COMEDK 2024 Shift 1 Paper

We know that ‌nCr=‌

n!

r!(n−r)!

. So we can write the given ratio as:
‌

‌n+1Cr+1

‌nCr

:‌

‌nCr

‌n−1Cr−1

=11:6:3

Let's simplify each of the ratios on the left-hand side:
Now we can substitute these simplified expressions back into the original ratio:
‌

n+1

r+1

:‌

n

r

=11:6:3

From the first two terms of this ratio, we get the equation:
‌

n+1

r+1

=‌

11

6

Cross-multiplying gives us:
‌6n+6=11r+11
‌6n−11r=5
From the second and third terms of the original ratio, we get:
‌‌

n

r

=‌

6

3

=2
‌n=2r
Substituting this value of n into the equation 6n−11r=5, we get:
‌6(2r)−11r=5
‌12r−11r=5
‌r=5

Now, substituting r=5 back into n=2r, we get:
n=2(5)=10
Therefore, nr=10×5=50