UP Police Constable Mock Test - 6 - UP Police Constable MCQ

10 men = 20 women
Man : Woman = 2 : 1

Hence, Option B is correct.

The number of students who play both the games = (30 + 50 + 40)% – 100% = 20%
Hence, Option D is correct.

Sundays → 2nd, 9th, 16th, 23rd and 30th (5 Sundays)

Hence, Option C is correct.

Diameter of the circle = breadth of the rectangle = 42 meters
Radius of the circle

So the answer 

Hence, Option D is correct.

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
Let LCM be L and HCF be H, then L = 4H
∴ H + 4H = 125
⇒ 5H = 125

∴ L = 4 × 25 = 100

Reqd. ratio = 3 : 4.50 = 2 : 3
Hence, Option C is correct.

On squaring both sides,

On squaring again,

Let us assume 1 pen cost be ₹ x and 1 pencil cost be ₹ y.
According to question,
The Cost of 36 pens and 42 pencils is 460.
36x + 42y = 460 ...................(1)
then the cost of 18 pens and 21 pencils = 18x + 21y.
Now divide the Equation (1) by 2. We will get,
18x + 21y = 230
So the Cost of 18 pens and 21 pencils = 18x + 21y = 230

I. x² + 48x – 153 = 0
x² + 51x – 3x – 153 = 0
x = – 51 and 3

II. y² = 32y – 156
y² – 32y + 156 = 0
y² – 26y – 6x + 156 = 0
y = 26 and 6
Answer: x < y
Hence, Option D is correct.

∵ log_a x = ( log_abx) / (log_aba)
∴ The given expression = [[(log_abx) / (log_aba)] / [( log_abx )] - ( log_ab)
= (1/log_aba) - log_ab = log_aab - log_ab = log_a(ab/b)
= log_aa = 1 

Here a = 5, d = 8 – 5 = 3 and n = 14
T₁₄ = a + (n – 1)d
T₁₄ = 5 + (14 – 1)3
T₁₄ = 5 + 13 × 3
T₁₄ = 44 

The numbers ending with 0 gives 0,numbers ending with 1,9 gives 1, numbers ending with 2,8 gives 4, numbers ending with 3,7 gives 9, numbers ending with 5 gives 5 and numbers ending with 4,6 gives 6. Hence we get only 0,1,4,5,6,9 at the unit's place.

A triangle needs 3 points.
And polygon of 8 sides has 8 angular points.
Hence, number of triangle formed,

Logic: If we see carefully we can find that these dates have property yy² = dd² + mm²
3rd April, 2005 - 03/04/05  
(05)² = (03)² + (04)²
6th August, 2010 - 06/08/10
(10)² = (06)² + (08)²
5th December, 2013 - 05/12/13
(13)² = (05)² + (12)²
Similarly,
Independence day 2017 - 15 August 2017 - 15/08/17
By above logic: (17)² = (15)² + (08)²  
No other option satisfy the above condition. So, Indian Independence Day of 2017 has the same property.
Hence, option 1) is the correct answer.

Upstream speed of the boat = 19 – 4 × 2 = 11 km/hr
Hence, Option C is correct.

Speed → Old : New = 3 : 2
Time → Old : New = 2 : 3

Hence, Option B is correct.

Using Rule 1,
Part of tank filled by pipes A and B in 1 hour

Required time 

= 1 hour 12 minutes

Hence, Option B is correct.

There should be 199 in place of 201.
Hence, Option D is correct. 

Let AB be the building and the man is standing at A.

When the car is 200m away from the building, the angle of depression is 60°

tan 60° = BD/AB = √3

⇒ 200/AB = √3

⇒ AB = 115.47 m

⇒ tan30° =BC/AB = x/115.47 = 1/√3

⇒ x = 66.67

Now, the car travels distance CD in 8 seconds

 CD = BD – BC = 200 – 66.67 = 133.33 m

 Speed = 133.33/8 = 16.67 m/s

Let the number be x.

P (Amit) = 1/3

P (Vikas) = 2/7

P (Vivek) = 1/8.
Required Probability = 1/3 + 2/7 + 1/8 = 125/168.

Let the consecutive integers(even) be 2p and (2p + 2):
= (2p + 2)² - 2p² = (2p + 2 + 2p)(2p + 2 -2p)
= 2(4p + 2)
= 4 (2p + 1)
Therefore, divisible by 4.

Using Statement I : No value is given, thus it is insufficient.

Using Statement II :
x₂ – 9x + 20 = 0
(x – 4) (x – 5) = 0
x = 4, 5
p + 1 = 4 and 2q = 5
p = 3, q = 5/2
p + 1 = 5 and 2q = 4
p = 4 and q = 2
Multiple values are possible.
So, statement II alone is not sufficient.

Using both Statement I and II :
p + 1 = 4 and 2q = 5

p + 1 = 5 and 2q = 4
p = 4 and q = 2 (not possible)

So, both the statements are together necessary.
Hence, option D is correct.

Given: 
(7 men + 6 women) 5 persons are to be chosen for a committee.

Formula used:
ⁿC_r = n!/(n - r)! r!

Calculation:
Ways in which at least 3 men are selected;
⇒ 3 men + 2 women
⇒ 4 men + 1 woman 
⇒ 5 men + 0 woman 

Number of ways = ⁷C₃ × ⁶C₂ + ⁷C₄ × ⁶C₁ + ⁷C₅ × ⁶C₀
⇒ 7!/(3! × 4!) × 6!/(2! × 4!) + 7!/(4! × 3!) × 6!/(1! × 5!) + 7!/(5! × 2!) × 6!/(6!× 0!)
⇒ 35 × 15 + 35 × 6 + 21 
⇒ 735 + 21 = 756
∴ The required no of ways = 756.

From 9 pm to 12 am angle rotated = 90°
⇒ Angle rotated from 12 am to 6 am = 180°
⇒ Therefore , total angle rotated = (90 + 180)°
⇒ 270°
Hence Total angle rotated = 270° 

Upstream speed of the boat = 14 – 3 = 11 km/hr
Hence, Option D is correct.

Speed of the train – Speed of the man

So the answer = 9 + 3 = 12 m/s
Hence, Option D is correct.

Part of the tank filled in 1 hour by pipe A = 1/2
Part of the tank filled by both pipes in1 hour

So, Time taken to fill 2/3 part = 60 minutes
Time taken to fill 1/2 part

The tank will be filled at 11:45 A.M.

A's  speed  =(5*5/18) m/s = 25/18m/s.
Time taken by A to cover 100m  = (100* 18/25) sec.  =72 sec.
∴ B covers 92 m in (72+8) sec.= 80 sec.
∴ B's speed = (92/80)m/sec. = (92/80* 18/5) km/hr =  4.14km/hr