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JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Binomial Theorem

If the coefficients of

x

and

x^{2}

in

(1 + x)^{p} (1 - x)^{q}

are 4 and -5 respectively, then

2 p + 3 q

is equal to

(A)63✓ Correct
(B)69
(C)66
(D)60

Answer: (A)

Solution

In

(1 + x)^{p} (1 - x)^{q}

the coefficient of

x

is

p - q = 4

, and that of

x^{2}

is

(2 p) + (2 q) - pq = - 5

, which reduces to

(p - q)^{2} - (p + q) = - 10

. With

(p - q)^{2} = 16

, this gives

p + q = 26

, so

p = 15, q = 11

. Therefore

2 p + 3 q = 30 + 33 = 63

.

JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Single correct option

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