• Space complexity is a measure of how efficient your code is in terms of memory used.

n(S) = Total number of ways of drawing 2 cards from 52 cards = 52C2.
Let E = event of getting 1 club and 1 diamond.
We know that there are 13 clubs and 13 diamonds in the total 52 cards.
Hence, n(E) = Number of ways of drawing one club from 13 and one diamond from 13 = ¹³C₁ × ¹³C₁ = 13/102
P(E) = n(E)/n(S)
= (¹³C₁ × ¹³C₁) / ⁵²C₂
= 13/102.

The number of ways = ²⁵c₃
= (25 x 24 x 23) / (1 x 2 x 3)
= 2300

⁵⁶P_{r + 6} = 56! / [56 – (r + 6) ]! = 56! / (50 – r)!
⁵⁴P_{r + 3} = 54! / [54 – (r + 3) ]! = 54! / (51 – r)!
⁵⁶P_{r + 6} / ⁵⁴P_{r + 3} = [ ( 56! / (50 – r)! ) x ( (51 – r)! / 54!) ] ( 56 x 55 x 54! / (50 – r)! ) x ( (51-r).(50-r)! ) / 54 !
= 56 x 55 x (51-r)

⁵⁶P_{r + 6} / ⁵⁴P_{r + 3} = 30800 / 1
=> 56 x 55 x (51-r) = 30800
=> (51-r) = 10
=> r = 41

Required number of lines
= nC2 = 15C2
= 15 x 14 / 2 = 105

Total letters = 7, but N has come twice.
So, the required number of arrangements
= 7! / 2!
= 7 × 6 × 5 × 4 × 3 × 2! / 2!
= 2520

The word ‘INHALE’ has 6 particular letters .
Number of courses of action = n !
= 6 ! = 6 x 5 x 4 x 3 x 2 x 1
= 720

⁵P₂ = 5 ! / (5 – 2) ! = 5 x 4 = 20

Required no. of hand shakes = { 8 x (8 – 1) } / 2 = 28

Total number of person = 8 men + 7 women = 15
No. of groups can be formed of 6 persons = ¹⁵C₆
= 15! /{6! (15 – 6)!}
= 15! /(6! 9!)
= (15 x 14 x 13 x 12 x 11 x 10)/(6 x 5 x 4 x 3 x 2 x 1)
= 5005

0.36 = 36/100 = 9/25.
Sum of the numerator and denominator is 9 + 25 = 34

1 / (60 * 60)
= 1 / 3600
= .0027

If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is [ (R / 100 + R) * 100 ]%
Here R% = 25%
Hence % decrease in the consumption of sugar [ (25 / 100 + 25) * 100 ]%
= [ (25 / 125) * 100 ]%
= [ (1 / 5) * 100 ]%
= 20%

Let the number of men in the village is x.
Number of women in the village is (8000 – x)
If 6% men and 10% women are added population becomes 8600,
x(106 / 100) + (8000 – x) (110 / 100) = 8600
[(110 – 106) / 100] * x = 8800 – 8600
x = 200 * 100 / 4 = 5000
Hence the number of men in the village is 5000.

20% means for every 100 rupees 20 rupees decreases
We have 600 rupees = 6 * 20 = 120
So, 120/5 = 24

Each year decreses by 10% and for continuous 4years
350000 * (90/100) * (90/100) * (90/100) * (90/100)
= 229635

Let the original price be Rs. 100.
New final price = 120 % of (90 % of Rs. 100)
= Rs. (120/100 * 90/100 * 100)
= Rs. 108.
Increase = 8%

It is based on inverse proportion or product constancy concept. Reduction in price 20% amount of salt will increase 25%.
25% is equivalent to 10 kg
So, total salt = 10 * 4 = 40
Original price of the salt is, 100/40 = 2.5 kg

Given :
Cost Price = 13 and Selling Price = 11

According to the formula,
Profit % = ( (C.P – S.P / S.P) * 100 ) %

Profit % = ( (13 – 11 / 11) * 100 ) %
= ( (2 / 11) * 100 ) %
= 18 2/11 %