The correct answer is option 1 i.e. [(√2 + 3√3)/√6] - 15/4.

sin² 30° + tan 30° - 2sec 45°cosec 45° + 3 sin π/4

= (1/2)² + 1/√3 - 2 × √2 × √2 + 3 × 1/√2

= 1/4 + 1/√3 - 4 + 3/√2

= [(√2 + 3√3)/√6] - 15/4

The correct answer is option 1 i.e. Rs 285000.

Selling chain - Aryan - Bikram - Chandu - Dev.

because we are supposed to find out the cost price for Bikram and have been given the cost price of Dev, we can assume this cycle starts from Bikram only.

Let the cost price for Bikram = x

Selling price for Bikram = Cost price for Chandu = (100 - 9) % of x = 91% of x

Selling price for Chandu = Cost price for Dev = (100 + 8)% of 91% of x = Rs 280098

(100 + 8)% of 91% of x = Rs 280098

⇒ (108/100) × (91/100)x = 280098

⇒ x = Rs 285000

Hence,

Cost price of this bike for Bikram = Rs 285000

The correct answer is Option 1 i.e. 11.11%.

Let Cost price = 100

Marked price = 100 + 20% of 100 = 120

Discount per cent = 25%

Selling price = (100 - 25) % of 120 = 90

Selling price for no profit, no loss = 100

Increase required = 100 - 90 = 10

Hence,

Percentage increase = (10/90) × 100 = 11.11%

The correct answer is option 2 i.e. Rs. 12000.

20% = 1/5

25% = 1/4

Let monthly salary be S 

S × (1 - 1/5) × (1 - 1/4) = 7200

⇒ S × 4/5 × 3/4 = 7200 

⇒ S = 12000

∴ The monthly salary of man = Rs. 12000

The correct answer is option 1 i.e. 422.

56 + 12% of 1750 + [(520 ÷ 5 ÷ 2) of 3]

⇒ 56 + 210 + [(104 ÷ 2) of 3]

⇒ 266 + 156 = 422

The correct answer is option 3 i.e. 25 cm.

The highest possible value is obtained after taking the H.C.F of given lengths

H.C.F of 75, 225, 125 is equal to 25

So, The greatest possible value is 25 cm.

The correct answer is option 2 i.e. 80%.

Quantity of wheat produced by Q = 160 kg

Quantity of rice produced by P = 200 kg

Required percentage = (160 × 100)/200 = 80%

The correct answer is Option 3 i.e. 75.

Let the original speed and time of travel be ‘x’ and ‘y’

Original distance planned = xy [∵ Distance = Speed × Time]

Increased speed = (100 + 25)/100 × x = 1.25x

Increased time of travel = (100 + 40)/100 × x = 1.4y

Increased distance = 1.25x × 1.4y = 1.75xy

Hence,

% increase in distance covered = (1.75xy – xy)/xy × 100 = 75%

The correct answer is option 2 i.e. 13/6 < 11/5 < 7/2 < 17/3.

7/2 = 3.5

13/6 = 2.17

11/5 = 2.2

17/3 = 5.67

So, ascending order of fractions = 13/6 < 11/5 < 7/2 < 17/3

The correct answer is option 2 i.e. 52 : 43.

Amount chemical A in the first solution = 4/(4 + 3) × 385 = 220 ml

Amount of chemical B in the first solution = (385 – 220) = 165 ml

Amount of chemical A in the second solution = 7/(7 + 6) × 1040 = 560 ml

Amount of chemical B in the second solution = (1040 – 560) = 480 ml

Amount of chemical A obtained by mixing both the solutions = (220 + 560) = 780 ml

Amount of chemical B obtained by mixing both the solutions = (165 + 480) = 645 ml

Required ratio = 780 : 645 = 156 : 129 = 52 : 43