Even numbers between 9 to 77 = 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76

Average of consecutive even numbers = ((First number + Last number))/2

So, average = (10+76)/2 = 43

The number 7710312401 is completely divisible by 11.

Formula:

M₁D₁H₁/W₁ = M₂D₂H₂/W₂

Let first work be a, then second work is 3a.

16 x 8 x 12 / a = M₂ x 24 x 8 /3x

Or, M₂ = 24

Let the numbers of terms be ‘n’

First term = a = 20

Common difference = d = 19 1/3 - 20 = - 2/3

Sum of ‘n’ terms of an A.P is:

S_n = n/2 {2a + (n – 1)d}

After substituting the values, we get the equation: n² - 61n + 900 = 0

So, the value of n is 25 or 36.

Full marks = 300

The break-up of the marks into theory (X), practical (Y) and (Z) project, which are the three components of evaluation is 6 : 5 : 4.

So, 300 ÷ (6 + 5 + 4) = 20

Break-up of marks in:

Theory (X) = 6 x 20 = 120   Pass Marks = 40% of 120 = 48

Practical (Y) = 5 x 2 = 100    Pass Marks = 50% of 100 = 50

Project (Z) = 4 x 20 = 80      Pass Marks = 50% of 80 = 40

Aggregate % in overall = 60% of 300 = 180

Marks:

A – 180

B – 130 (Fail in aggregate)

C – 210

D – 180 (Fail in Practical)

Only A and C passed in the exam.

The total production of type B cars in 2012, 2014 and 2015 = 42 + 40 + 38 = 120

The total production of type A cars in 2013 and 2016 = 35 + 56 = 91

Difference = (120 – 91) = 29

% = (29 / 91) x 100 = 31.86

Let the number of boys be ‘b’ and number of girls be ‘g’

So, according to question:

14b + 17g = 15(b + g)

→ 17g – 15g = 15b – 14b

→ 2g = b

→ g / b = ½

→ g : b = 1 : 2

x = -2

f(x) = -2³ + 13(-2)² + a(-2) + 20 = 0

-8 + 52 - 2a + 20 = 0

-2a = -64

a = 32

8028 = P (1 + r/100)³ ________ (i)

12042 = P (1 + r/100)⁶ ________ (ii)

Dividing (ii) from (i), we get:

1.5 = (1 + r/100)³

If we put the above value in (i), we get:

8028 = 1.5 × P

Or, P = Rs. 5,352

First term = a = 5

Common ration = r = 10 ÷ 5 = 2

The 8^th term can be find by the formula:

T_n = ar^n-1

T₈ = 5 × (2)⁷ = 5 × 128 = 640