UKPSC Prelims Paper 2 Mock Test - 4 - UKPSC (Uttarakhand) MCQ

The logic followed here is:
Spearhead: Mislead → Spearhead is the antonym of mislead.
Similarly,
Conceal: ? → Conceal is the antonym of reveal.
Hence, the correct answer is "Option 1".

The correct figure from the given alternatives which will exactly fit into the given figure to make it rectangle

Hence, the correct answer is "Option 2".

Given:

Cost Price (CP1) = ₹10200

Loss% = 10%

Gain% = 10% (on the selling price of the article)

Formula Used:

Selling Price (SP) = CP × (1 - Loss%)

Cost Price (CP) = SP / (1 + Gain%)

Overall Gain/Loss = Final SP - Initial CP

Overall Gain/Loss % = [(Final SP - Initial CP) / Initial CP] × 100

Calculation:

SP1 = 10200 × (1 - 10/100)

⇒ SP1 = 10200 × 0.9 = ₹9180

CP2 = SP1 = ₹9180

SP2 = 9180 × (1 + 10/100)

⇒ SP2 = 9180 × 1.1 = ₹10098

Overall Gain/Loss = SP2 - CP1

⇒ Overall Gain/Loss = 10098 - 10200 = -₹102

⇒ Overall Loss = ₹102

The correct answer is Option (4).

​

Given:
A woman's mother's father's only son related to the woman's father.

Here, the woman's mother's father's only son is woman's father's brother-in-law.
Hence, the correct answer is "Option 3".

Given:
1) A is the spouse of B who has no female child.
2) C is the brother of D and E who is the son of B.

3) A is not the mother of D.

So, D is the son of B.
Hence, the correct answer is "Option 1".

The Correct answer is Option 1
Explanation
The given expression is definitely divisible by 3, as 9 is divisible by 3.
The terms, after division with 3, would be:
9³/3 = 3 × 9²
9⁴/3 = 3 × 9³
9⁵/3 = 3 × 9⁴
……and so on.
All these terms would be odd, as in each of them only odd numbers are getting multiplied.
In total, there would be 98 of these odd terms, whose sum would obviously be even. So, the resultant would be divisible by 2.
So, the original expression is divisible by 3, as well as 2. Which means that it must be divisible by 6 too. So, remainder left would be zero.

Total number of triangles in figure is 18.

Hence, the correct answer is "Option 3".

Given:

The analogue clock is divided into 12 sectors, 1 – 12. One sector represents 30 degrees (360/12 = 30).

If the hour hand is at 10, and the minute hand is at 20, which means there are 6 sectors of 30 degrees each.

Therefore, the hour and minute hand is 180° apart from each other but, at 10:20 hrs hour hand must have travelled some degrees.

Thus, to find the exact angle we use the following formula.

Here, H is time in hour and M is time in minutes.

Therefore, we have time 10:20 hrs, H = 10, M = 20.

We get 300 – 110 = 190 which is reflex angle.

NOTE: The reflex angle is the angle which measures greater than 180°.

Thus, 360 – 190 = 170

Hence, the correct answer is "Option 1".

Given:

The average weight of a kabaddi team of 121 players = 71 kg

The average weight increases by 1 kg when the manager is included

Formula used:

New average = (Total weight of players + Weight of manager) / (Number of players + 1)

Calculation:

Total weight of the team (players only) = 121 × 71 = 8591 kg

New average weight = 71 + 1 = 72 kg

⇒ (Total weight of players + Weight of manager) / (121 + 1) = 72

⇒ (8591 + Weight of manager) / 122 = 72

⇒ 8591 + Weight of manager = 72 × 122

⇒ 8591 + Weight of manager = 8784

⇒ Weight of manager = 193 kg

∴ The correct answer is option (3).

The logic followed here is:

Colt is the young one (offspring) of horse.

Similarly,

Larva is the young one of a butterfly.

Hence, "Option 2" is the correct answer.

Given:

Two-third of a number = 48

Calculations:

Let the number be x. Then,

⇒

⇒ x = 72

30% of x =

⇒

∴ The correct answer is option (1).

Given:

The greatest number which divides 943 and 1957 leaving remainders 7 and 1 respectively.

