a + 4a + 3a)/6 = 65
13a = 65 x 6
a = 5 x 6 = 30
Put the value of a in equation (3) and (4) in order to get the value of b and c,
b = 2 x 30/3 = 2 x 10 = 20
c = 30/2 = 15
The Total number of Guests = 2a = 3b = 4c = 60 

I. x² – 44x + 475 = 0
x² – 25x – 19x + 475 = 0
x = 25 and 19
II. y² – 34y + 285 = 0
y² – 19y – 15y + 285 = 0
y = 19 and 15
Answer: x ≥ y
Hence, Option C is correct.

A.P. given in the question is 10, 7, 4, …
a = 10
d = a(2) – a(1) = 7 − 10 = −3
a(n) = a + (n−1) x d
a(30) = 10 + (30−1) x (−3)
a(30) = 10 + (29) x (−3)
a(30) = 10 − 87 = −77

Given:

Arithmetic mean = 14

Geometric mean = 12

Formula used:

Calculation:

By using the above formula,

HM = 12²/14

⇒ 144/14 = 72/7

∴ The correct answer is 72/7.

The square of 60 is 3600. Therefore, the number of zeroes is 2. 

l² + h² = 193 and b² + h² = 170
l² – b² = 23 --------------- (1)

Using Statement I:
l × b = 132 --------------- (2)
Using equations 1 and 2 we can find the value of l and b, and therefore h
Volume = l × b × h
So, statement I is alone sufficient.

Using Statement II:
2(l + b) = 46
l + b = 23 --------------- (3)
Using equations 1 and 3 we can find the value of l and b, and therefore h
Volume = l × b × h
So, statement II is alone sufficient.
Hence, option C is correct.

Taking all person of same nationality as one person, then we will have only three people.
These three person can be arranged themselves in 3! Ways.
8 Indians can be arranged themselves in 8! Way.
4 American can be arranged themselves in 4! Ways.
4 Englishman can be arranged themselves in 4! Ways.
Hence, required number of ways = 3! 8! 4! 4! Ways.

An hours + C hours = B hours … (I)
A, C and B can’t possess values greater than or equal to 24 B minutes + A minutes = C minutes … (ii)
From the above two equations, it is assumed that no value of A satisfies both the equations.
Hence, option 1 is the correct answer.

Speed of the boat in still water = 17 + 4 = 21 km/hr
Hence, Option C is correct.

Hence, Option C is correct.

Part filled in 1 hour = (1/6-1/8)= 1/24
So, the inlet can fill the tank in 24 hours.
Capacity of the tank= volume of water that flows in 24 hrs
= (4*60*24) ltr. = 5760 liters.

B runs 45/2 m in 6 sec.

= 80 sec.

Let B’s capital = Rs x
So, A’s one month equivalent capital = 3500*12 = 42000
And B’s one month equivalent capital = x*7 = 7 x
Therefore,  42000/7x = 2/3
=> x = 9000 (option ‘D’)

To expenditure = 100 × 8 = 800
Total revenue = 80% of 100 × 15 = 1200

Hence, Option D is correct.

Hence, Option A is correct.

Let AB be the tower and let C and D be the two's positions men.
At that point ∠ACB = 30°,∠ADB = 45°and AB = 50 m
AC/AB = Cot30° = √3 => AC/50 = √3
=> AC = 50√3m
AD/AB = cot 45° = 1 => AD/50 = 1
=> AD = 50M.
Separation between the two men = CD = (AC + AD)
= (50√3 + 50) m = 50(√3 + 1)
=50(1.73 + 1)m = (50 * 2.73)m = 136.5m.

First 13 whole numbers = 0 to 12
Total prime numbers = 5 (2, 3, 5, 7 and 11)

∵ In 2/3h, 1 article is made.
∴ In 1h, 3/2 article are made.
∴ In 7¹/2 = 15/2h, 3/2 x 15/2 = 45/4 article are made.
∴ Required articles = 45/4 = 11²/4

AB || CD and t transversal intersects them at E and F
∠BEF + ∠EFD = 180° (co-interior angles)

⇒ ∠FEG + ∠EFG = 90°
In Δ GEF
∠EGF + ∠FEG + ∠EFG = 180°
∴ ∠EGF + 90° = 180°
∴ ∠EGF = 90°.
The above result can be restated as :
If two parallel lines are cut by a traversal, then the bisectors of the interior angles on the same side of the traversal intersect each other at right angles.

From the given figure, we know that the sum of all the angles of a linear pair is always 180°. Here,  form a linear pair.

Hence, option B is the correct answer.