The correct answer is option 1 i.e. 1797√3.

x + 1/x = 3√3

We know that,

⇒ x² + 1/x² = (x + 1/x)² - 2

⇒ x² + 1/x² = 27 - 2 = 25

And also

⇒ x³ + 1/x³ = (x + 1/x)³ - 3(x + 1/x)

⇒ (3√3)³ - 3(3√3)

⇒ 81√3 - 9√3 = 72√3

Now multiplying both,

⇒ (x² + 1/x²)(x³ + 1/x³) = x⁵ + 1/x⁵ + x + 1/x

⇒ (25)(72√3) =  x⁵ + 1/x⁵ + 3√3

⇒ 1800√3= x⁵ + 1/x⁵ + 3√3

⇒ x⁵ + 1/x⁵ = 1797√3

The correct answer is option 1 i.e. 10%.

Let the cost price is 300x

After marking up the price by 33.33%,

⇒ 300x × (4/3) = 400x

The profit is 20%

Selling price = 1.2 × 300x ⇒ 360x

Discount = 400x - 360x ⇒ 40x

Discount% = 40x/400x × 100 ⇒ 10%

The correct answer is Option 4 i.e. None of these.

⇒ √289 + 16 ( 8 ÷ 4 + 3 - 9 + √121)

⇒ 17 + 16 (2 + 3 - 9 + 11)

⇒ 17 + 16 × 7

⇒ 129

The correct answer is option 2 i.e. 2312

Smallest number divisible by 3, 5, 7 and 11 = LCM (3, 5, 7, 11)

⇒ 3 × 5 × 7 × 11 = 1155

Second smallest number = 2 × 1155 = 2310

To leave a remainder of 2, the number should be = 2310 + 2 = 2312

The correct answer is option 3 i.e. 6.45 days.

2 men and 3 women can do a piece of work in 10 days while 3 men and 2 women can do the same work in 8 days

So, 

Total work = total person × total time

(2M + 3W) × 10 = (3M + 2W) × 8 

⇒ M/W = 7/2

So, the total work = (2M × 3W) × 10 = (2 × 7 + 3 × 2) × 10 = 200 unit

3 men and 5 women can do the same work = 200/(3 × 7 + 5 × 2) = 200/31 = 6.45 days

The correct answer is option 4 i.e. Rs.400.

Effective investment of Shri = 8 × 1000 = Rs.8000

Effective investment of Shankar = 5 × 1200 = Rs.6000

Effective investment of Sabri = 10 × 800 = Rs.8000

Share of Shri = 8000/(8000 + 6000 + 8000) = 4/11

Share of Shankar = 6000/(8000 + 6000 + 8000) = 3/11

Difference between the share of Shri and Shankar

⇒ 4/11 - 3/11 = 1/11

⇒ (1/11) × 4400 = 400

The correct answer is Option 2 i.e. 2560.

The total number of votes cast by villagers was 8000 votes.

As 20% of votes which Manoj received are invalid, the total number of valid votes remaining is 80% votes.

⇒ 8000 × 0.8 = 6400 votes.

Since candidate Ram received 60% of valid votes, Shyam must have received the remaining 40% of total valid votes.

⇒ 6400 × 0.4 = 2560 votes.

The correct answer is option 3 i.e. 24

Such a number can be found out if we take LCM of all given number and add 1 to it.

N = n × LCM of (2, 3, 4, 5 and 7) + 1 , where n = 0, 1, 2, 3 etc.

LCM of (2, 3, 4, 5 and 7) = 420

N = n × 420 + 1

Minimum value of n = 0

Maximum value of n (N < 10000),

n × 420 + 1 < 10000

420n < 9999

n < 23.8 or n can be 23

Number of values = (0, 23) = 24

The correct answer is option 3 i.e. 221.

Let's assume x is the fourth proportion of 189, 273, and 153.

189 : 273 :: 153 : x

⇒ 189x = 273 × 153

⇒ x = (273 × 153)/189

⇒ x = 221

The correct answer is Option 4 i.e. 0.

For the expression 12 × 3³ × 75 × 54² × 18³ × 64 

12 × 75 will have the unit digit as 0. Thus the expression will also have a unit digit as 0.