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Mathematics - Determinants

Practise 124 NTA Abhyas (JEE Main) questions on Determinants. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Determinants has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 124 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1Let a , λ , μ ∈ R . Consider the system of linear equations a x + 2 y = λ and 3 x - 2 y = μ . Which of the following statement is INCORRECT?
  2. 2Let A be a square matrix of order 3 , A T be the transpose matrix of matrix A and A A T = 4 I . If d = 2 A T + A A T + a d j A 2 , then the
  3. 3If f = cos 2 cos sin - sin cos sin sin 2 cos sin - cos 0 then, f 6 + f 3 + f 2 + f 2 3 + f 5 6 + f + . . + f 53 6 is equal to
  4. 4Let a , x , y , z be real numbers satisfying the equations a x + a y = z x + a y = z x + a y = a z , where x , y , z are not all zero, then
  5. 5Let A = - 1 2 - 3 - 2 0 3 3 - 3 1 be a matrix, then A a d j A - 1 is equal to
  6. 6The number of values of α in - 10 π , 10 π for which the equations sin ⁡ α x - cos ⁡ α y + 3 z = 0 , cos ⁡ α x + sin ⁡ α y - 2 z = 0 and 2 x
  7. 7Let P = 2 5 - 3 2 and Q = 2 l - m 5 n are two matrices, where l , m , n , R , then the value of determinant P Q is equal to
  8. 8If 2 + x x x 2 x 2 + x x 2 x 2 x 2 + x = 1 6 x - a x - b x - c x - d be an identity in x where a , b , c , d are independent of x , then the
  9. 9If a , b , c are non-zero real numbers, the system of equations y + z = a + 2 x , x + z = b + 2 y , x + y = c + 2 z is consistent and b = 4
  10. 10If a , b , c are sides of the triangle A B C and 1 a b 1 c a 1 b c = 0, then the value of cos ⁡ 2 A + cos ⁡ 2 B + cos ⁡ 2 C is equal to
  11. 11Let A = a i j be a 3 × 3 matrix where a i j = i j - j i + 2 i j x i j 1 i j 0 i = j , then the minimum value of A is equal to (where x is a
  12. 12If x 0 , y 0 , z 0 is any solution of the system of equations 2 x - y - z = 1 , - x - y + 2 z = 1 and x - 2 y + z = 2 , then the value of x
  13. 13If A = 1 2 3 4 5 6 and B = 1 4 2 5 3 6 , then the determinant value of B A is
  14. 14Consider three square matrices A , B and C of order 3 such that A T = A - 2 B and B T = B - 4 C , then the incorrect option is
  15. 15If the matrix A = 2 5 1 3 , then the value of A 100 + A 98 A 20 + A 18 is equal to
  16. 16Let A = a b c a ∀ a , b , c , ∈ 0 , 1 , 2 . If A is a singular matrix, then the number of possible matrices A are
  17. 17The value of ∆ = 1 sin ⁡ 3 θ sin 3 ⁡ θ 2 cos ⁡ θ sin ⁡ 6 θ sin 3 ⁡ 2 θ 4 cos 2 ⁡ θ - 1 sin ⁡ 9 θ sin 3 ⁡ 3 θ is equal to
  18. 18The number of triplets a , b , c of positive integers satisfying the equation a 3 + 1 a 2 b a 2 c a b 2 b 3 + 1 b 2 c a c 2 b c 2 c 3 + 1 =
  19. 19Let A = a i j 3 3 be a square matrix such that A A T = 4 I , A 0 . If a 11 + 4 a 12 a 13 a 21 a 22 + 4 a 23 a 31 a 32 a 33 + 4 = 5 A + I . T
  20. 20Let 2 x + a y + 6 z = 8 , x + 2 y + b z = 5 and x + y + 3 z = 4 be three equations. If these 3 equations are consistent, then
  21. 21The number of integral value(s) of k such that the system of equations k x - 2 y - z = x , k y - z = z + 3 x and 2 x + k z = 2 y - z has non
  22. 22If A , B are two non-singular matrices of order 3 and I is an identity matrix of order 3 such that A A T = 5 Ι and 3 A - 1 = 2 A T - A a d j
  23. 23Let A be a matrix of order 3 × 3 such that det( A ) = 2, B = 2 A –1 and C = ( a d j A ) 16 3 , then the value of det( A 3 B 2 C 3 ) is
  24. 24If the system of equations C 3 n x + C 4 n y + 35 z = 0 , C 4 n x + 35 y + C 3 n z = 0 and 35 x + C 3 n y + C 4 n z = 0 has a non-trivial so
  25. 25If one of the roots of the equation 7 6 x 2 - 25 2 x 2 - 25 2 x 2 - 25 3 7 = 0 is x = 3, then the sum of all other five roots is
  26. 26The product of a 9 × 4 matrix and a 4 × 9 matrix contains a variable x in exactly two places. If D x is the determinant of the matrix produc