Formula used:

To find the greatest number, use the concept of HCF (Highest Common Factor) between the adjusted numbers:

Required number = HCF(943 - 7, 1957 - 1)

Calculations:

Adjusted numbers:

⇒ 943 - 7 = 936

⇒ 1957 - 1 = 1956

HCF of (936, 1956):

Prime factorization of 936 and 1956:

936 = 2³ × 3² × 13

1956 = 2² × 3 × 163

Common prime factors = 2² × 3 = 12

⇒ HCF(936, 1956) = 12

∴ The greatest number is 12. The correct answer is option (1).

Given:
Cost price of 12 pairs of shoes = ₹22,400
Overhead expenses = ₹1,600
Total selling price of 12 pairs of shoes = ₹28,500
Formula used:
Profit Percentage =  Profit /Cost Price × 100 
Profit = Selling Price - Total Cost Price
Total Cost Price = Cost Price + Overhead Expenses
Calculation:
Total Cost Price = ₹22,400 + ₹1,600
⇒ Total Cost Price = ₹24,000
Profit = ₹28,500 - ₹24,000
⇒ Profit = ₹4,500

Profit Percentage = 

⇒ Profit Percentage =
⇒ Profit Percentage = 18.75%
∴ The correct answer is option (2).

Given:
First number (a) = 16
Second number (b) = 48
Formula used:
Third proportional (c) = b²/a 
Calculations:
c = 48²/16
⇒ c =  2304/16
⇒ c = 144
∴ The correct answer is option (4).

Given:

The ratio between two numbers = 19 : 24.

If each number is reduced by 36, the ratio becomes 3 : 4.

Calculation:

Let the two numbers be 19x and 24x.

When each number is reduced by 36, the ratio becomes:

Cross-multiplying, we get:

4(19x - 36) = 3(24x - 36)

⇒ 76x - 144 = 72x - 108

⇒ 76x - 72x = 144 - 108

⇒ 4x = 36

⇒ x = 9

Now, the two numbers are:

19x = 19 × 9 = 171

24x = 24 × 9 = 216

The sum of the numbers = 171 + 216 = 387

The sum of the numbers is 387.

Given:

Principal (P) = ₹96,000

Rate (R) = 20% per annum ⇒ 10% per half-year

Time = 1 year = 2 half-years

Formula used:

Amount A = P

Required = 80% of A

Calculations:

A = 96000 × (1 + 10/100)² = 96000 × (1.1)² = 96000 × 1.21 = ₹116160

80% of ₹116160 = 116160 × 0.8 = ₹92928

∴ 80% of the amount on maturity = ₹92,928

Given:

The speed of a vehicle increases by 5 km every hour

The distance traveled in the first hour = 30 km

Formula used:

The sum of n numbers in Arithmetic progression =

where, n = number of terms; a = first term; d = difference

Calculation:

The speed increased by 5 km for every hour,

30 km, 35 km, 40 km ...

Hence the speed for 10 hours is in Arithmetic progression with a difference of 5 km

Since the speed is given for an hour it will also be equal to the distance traveled for that hour

The sum of distance for 10 hours =

⇒ [2 × 30 + (10 - 1)5] = 5[60 + 9 × 5]

⇒ 5 (60 + 45) = 5 × 105 = 525 km.

∴ The correct answer is 525 km.

Family Chart:

Given:
Nia is the paternal aunt of Khushi. Noora is the wife of Amit. Diksha has only one daughter, Noora. Manish is the father of Nia. Samay is the husband of Diksha. Leena is the paternal grandmother of Khushi. Nia is the sister of Amit. If Manish has only two children.

From the family chart, we can see that Leena is the mother of Amit.
Since Noora is the wife of Amit, Leena is the mother-in-law of Noora.
Hence, the correct answer is Mother-in-law.

The Correct answer is Option 3.

Explanation

• Row 1: D → D → D ( No Change )
• Row 2: D → (+2) F , F → (+3) I
• Hence Apply Logic on Row 3
• Row 3: I → (+3) L , L → (+4) P
• Hence the Correct answer is Option 3.

The Correct answer is Option 2.

Explanation

Initial order (bottom to top): A (bottom), B, C, D, E (top)

Step 1: Remove bottom book A and place it on top

New order: B (bottom), C, D, E, A (top)

Step 2: Remove bottom book B and place it on top

New order: C (bottom), D, E, A, B (top)

Step 3: Remove bottom book C and place it on top

New order: D (bottom), E, A, B, C (top)

Now find the middle book:

Books from bottom to top: D, E, A, B, C

The middle (3rd) book is A.

Hence the Correct answer is Option 2.

The Correct answer is Option 3.

