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Given:

Statement I. (3/11) > 0.3

Statement II. (7/8) > 0.86

Calculation:

From statement I we take L.H.S

3/11 = 0. 27

Since, 0.27 < 0.3

⇒ 3/11 < 0.3 

⇒ statement I is incorrect

From statement II we take L.H.S

7/8 = 0.87

Since, 0.87 > 0.86

⇒ 7/8 > 0.86

⇒ statement II is correct

∴ Only II statement is correct (option 3)

Given:

\(X = \dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}:and:Y:=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}\)

Calculation:

We need to find (Y - X)

 ⇒ \((\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20})~-~(\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63})\)

⇒ \((\frac{1}{6}-\frac{1}{3}) + (\frac{1}{20}-\frac{1}{15}) + (\frac{1}{2}+\frac{1}{12})-(\frac{1}{35}+\frac{1}{63}) \)

⇒ \(-\frac{1}{6}-\frac{1}{60}+\frac{7}{12}-\frac{2}{45}\)

⇒ \(-\frac{11}{60}+\frac{7}{12}-\frac{2}{45}\)

⇒ \(\frac{6}{15}-\frac{2}{45}\)

⇒ \(\frac{16}{45}\)

∴ The value of (Y - X) is 16/45.

Given:

The number is J 

First increased by 40% and then decreased by 30% 

Formula used:

Net change = [a + b + (ab/100)]%

Where a and b are the rate of change 

Calculation:

According to the question,

a = 40% and b = -30%

⇒ Net change = [40% - 30% - {(40 × 30)/100]

⇒ Net change = -2% 

⇒ Finally the value of J decreased by 2%

⇒ Final value of J = (100 - 2)% of J

⇒ Final value of J = 98% of J

∴ The final value of J is 98% of initial value of J

Given:

(4.7 + 2.1)2 - (4.7 - 2.1)2

Formula Used:

(a + b)² - (a - b)² = 4ab

Calculation:

Let a = 4.7

& b = 2.1

Now, we know,

(a + b)2 - (a - b)2 = 4ab

⇒ (4.7 + 2.1)2 - (4.7 - 2.1)² = 4 × 4.7 × 2.1 

⇒ 4 × 9.87

⇒ 39.48

∴ The value of (4.7 + 2.1)2 - (4.7 - 2.1)2 is 39.48.

Given:

B1 = 75% of B2

Calculation:

According to the question,

B1 = 75% of B2

⇒ B1 = (75/100) × B2

⇒ B2 = (100/75) × B1

⇒ B2 = (4/3) × B1 

⇒ B2 = 1.3333 × B1

⇒ B2 = (133.33/100) × B1

⇒ B2 = 133.33% of B1

∴ B2 is 133.33% percent of B1.

Given:

Numbers are 32, 33, 34, ................,333

Concept used:

When a and b are factors of a number then the LCM of a and b will also be a factor of that number.

Formula used:

Number of terms = [(b - a)/d] + 1

Where, b = Last Term, a = First Term, d = Common Difference

Calculation:

LCM of 3 and 4 = 12

Factors of 12 from 32 to 333 = 36, 48, 60,................,324.

Total number of factors of 12 = [(324 - 36)/12] + 1

⇒ Total number of factors of 12 = (288/12) + 1

⇒ Total number of factors of 12 = 25

Now,

LCM of 12 and 5 = 60

Factors of 60 from 32 to 333 = 60, 120, 180, 240, 300

⇒ Factors of 60 from 32 to 333 = 5

Required number of factors = 25 - 5

⇒ Required number of factors = 20

∴ Total numbers from 32 to 333 which are divisible by 3 and 4 but not by 5 are 20.

Given:

\(\dfrac{(5.17-2.19)^2-(5.17+2.19)^2}{11.3223}\)

Formula used:

(a - b)² - (a + b)² = -4ab

Calculation:

\(\dfrac{(5.17-2.19)^2-(5.17+2.19)^2}{11.3223}\)

⇒ [(-4) × 5.17 × 2.19]/11.3233

⇒ (-4 × 11.3233)/(11.3233)

⇒ -4

∴ The value of \(\dfrac{(5.17-2.19)^2-(5.17+2.19)^2}{11.3223}\) is -4.

Given:

\(\dfrac{\sqrt81+\sqrt[3]{0.027}+\sqrt[4]{0.0081}}{\sqrt9+\sqrt[3]{0.729}+\sqrt[4]{0.6561}}\)

Calculation:

\(\dfrac{\sqrt81+\sqrt[3]{0.027}+\sqrt[4]{0.0081}}{\sqrt9+\sqrt[3]{0.729}+\sqrt[4]{0.6561}}\)

⇒ \(\dfrac{9+{0.3}+{0.3}}{3+{0.9}+{0.9}}\)

⇒ \(\dfrac{9.6}{4.8}\)

⇒ 2

∴ The value of \(\dfrac{9+{0.3}+{0.3}}{3+{0.9}+{0.9}}\) is 2.

Given:

A = (3.1)2 - (2.2)2 

B = (2.2)2 - (3.1)2

Calculation:

A - B = [(3.1)2 - (2.2)2] - [(2.2)2 - (3.1)²]

⇒ (3.1)2 - (2.2)2 - (2.2)2 + (3.1)2

⇒ 2 × (3.1)2 - 2 × (2.2)2 

⇒ 2 × [(3.1)2 - (2.2)2]

⇒ 2 × [9.61 - 4.84]

⇒ 2 × 4.77

⇒ 9.54

∴ The value of A - B is 9.54.

Given:

M1 = M2 + 30% of M2

M2 = M3 + 50% of M3

M3 = M3 - 40% of M₄ 

Concept used:

30% = 3/10

50% = 1/2

40% = 2/5

Calculation:

Let M₁ be x% of M₄.

M1 = M2 + (3/10) of M₂

⇒ M1 = (13/10)M2

⇒ M1/M2 = 13/10

M2 = M3 + (1/2) of M₃

⇒ M2 = (3/2)M3 

⇒ M2/M3 = 3/2

M3 = M4 - (2/5) of M4 

⇒ M3 = (3/5)M4 

⇒ M3/M4 = 3/5

Step 1:

Step 2:

M1 : M2 : M3 : M4 = (13 × 3 × 3) : (10 × 3 × 3) : (10 × 2 × 3) : (10 × 2 × 5)

⇒ 117 : 90 : 60 : 100

Required percentage = (M₁/M₄) × 100%

⇒ (117/100) × 100%

⇒ 117%

∴ M1 is 117% percentage of M4.