AP Police Constable Mock Test - 4 - AP Police Constable MCQ

7 × 57 + 7 × 65 = 854
Since the 7th number came twice, it is added two times.
So the answer = 854 – 13 × 60 = 74
Hence, Option D is correct.

Height of the triangle = √(13² – 12²) = 5 meters


Hence, Option A is correct.

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
First number × Second number = HCF × LCM
⇒ 75 × Second number = 15 × 225

At 20% loss : At 40% loss = 15% : 5% = 3 : 1

Hence, Option B is correct.

⇒ a² + b² = ab
⇒ a² – ab + b²
= 0
∴  a³ + b³ = (a + b) (a² – ab + b²) = 0 

Let us assume the numbers are a and b.
According to question,
a² - b² = 256000 .......................(1)
and a + b = 1000 .........................(2)
On dividing the Equation (1) with Equation (2),
(a² - b²)/(a + b) = 256000/1000
(a² - b²)/(a + b) = 256
(a + b)(a - b)/(a + b) = 256
a - b = 256...............................(3)
Add the equation (2) and (3), we will get
a + b + a - b = 1000 + 256
2a = 1256
a = 628
Put the value of a in equation (2), we will get
658 + b = 1000
b = 1000 - 628
b = 372
So answer is 628 , 372. 

I. x² + 11x + 28 = 0
x² + 4x + 7x + 28 = 0
x = – 4 and – 7

II. 2y² + 30y + 112= 0
2y² + 14y + 16y + 112 = 0

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

Concept:
The nth number in A.P. series = T_n = a + (n - 1)d
Where 'a' is the first number of the series and 'd' is the common difference

Calculation:
Let the first element of A.P. is 'a' and common difference is 'd'

Given:
T₂₅ = T₁₅ + 70
According to the question,
T₂₅ = T₁₅ + 70
⇒ a + (25 – 1)d = a + ( 15 – 1)d + 70
⇒ 24d – 14d = 70
⇒ 10d = 70
⇒ d = 7
∴ The common difference is 7.

Given, 3, 8, 13, 18, … is the AP.
a = 3
d = a(2) – a(1) = 8 − 3 = 5
Let a(n) term be 78.
a(n) = a + (n − 1) x d
78 = 3 + (n − 1) x 5
75 = (n − 1) x 5
(n − 1) = 15
n = 16

First five prime numbers are 2, 3, 5, 7, 11. Sum - 28

Total digits = 5 → 0, 2, 4, 6, 8
Possible numbers for hundreds place = 4 = 2, 4, 6 and 8
Possible numbers for tens place = 4
Possible numbers for ones place = 3
So the answer = 4 × 4 × 3 = 48

According to given question,
Since 900 books are bonded in 10 days by 18 binders.
∴ 1 books are bonded in 10 days by 18 / 900 binders.
∴ 1 books are bonded in 1 days by 18 x 10 / 900 binders.
∴ 660 books are bonded in 1 days by 18 x 10 x 660 / 900 binders.
∴ 660 books are bonded in 12 days by 18 x 10 x 660 / 12 x 900 binders.
∴ 660 books are bonded in 12 days by 18 x 10 x 55 / 900 binders.
∴ 660 books are bonded in 12 days by 18 x 55 / 90 binders.
∴ 660 books are bonded in 12 days by 55 / 5 binders.
∴ 660 books are bonded in 12 days by 11 binders.

Since A, B and C are the angles of a Δ,
∴ A + B + C = 180° .................... (1)
According to question,
A – B = 15° ;
⇒ A = B + 15°...................(2)
B – C = 30°;
⇒ B = C + 30°;....................(3)
Put the value of B from equation (2) in Equation (1), we will get
∴ A = B + 15°
A = C + 30° + 15°
A = C + 45° ......................(4)
From a equation,
∴ A + B + C = 180°
⇒ (C + 45°) + (C + 30°) + C = 180°
⇒ 3C + 45° + 30° = 180°
⇒ 3C = 180° – 75° = 105°
⇒ C = 35° ...........................(5)
From equation (4)
A = C + 45°
Put the value of C from equation (5) , we will get
∴ ∠A = 35° + 45° = 80°.

Hence, Option D is correct.

Using Rule 1,

If the slower pipe fills the tank in x hours, then

Required time = 30 - 10 = 20 hours

Distance covered by B in 6 sec. =(1000/300*6)m = 20m
∴  A beats B by 20 m.
For a dead heat race, A must give B a start of 20m.

Investment of Sumit = Rs.45000
Duration of Sumit = 1 year
Investment of Ravi = Rs.81000
Duration of Sumit = 1 year
Investment of Puneet = Rs.90000
Duration of Puneet = 1 year
Ratio of profits = Ratio of investments...

Given, Total profit = Rs.4800 30% of total profit donated to charity
Amount donated to charity = 30% of Rs.4800 = Rs.1440...
Remaining amount = Rs.4800-1440 = Rs.3360
Let the profits of Sumit, Ravi and Puneet be Rs.5x, Rs.9x and Rs.10x respectively....
Total profit = Rs.5x+9x+10x = Rs.24x...
Given, 24x = 3360 => x = 140 Therefore, Profit of Sumit = 5x = 5*140 = Rs.700.

Hence, Option C is correct.

There should be 16 in place of 12.
Hence, Option A is correct. 

Tan(60) = h₁/AB
=> h₁ = √3AB
Tan(45) = h₁/BC
=> h₂ = BC
h₁/ h₂ = √3/1
=> h₁ : h₂ = √3 : 1

Total cards = 52
Numbered cards = 2 to 10
Total numbered cards = 4 × 9 = 36

According to question,
40 cows eat 40 bags of husk in 40 days.
1 cows eat 40 bags of husk in 40 x 40 days.
1 cows eat 1 bags of husk in 40 x 40 / 40 days.
1 cows eat 1 bags of husk in 40 days.

In ΔACE
∠A + ∠C + ∠E = 180°
Similarly in ΔDFB
∠D + ∠F + ∠B = 180°
∴ (∠A + ∠C + ∠E) + (∠D + ∠F + ∠B) = 360°
∠A + ∠B + ∠C + ∠D + ∠E + ∠F = 360°

Let the breadth of the rectangle = B
Length of the rectangle = L
L × B = 2 B × 2 B
L = 4B
L : B = 4 : 1
Hence, Option C is correct.

10 rupee coins : 5 rupee coins = 480 : 230 = 3 : 2

Hence, Option C is correct.

Midpoint formula:

I. x² – 1200 = 169
x² = 1200 + 169
x² = 1369 = √(1369) = ± 37

II. y + 122 = 159
y = 159 – 122 = 37
Answer: x ≤ y
Hence, Option B is correct.

log₁₀xy = z
⇒ xy = 10^z
⇒ x = 10^z/y