UP Police Constable Mock Test - 5 - UP Police Constable MCQ

Hence, Option C is correct.

Expenditure : Savings = 100 : 125 = 4 : 5

Hence, Option C is correct.

Weight of the car = (180 × 7 – 72 × 6) = 828 kg
Hence, Option B is correct.

6l + 6b = 8l
6b = 2l
l : b = 3 : 1
Hence, Option B is correct.

HCF of two-prime numbers = 1
∴ Product of numbers = their LCM = 117
117 = 13 × 9 where 13 & 9 are co-prime. L.C.M (13,9) = 117.

50 × R + 60 × 80 = 70 × (50 + 60)
50 × R + 4800 = 7700 
50R = 2,900
R = 58
Hence, Option B is correct.

On cubing both sides,


⇒  a⁶ + 1 = 0
∴  a¹⁸ + a¹² + a⁶ + 1
= a¹² (a⁶ + 1) + 1 (a⁶ + 1)
= (a⁶ + 1)(a¹² + 1) = 0 

Let us assume the number is n.
According to question,
If 24 is subtracted, it becomes 4/7 of the number.
n - 24 = n x 4/7
⇒ n - 4n/7 = 24
⇒ (7n - 4n)/7 = 24
⇒ 3n/7 = 24
⇒ 3n = 24 x 7
⇒ n = 24 x 7/3
⇒ n = 8 x 7
⇒ n = 56
Sum of the digits of the number = 5 + 6 = 11

I. 3x + 3y = √1764
3x + 3y = 42
x + y = 14

II. 7x – 5y = √1444
7x – 5y = 38
5 × I + II
12x = 70 + 38
x = 9
y = 14 – 9 = 5
x > y
Hence, Option A is correct.

Here 7^th term = 20
11^thterm = 40
Let the first term of the AP be a and common difference be d
T₇ = a + (n – 1)d = 20
T₇ = a + (7 – 1)d = 20
T₇ = a + 6d = 20     (1)
T₁₁ = a + (n – 1)d = 40
T₁₁ = a + (11 – 1)d = 40
T₁₁ = a + 10d = 40     (2)
Subtracting (1) from (2)
We get,
a + 10d – (a + 6d) = 40 – 20
4d = 20
d = 5 

Calculation:

The harmonic mean of the the x₁ , x₂ , x₃ ......x_n is given by

The above is geometric mean of common ratio 1/2 and first term 1. The sum of above G.P would be

(64)² - (36)² = 20 x y Using formulae (a + b)(a - b) = a^{2 - b2}
=> (64 + 36)(64 - 36) = 20 x y => 100 x 28 = 20 x y => y = 5 x 28 = 140

Statement I :

R = 100

Statement II :
5% of 5% of R = 0.25
R = 100
So, statement I alone or II alone is sufficient.
Hence, option C is correct.

ALLAHABAD = 9 letters. Out of these 9 letters there is 4 A's and 2 L's are there.
So, permutations 
(a) There are 4 vowels and all are alike i.e. 4A's.

These even places can be occupied by 4 vowels. In 
In other five places 5 other letter can be occupied of which two are alike i.e. 2L's.
Number of ways = 5!/2! Ways.
Hence, total number of ways in which vowels occupy the even places  = 60 ways.

(b) Taking both L's together and treating them as one letter we have 8 letters out of which A repeats 4 times and others are distinct.
These 8 letters can be arranged in = 8!/4! Ways.
Also two L can be arranged themselves in 2! ways.
So, Total no. of ways in which L are together = 1680 × 2 = 3360 ways.
Now,
Total arrangement in which L never occur together,
= Total arrangement - Total no. of ways in which L occur together.
= 7560 - 3360
= 4200 ways

At any time, A hours and B minutes, the angle made by the hours hand is 30 A + B / 2. 30A+B/2. Similarly, the angle made by the minutes hand is 6B.

For a person to not be able to find the correct time, there should be another time     A1:B1 such that 30 A1 + B1 / 2 = 6B and 6B1 = 30 A + B / 2 6B1=30A+B/2

There is no integral solution existing when 0 < B < 60

Option 4 is the correct answer.

Speed of the boat in still water = 15 – 2 = 13 km/hr
Hence, Option D is correct.

Required time 

Hence, Option A is correct.

Net part filled in 1 hr = (1/8 ? 1/16) = 1/16
Total time taken to fill the tank = 16 hrs.

Time taken by A to run 1 km = 290 sec.
Time taken by B to run 1 km = 300 sec.
A can give B a start of (300-290) = 10sec.
In 300 sec, B runs (1000/300*10) m = 100/3 m
∴ A can give B start of 100/3 m.

Simran invested Rs 50000 for 36 months and Nanda invest Rs 80000 for 30 months
Jitesh’s one month equivalent investment = 50000*36
Rahul’s one month equivalent investment = 80000*30
Thus, ratio of their investments =  = 50000*36 : 80000*30 = 3 : 4
Therefore Jitesh’s share in the profit = 24500 x 3/7 = Rs 10,500 (option ‘D’)

Let CP = 100
MP = 160
SP = 125

Hence, Option D is correct.

There should be 56 in place of 57.
Hence, Option C is correct. 

One of AB, AD and CD must have given.

So, the data is inadequate.

Total milk bought =8.5l+7.25l+9.4l=25.15l

∴ Milk left in booth = 30l−25.15l = 4.850 liters

11/17 (if the first one is black, there will be 11 black balls left out of 17)

∵ 8 m shadow means original height = 12 m
∴ 1 m shadow means original height = 12/8 m
∴ 100 m shadow means original height = (12/8) x 100 m
= (6/4) x 100 = 6 x 25 = 150 m

On the basis of question we draw a figure of a circle with centre O ,

Let OE = y cm
then OF = (y +1) cm
OA = OC = r cm
AE = 4 cm; CF = 3 cm
From ∆ OAE,
OA² = AE² + OE²
⇒ r² = 16 + y²
⇒ y² = r² – 16 ......(i)
From ∆OCF,
(y + 1)² = r² – 9 ..... (ii)
By equation (ii) – (i),
(y + 1)² – y² = r² – 9 – r² + 16
⇒ 2y + 1 = 7
⇒ y = 3 cm
∴ From equation (i),
9 = r² – 16
⇒ r² = 25
⇒ r = 5 cm

Let total work be LCM of (90, 60) = 180 unit
Ratio of number of days by Sarthak and Deepak = 90 : 60 = 3 : 2
Ratio of efficiency of Sarthak and Deepak = 2 : 3
Total unit in one day = 2 + 3 = 5 unit
Number of days taken = 180/5 = 36 days 
Hence, Option B is correct.

So the answer = (100 – 50)% of 700 + (100 – 60)% of 500 = 550
Hence, Option D is correct.

All even numbers between 1 and 50 = 2 to 48

Hence, Option D is correct.