UP Police Constable Mock Test - 7 - UP Police Constable MCQ

Hence, Option C is correct.

x% of a = y% of b
z × x% of a = z × y% of b

Hence, Option C is correct.

Hence, Option D is correct.

Side of the cube = ∛729 = 9 meters
So the answer = Side √3 = 9√3 meters
Hence, Option C is correct.

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,

Obviously, numbers are 111 and 37 which satisfy the given condition.
Hence, the greater number = 111

Initial mixture : added water = 40 : 15 = 8 : 3

Hence, Option D is correct.

x + y + z = 9
x² + y² + z² = 31
(x + y + z)² = x² + y² + z² + 2 (xy + yz + zx)
⇒  81 = 31 + 2 (xy + yz + zx)
⇒  2 (xy + yz + zx)
= 81 – 31
= 50
⇒  xy + yz + zx = 25
∴  x³ + y³ + z³ – 3xyz
= (x + y + z) (x² + y² + z² – xy – yz – zx)
= 9 (31 – 25)
= 9 × 6 = 54 

Let us assume the first number is a and common difference is d.
According to question,
4th term of A.P = 37
a + (n - 1) x d = 37
Put the value of a , n and d, we will get,
a + (4 - 1) x d = 37
a + 3d = 37..................(1)
sixth term is 12 more than the fourth term,
6th term = 12 + 4th term
a + (n - 1) x d = 12 + 37
a + (6- 1) x d = 39
a + 5d = 39................(2)
subtract the equation (1) from (2)
a + 5d - a - 3d = 39 - 37
5d - 3d= 2
2d = 2
d = 1
Put the value of d in equation (1), we will get
a + 3 x 1 = 37
a = 37 - 3
a = 34
Second term = a + (n - 1) x d = 34 + (2 - 1) x 1 = 34 + 1 = 35
Six term = a + (n - 1) x d = 34 + (6 - 1) x 1 = 34 + 5 = 39
Sum of Second and Six term = 35 + 39 = 74
Sum of Second and Six term = 74
Answer is 74.

8x + 2y = 3x + 7y
8x –  3x = 7y –  2y
x = y
Answer: x = y
Hence, Option D is correct.

Concept:
Arithmetic Progression (AP):

• The sequence of numbers where the difference of any two consecutive terms is same is called an Arithmetic Progression.
• If a be the first term, d be the common difference and n be the number of terms of an AP, then the sequence can be written as follows:
• a, a + d, a + 2d, ..., a + (n - 1)d.
• The sum of n terms of the above series is given by:
  

Calculation:
The given series is 5 + 9 + 13 + … + 49 which is an arithmetic progression with first term a = 5 and common difference d = 4.
Let's say that the last term 49 is the nth term.
∴ a + (n - 1)d = 49
⇒ 5 + 4(n - 1) = 49
⇒ 4(n - 1) = 44
⇒ n = 12.
And, the sum of this AP is:

CONCEPT:

Let us suppose a be the first term and d be the common difference of an AP. Then the nth term of an AP is given by:a_n = a + (n - 1) × d.

Note: If l is the last term of a sequence, then l = a_n = a + (n - 1) × d.

CALCULATION:

Here we have to find two digit numbers which are divisible by 7.

i.e 14, 21,............,98 is an AP sequence with first term a = 14, common difference d = 7 and the last term l = 98.

As we know that, if l is the last term of a sequence, then l = an = a + (n - 1) × d

⇒ 98 = 14 + (n - 1) × 7

⇒ 84 = 7(n - 1)

⇒ 12 = n - 1

⇒ n = 13

Let the natural number be 'x'.

∴ x³ − x² = 48

⇒ x²(x - 1) = 48

⇒ 4²(4 - 1) = 48

∴ x = 4

Statement I: 2X7Y00 is divisible by 8 and 9
Y00 is divisible by 8
So, Y can be 0, 2, 4, 6, 8
2 + X + 7 + Y is divisible by 9
So, X + Y = 0, 9, 18
Multiple possibilities for X and Y.
So, statement I alone is not sufficient.

Statement II: 2X7Y00 is divisible by 11
(2 + 7 + 0) – (X + Y + 0) = Multiple of 11
So, X + Y = 9
But we can’t find the value of X and Y.
So, statement I alone is not sufficient.

Using both the Statements:
X + Y = 9
Y can be 0, 2, 4, 6, 8
We get no definite value of X and Y
So, both the statements are together insufficient.
Hence, option D is correct.

Given:
The given number is 'GEOGRAPHY'

Calculation:
The word 'GEOGRAPHY' has 9 letters. It has the vowels E, O, A in it, and these 3 vowels must always come together. Hence these 3 vowels can be grouped and considered as a single letter. That is, GGRPHY(EOA).

Let 7 letters in this word but in these 7 letters, 'G' occurs 2 times, but the rest of the letters are different.

Now,
The number of ways to arrange these letters = 7!/2!
⇒ 7 × 6 × 5 × 4 × 3 = 2520
In the 3 vowels(EOA), all vowels are different
The number of ways to arrange these vowels = 3!
⇒ 3 × 2 × 1 = 6

Now, 
The required number of ways = 2520 × 6 
⇒ 15120
∴ The required number of ways is 15120.

Given - 
January 1, 2018 was Monday

Concept used - 
in a normal year number of days = 365
number of odd days = (365/7) = + 1

1 January 2018 = Monday
1 January 2019 = Monday + 1 = Tuesday
∴ January 1, 2019 = Tuesday  

Downstream speed = 15 + 3 = 18 km/hr
So the answer = 18 × 3 = 54 km
Hence, Option D is correct.

Speed → Old : New = 100 : 25 = 4 : 1
Time → Old : New = 1 : 4

Hence, Option D is correct.

Let the capacity of the tank = x gallons
Quantity of the water filled in the tank in 1 min when all the pipes A, B and C are opened simultaneously= x/20 + x/24 - 3
According to question,
x/20 + x/24 - 3 = x/15
or, x/20 + x/24 - x/15 = 3
or, (6x + 5x  - 8x)/120 = 3
or, 3x/120 = 3
or, x = 120 gallons

Time taken by A to run 100m = (60*60/6000*100) sec. = 60 sec.
B covers (100-4) m in (60 +12) sec.
∴ B's speed = 96/72m/sec. = (96/72*18/5) km/hr = 4.8 km/hr

Their one month equivalent use of the pasture 
A = 10*7 = 70 months
B = 12*5 = 60 months
C = 15*3 = 45 months
Hence their expenditure sharing ratio = 70 : 60 : 45 = 14 : 12 : 9
Therefore C’s share of the rent = 175*(9/35) = Rs 45 (option ‘A’)

20% of CP = 400 + 100
CP = 2500
So the answer = 2500 + 100 = Rs. 2600
Hence, Option D is correct.

Hence, Option C is correct.

From ∠APB = 60° and AB = 180 m.
AB/AP = tan 60° =√3
AP = AB/√3 = 180/√3 = 60√3

15 wickets= 330 runs 1 wickets

Total balls = 4 + 10 + 6 = 20
Red balls + white balls = 4 + 6 = 10

According to given question,
Price of 23 toys = Rs. 276.

∴ Price of 12 toys = 12 x 12 = 144

We know that in a triangle, if three altitudes are equal, then the triangle is called equilateral.

Hence, Option D is correct.

Hence, Option B is correct.

Hence, Option A is correct.