Explanation

To evaluate the expression 2^2n + 1, we need to follow the order of operations (PEMDAS):

Calculate the exponent: 2^2n = 2^(2*3) = 2^6

Calculate the value of 2^6: 2^6 = 64

Add 1 to the result: 64 + 1 = 65

Therefore, the correct answer is: 65

Explanation

Given expression = (3a + 2b) / (3a - 2b)

= [3(a/b) + 2] / [3(a/b) - 2]

= [3 x 1/3 + 2] / [3 x 1/3 - 2]

= 3 / -1

=-3

Explanation

⇒  Let total examines is x.

⇒  65% of total examines has passed. 

⇒  student failed =100%−65%=35%

Then, 35% of examines have failed.

⇒  Number of failures is 420

∴  35% of x=420

∴   35x/100 = 420

 x=(420 * 100)/35

∴  x=1200

Thus, Total number of examines are 1200.

Explanation

Given:

(x1 + x2 + x3 + x4) / 4 = 16

Multiply both sides by 4:

x1 + x2 + x3 + x4 = 64 ... (Equation 1)

Also, (x2 + x3 + x4) / 2 = 23

Multiply both sides by 2:

x2 + x3 + x4 = 46 ... (Equation 2)

Now, substitute Equation 2 into Equation 1: x1 + 46 = 64

Subtract 46 from both sides: x1 = 18

Therefore, the correct answer is: 18

Explanation

Given:

a^2 + b^2 = 8 ... (Equation 1)

(a - b)^2 = 4

Expanding the left side of the equation: a^2 - 2ab + b^2 = 4

Now, substitute Equation 1 into this equation: 8 - 2ab = 4

Subtract 8 from both sides: -2ab = -4

Divide both sides by -2: ab = 2

So, the value of ab is 2.

Explanation

Let N of 1/12 = 3/48.

Then, N = 3/48 x 12 = 3/4

Explanation

Savings % = (100 – 65) % = 35 %

Saving = 35 % of Rs. 720

= Rs(35/100 ×720) = Rs. 252

Explanation

Total marks of 28 students in Mathematics = 28 x 50 = 1400

New number of students = 28 - 8 = 20

New average of marks in Mathematics = 50 + 5 = 55

∴

Total marks of 20 students in Mathematics = 20 x 55 = 1100

∴

Total marks of 8 students who left the school = 1400 - 1100 = 300

∴

Average marks of these 8 students = 

300/8 = 37.5

Explanation

For one digit number 1 to 9

→1 × 9 = 9

For two digit number 10 to 99

→ 2 × 90 = 180

For three digit number 100 to 300

→3 × 201 = 603

Hence, total number of required digits

= 9 + 180 + 603 = 792

Explanation