Explanation

Using the formulas:

Sum of cubes: 1³ + 2³ + ... + n³ = (n(n + 1)/2)²

Sum of first n natural numbers: 1 + 2 + ... + n = n(n + 1)/2

Calculate the expression:

(n(n + 1)/2)² - n(n + 1)/2

= (n(n + 1)/2) × ((n(n + 1)/2) - 1)

= (n(n + 1)/2) × ((n(n + 1) - 2)/2)

= [n(n + 1)(n(n + 1) - 2)] / 4

Let n² + n = n(n + 1), then:

= [(n² + n)(n² + n - 2)] / 4

Therefore, the answer is option (c): (n² + n)(n² + n - 2) / 4​

The Correct answer is Option 3.

Key Points

Find the unit digit of the product 31 × 49 × 34

Unit digit of 31 = 1

Unit digit of 49 = 9

Unit digit of 34 = 4

Now calculate the unit digit:

1 × 9 = 9 → 9 × 4 = 36 → Unit digit = 6

Let ✶ be the unknown unit digit

We know: ✶ × 6 ≡ 2 (mod 10)

Try values for ✶:

2 × 6 = 12 → unit digit = 2

7 × 6 = 42 → unit digit = 2

Only 2 and 7 give the desired result.

Hence the Correct answer is Option 3.

The diagram for the given blood relation is,

Therefore, Option 3 is the correct answer.

The logic followed here is:

Similarly, the code for MODE will be

Hence, the code for 'MODE' will be '%@35'.

Formula used:

Volume of cube = a³

Volume of sphere = 4/3πr³

Calculation:

Let radius of sphere be r

Then, each side of cube = 2r

Ratio = volume of cube/volume of sphere

⇒ (2r)³/[4/3π × (r)³]

⇒ 6 : π

∴ Required ratio is 6 : π

Given letters: ALEP

The meaningful English words that can be formed are:

PEAL, PLEA, LEAP, PALE

Hence, the correct answer is Option 4.

Key Point

PEAL - गड़गड़ाहट

​PLEA - कृपया

LEAP - उछलना

PALE - फीका

Given:

The average of 10 numbers is 15

one number 36 was wrongly copied = 26

Formula used:

Average = sum of observations/Total number of observations

Calculation:

Average of ten numbers = (sum of 10 numbers)/10

⇒ 15 × 10 = sum of 10 numbers

⇒ 150 = sum of 10 numbers

Later on, one number was written wrong as 26,

Now,

correct sum of numbers is = 150 – 26 + 36

⇒ 160

Correct average = sum of 10 numbers/10

⇒ 160/10

⇒ 16

∴ Correct average is 16

The correct answer is 'Proscenium stages.'
Explanation

• Let's have a look at these sentences in the first paragraph of the passage:
  • “ Proscenium stages have an architectural frame, known as the proscenium arch, although they are not always arched in shape. Their stages are deep and sometimes raked, meaning the stage is gently sloped, rising away from the audience.”
• From the passage, it can be concluded although not always arched in shape, proscenium stages have an architectural frame known as the proscenium arch.
• Their stages are deep and occasionally raked, which means the stage is gently sloped and rises away from the audience.

Therefore, the correct answer is Option 2.

सही उत्तर 'तुर्की' है।
 प्रमुख बिंदु

• दिए गए विकल्पों में से 'लाश' शब्द मूलत: तुर्की भाषा का है।
• लाश अर्थात किसी प्राणी का मृत शरीर।
• यह विदेशज शब्द है।

 अतिरिक्त जानकारी

• विदेशज शब्द - विदेशी भाषाओं से हिंदी में आये शब्दों को विदेशीया विदेशज शब्द कहा जाता है।
• इन विदेशी भाषाओं में मुख्यतः अरबी, फारसी, तुर्की, अंग्रेजी व पुर्तगाली शामिल है।

सही उत्तर 'धनु: + टंकार' है।
 प्रमुख बिंदु

• धनुष्टंकार का उचित संधि विच्छेद 'धनु: + टंकार' होगा।
• धनुष्टंकार शब्द में विसर्ग संधि है।
• स्वर और व्यंजन के मेल से विसर्ग में जो विसर्ग होता है उसे विसर्ग संधि कहते है।

अतिरिक्त जानकारी

• दो निकटवर्ती वर्णों के परस्पर मेल से जो विकार (परिवर्तन) होता है वह संधि कहलाता है।
• इसके तीन भेद हैं -

1. स्वर संधि
2. व्यंजन संधि
3. विसर्ग संधि