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Determinants

JEE Main 2024 (Online) 30th January Evening ShiftMCQMedium📈 Topic in 59% papers+4−1
Ques. 1JEE Main 2024, 30 January (Evening Shift)

Consider the system of linear equations x+y+z=5, x+2y+ 2 z=9, x+3y+ z= , where , R. Then, which of the following statements is NOT correct?

  1. System is consistent if 1 and =13
  2. System is inconsistent if =1 and 13
  3. System has unique solution if 1 and 13
  4. System has infinite number of solutions if =1 and =13

Answer

(3) System has unique solution if 1 and 13

Solution

= vmatrix1&1&1\\1&2& 2\\1&3& vmatrix=-(2 2- -1)=-( -1)(2 +1)

=0 for =1 or =- 12

R2-R1: y+( 2-1)z=4; R3-R2: y+( - 2)z= -9

∵ for =1, - 12: 2-1= - 2 (same left sides) consistent only if -9=4, i.e. =13

(A): =13 unique ( - 12) or infinite ( =- 12) solutions (A) is correct

(B): =1, 13 y=4 and y= -9 clash (B) is correct

(C): =- 12 ( 1), 13 =0 and no solution (C) is NOT correct

(D): =1, =13 two equations only infinitely many solutions (D) is correct

Answer: (3)

Keep practising — Determinants

Ques. 2JEE Main 2024, 29 January (Morning Shift)

Let A= bmatrix1&0&0\\0& & \\0& & bmatrix and |2A|3=221 where , Z. Then a value of is

  1. 9
  2. 17
  3. 3
  4. 5
Ques. 3JEE Main 2024, 29 January (Evening Shift)

Let A= bmatrix2&1&2\\6&2&11\\3&3&2 bmatrix and P= bmatrix1&2&0\\5&0&2\\7&1&5 bmatrix. The sum of the prime factors of |P-1AP-2I | is equal to

  1. 66
  2. 27
  3. 23
  4. 26
Ques. 4JEE Main 2024, 29 January (Evening Shift)

Let for any three distinct consecutive terms a, b, c of an A.P, the lines ax+by+c=0 be concurrent at the point P and Q( , ) be a point such that the system of equations x+y+z=6, 2x+5y+ z= and x+2y+3z=4, has infinitely many solutions. Then (PQ)2 is equal to .

Ques. 5JEE Main 2024, 27 January (Morning Shift)

Let A= bmatrix2&0&1\\1&1&0\\1&0&1 bmatrix, B= [B1, B2, B3 ], where B1, B2, B3 are column matrices, and AB1= bmatrix1\\0\\0 bmatrix, AB2= bmatrix2\\3\\0 bmatrix, AB3= bmatrix3\\2\\1 bmatrix If =|B| and is the sum of all the diagonal elements of B, then 3+ 3 is equal to .

Ques. 6JEE Main 2024, 27 January (Evening Shift)

The values of , for which vmatrix1 & 32 & + 32\ 1 & 13 & + 13\ 2 +3 & 3 +1 & 0 vmatrix=0, lie in the interval

  1. (-2,1)
  2. (- 32, 32 )
  3. (-3,0)
  4. (0,3)

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