AP Police Constable Mock Test - 3 - AP Police Constable MCQ

Hence, Option B is correct.

Fragment C of the sentence is erroneous.

Reason:

The sentence talks about hard facts of life between Henry Purcell and other great composers. Since the comparison is between the hard facts of life so, ‘than that of’ should be used instead of ‘than’ to make the sentence grammatically correct.

We usually use 'than' when we compare two objects or people directly Eg: My camera is better than your camera (or, than yours). But we usually use 'than that of'/ 'than those of' when we compare not the objects but the attributes or qualities of those objects Eg: The colour of my camera is brighter than that of yours.

Correct Sentence:

There are probably fewer hard facts about the life of Henry Purcell than that of any other great composer since the Renaissance.

Hence, option C is the correct answer.

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 

Simplify both sides of the equation as much as possible, and solve for x in the equation in terms of N:

3(4x−7)+12=2(5x−3)+N(x−3)
3⋅4x−3⋅7+12=2⋅5x−2⋅3+N⋅x−N⋅3
12x−21+12=10x−6+Nx−3N
12x−9=(10+N)x+(−6−3N)
12x−(10+N)x=(−6−3N)+9
(2−N)x=3−3N

 

x has exactly one solution unless the denominator is 0 - that is, N=2. We make sure that this value renders no solution by substituting:

3(4x−7)+12=2(5x−3)+N(x−3)
3(4x−7)+12=2(5x−3)+2(x−3)
12x−21+12=10x−6+2x−6
12x−9=12x−12
−9=−12

The equation has no solution, and N=2 is the correct answer.

I. 3x² – 21x + 36 = 0
3x² – 12x – 9x + 36 = 0

II. 5y² – 25y + 30 = 0
5y² – 10y – 15y + 30 = 0

Answer: x ≥ y
Hence, Option C is correct.

= log₁₀ 10^-5 = -5

Concept:
The nth term of an AP is given by: T_n = a + (n - 1) × d, where a = first term and d = common difference.

Calculation:
As we know that, the nth term of an AP is given by: T_n = a + (n - 1) × d, where a = first term and d = common difference.
Let a be the first term and d is the common difference.

By adding (1) and (2), we get

For this, calculate the sum of digits:
936: Sum of digits = 18 i.e. divisible by 3 and 9.
39987: Sum of digits = 36 i.e. divisible by 3 and 9.
2343: Sum of digits = 12 i.e. divisible by 3, but not by 9.
36: Sum of digits = 9 i.e. divisible by 3 and 9.

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.

Curved surface area = 2πrh

Plane surface area = 2 × πr² 

So the answer = 308 – 264 = 44 cm² 
Hence, Option B is correct.