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CTET 1 Mar 2026 Paper 1, Question 34

Topic: Numbers

Q34

If 3024=p4×q3×r3024 = p^4 \times q^3 \times r, where p, q and r are prime numbers, then what is the value of (3p−5q+r)(3p - 5q + r) ?

  1. (1) −4-4
  2. (2) −2-2Correct answer
  3. (3) 0
  4. (4) 2

Solution.

CBSE answer: (2)

Answer: (2) −2-2

  1. 3024=2×1512=24×1893024 = 2 \times 1512 = 2^4 \times 189, and 189=33×7189 = 3^3 \times 7.
  2. So 3024=24×33×73024 = 2^4 \times 3^3 \times 7, giving p=2, q=3, r=7p = 2,\ q = 3,\ r = 7.
  3. 3p−5q+r=6−15+7=−23p - 5q + r = 6 - 15 + 7 = -2.

Trap: swapping p and q gives a different value; match each power carefully.