We know that,

Given,

The average marks of 45 students was 70 for a unit test:

Average marks = Total marks of students/Number of students

Total marks of all 45 students = 70 × 45 = 3150

Total marks of all 45 students = 3150

Given,

It was noticed that 20^th roll number student marks which is 45 was wrongly taken as 60:

Total sum of marks of 44 students = Total sum of 45 students - 60

= 3150 - 60 = 3090

∴ Total sum of marks of 44 students is 3090.

New total sum of marks of 45 students = 3090 + 45 = 3135

New total sum of marks of 45 students = 3135

New average = 3135/45 = 69.66

∴ The corrected new average marks is 69.66

Let the number of diamonds, hearts and spades be x,y and z respectively

∴ According to the given conditions,

y = x       ----(1)

x = 3z     ---(2)

Total number of red cards = number of diamonds + number of hearts

∴ 6 = x + y

∴ 6 = x + x      ---- from (1)

∴ x = 3

∴ z = 1      --- from (2)

But number of black cards = number of spades + number of clubs

∴ 7 = 1 + number of clubs

∴ Number of clubs = 6

∴ there are in all 6 club cards.

Sum of the internal angles of a polygon with ‘n’ sides = (n - 2) × 180°

∴ For a hexagon, sum of the internal angles = (6 - 2) × 180° = 720°

Let the measure of each of the other 5 angles of the given hexagon be ‘x’

∴ According to the given conditions,

⇒ 90° + 5x = 720°

∴ x = 126°

∴ The measure of each of the other angles is 126°

Let,

Present ages of husband and wife are x years and y years respectively.

∵ Average of their ages = 39

∴ x + y = 2 × 39

⇒ x + y = 78

⇒ x = 78 – y----- (1)

Six years ago, the ratio between their ages was 6 ∶ 5

(x – 6) / (y – 6) = 6 : 5

⇒ 5x – 30 = 6y – 36

Put the value of x from Equation (1)

⇒ 5(78 – y) – 30 = 6y – 36

⇒ 390 – 5y – 30 = 6y – 36

⇒ 11y = 360 + 36

⇒ y = 36

Putting this value in (1)

x = 78 – 36 = 42

∴ Required difference between their ages = 42 years – 36 years = 6 years

Approximating values and then using BODMAS:

29.88% of 5103 - (17.48)² + (32.52)² = ?

= 0.2988 × 5103 - (17.48)² + (32.52)²

= 0.3 × 5103 - {(17.48)² - (32.52)²}

= 1530.9 - (17.48 - 32.52)(17.48 + 32.52)

= 1531 - (-15.04)(50)

= 1531 + 752

= 2283

72 × 2.48 + 12 + 4.9 × 7.01 + 6.93 = ?

⇒ 72 × 2.5 + 12 + 5 × 7 + 7 = ?

⇒ 180 + 12 + 35 + 7 = ?

∴ ? = 234.

We have each term of this series as follows:

⇒ 3 = 3 × 1²

⇒ 12 = 3 × 2²

⇒ 108 = 12 × 3²

⇒ ? = 108 × 4²

⇒ ? = 108 × 16

⇒ ? = 1728

We observe that

123 + 3 = 126 and 126 – 2 = 124

124 + 3 = 127

128 – 2 = 126 and 126 + 3 = 129

So, the series is a pattern of +3, -2, +3, -2

Hence, the next term in the series is: 127 – 2 = 125

We have,

762 – 656 = 106

656 – 557 = 99

557 – 465 = 92

The difference between successive terms is decreasing by 7. Hence, the second term must be greater than the third term by 106 + 7 = 113.

So, the term is = 762 + 113 = 875