  27. 27Let A , B and C are n n matrices such that A = 2 , B = 3 and C = 5 . If 2 A 2 3 B 5 C - 1 = 1728 125 , then the value of n is equal to
  28. 28Let a , b and c are the roots of the equation x 3 - 7 x 2 + 9 x - 13 = 0 and A and B are two matrices given by A = a b c b c a c a b and B =
  29. 29The value of the determinant = 13 + 3 2 5 5 15 + 26 5 10 3 + 65 15 5 is equal to
  30. 30The system of equations x - 1 + y + z = - 1 , x + y - 1 + z = - 1 and x + y + z - 1 = - 1 has no solution, if is equal to
  31. 31If x + y y + z z + x y + z z + x x + y z + x x + y y + z = k x z y y x z z y x , then k is equal to
  32. 32If a 1 b 1 c 1 a 2 b 2 c 2 a 3 b 3 c 3 = 5 , then the value of b 2 c 3 - b 3 c 2 a 3 c 2 - a 2 c 3 a 2 b 3 - a 3 b 2 b 3 c 1 - b 1 c 3 a 1 c
  33. 33Let A = a i j be a square matrix of order 3 and B = b i j be a matrix such that b i j = 2 i - j a i j for 1 ≤ i , j ≤ 3 , ∀ i , j ∈ N . If t
  34. 34If the matrix A = 0 2 R , 0 and 2 A 2 - 2 A = 144 , then the value of A + t r A is equal to (where t r A represent the trace of the matrix A
  35. 35Let matrix A = x y - z 1 2 3 1 1 2 , where x , y , z ∈ N . If adj adj adj adjA = 4 8 · 5 16 , then the number of such matrices A is equal to
  36. 36The number of positive integral solutions of the equation x 3 + 1 x 2 y x 2 z x y 2 y 3 + 1 y 2 z x z 2 y z 2 z 3 + 1 = 11 is/are
  37. 37If 2 a 1 , 2 a 2 , 2 a 3 . . . . . 2 a r are in geometric progression, then a 1 a 2 a 3 a n + 1 a n + 2 a n + 3 a 2 n + 1 a 2 n + 2 a 2 n +
  38. 38Consider the system of equations x + y + z = p , x + y + z = q and x + y + z = r , then the sum of all possible distinct value(s) of for whi
  39. 39Let a , b and c satisfy the system of equations a + 2 b + 3 c = 6 , 4 a + 5 b + 6 c = 12 and 6 a + 9 b = 4 . If the roots of the equation a
  40. 40The number of values of x in - 4 , - 1 , for which the matrix 3 - 1 + x 2 3 - 1 x + 2 x + 3 - 1 2 is singular, is
  41. 41The value of for which the system of equations sin 3 x - 2 y + 3 z = 0, ( cos 2 x + 8 y - 7 z = 0 and 2 x + 14 y - 11 z = 0 has a non-trivia
  42. 42If 2 n 2 n + 2 2 n + 4 2 n 2 n + 2 2 n + 4 2 n 2 n + 2 2 n + 4 = 1 2 - 1 2 1 2 - 1 2 1 2 - 1 2 {where 2 , 2 and 2 are all distinct}, then th
  43. 43Let A = a 0 3 0 b 5 - 1 3 0 c , where a , b , c are positive integers. If t r A = 7 , then the greatest value of A is (where t r A denotes t
  44. 44Let A = x 2 - 3 - 1 3 - 2 2 - 1 1 be a matrix and a d j a d j A = 12 4 , then the sum of all the values of x is equal to
  45. 45Let A = cos 0 sin 0 1 0 sin 0 cos and A x y z = 0 1 0 . If the system of equations has infinite solutions and sum of all the possible value
  46. 46The system of equations x + p y = 0 , y + p z = 0 and z + p x = 0 has infinitely many solutions for
  47. 47If x , y and z are the roots of the equation 2 t 3 - tan ⁡ x + y + z π t 2 - 111 t + 2020 = 0 , then x y z y z x z x y is equal to (where, x
  48. 48If A = 1 1 2 1 3 4 1 - 1 3 , B = a d j A and C = 3 A , then a d j B C is equal to
  49. 49If A = 2 3 - 1 - 2 and B = r = 1 10 A r , then the value of det B is equal to
  50. 50If A = 1 - 2 1 2 - 2 1 3 - 3 be the adjoint matrix of matrix B such that B = 9 , then the value of is equal to

Frequently Asked Questions

1.How many questions are available for Determinants?

This chapter includes 124 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

These are NTA Abhyas (JEE Main) questions specifically for the Determinants chapter. Questions from other exams like JEE Main or JEE Advanced are organised separately under their respective exam sections.

3.What is the difficulty level of Determinants questions in NTA Abhyas (JEE Main)?

Of the 124 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

4.Which topics in Determinants should I focus on?

All of this chapter's questions come from a single topic: Uncategorized.