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Binomial Theorem

JEE Main 2025 (Online) 23rd January Evening ShiftMCQMedium📈 Topic in 8% papers+4−1
Ques. 1JEE Main 2025, 23 January (Evening Shift)

If in the expansion of (1+x)p(1-x)q, the coefficients of x and x2 are 1 and -2, respectively, then p2+q2 is equal to :

  1. 8
  2. 20
  3. 13
  4. 18

Answer

(3) 13

Solution

Coefficient of x: p-q=1. Coefficient of x2: p(p-1)2-pq+ q(q-1)2=-2 (p-q)2-(p+q)=-4

1-(p+q)=-4 p+q=5 p=3, q=2

p2+q2=13

Answer: (3)

Keep practising — Binomial Theorem

Ques. 2JEE Main 2025, 22 January (Morning Shift)

If r=05 11C2r+12r+2= mn, (m,n)=1, then m-n is equal to .

Ques. 3JEE Main 2025, 22 January (Evening Shift)

Let , , and be the coefficients of x7,x5,x3 and x respectively in the expansion of (x+ x3-1 )5+ (x- x3-1 )5, x>1. If u and v satisfy the equations u+ v=18, u+ v=20, then u+v equals :

  1. 4
  2. 3
  3. 5
  4. 8
Ques. 4JEE Main 2025, 22 January (Evening Shift)

If r=130 r2 (30Cr )230Cr-1= 229, then is equal to .

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