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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 August 2021, Shift 1, Maths Q64

Question 64 of 90 in this shift, Maths question 4 of 30, Section A.

Let θ∈(0,π2)\theta \in \left(0, \frac{\pi}{2}\right). If the system of linear equations. (1+cos⁡2θ) x+sin⁡2θ y+4sin⁡3θ z=0(1+\cos^2\theta)\,x + \sin^2\theta\,y + 4\sin 3\theta\,z = 0 cos⁡2θ x+(1+sin⁡2θ) y+4sin⁡3θ z=0\cos^2\theta\,x + (1+\sin^2\theta)\,y + 4\sin 3\theta\,z = 0 cos⁡2θ x+sin⁡2θ y+(1+4sin⁡3θ)z=0\cos^2\theta\,x + \sin^2\theta\,y + (1+4\sin 3\theta)z = 0 has a non-trivial solution, then the value of θ\theta is :
  1. (1)π18\frac{\pi}{18}
  2. (2)7π18\frac{7\pi}{18}Official answer
  3. (3)5π18\frac{5\pi}{18}
  4. (4)4π9\frac{4\pi}{9}

Official answer

Option 2

NTA final key.

Chapter
Determinants
Topic
Cramer's Rule
Idea tested
Parameter Evaluation in Homogeneous Systems

Same idea in other shifts

Asked 9× in all
  1. 5 Apr 2026, Shift 1 · Q4Consider the system of linear equations in x,y,zx, y, z: x+2y+tz=0x + 2y + tz = 0, 6x+y+5tz=06x + y + 5tz = 0, 3x+t2y+f(t) z=03x + t^2y + f(t)\,z = 0, where…MediumSingle correct
  2. 4 Apr 2024, Shift 1 · Q4If the system of equations x+(2sin⁡α)y+(2cos⁡α)z=0x+(\sqrt{2}\sin\alpha)y+(\sqrt{2}\cos\alpha)z=0 x+(cos⁡α)y+(sin⁡α)z=0x+(\cos\alpha)y+(\sin\alpha)z=0…MediumSingle correct
  3. 6 Apr 2024, Shift 1 · Q22Let αβγ=45\alpha\beta\gamma=45; α,β,γ∈R\alpha, \beta, \gamma \in \mathbb{R}. If x(α,1,2)+y(1,β,2)+z(2,3,γ)=(0,0,0)x(\alpha,1,2)+y(1,\beta,2)+z(2,3,\gamma)=(0,0,0) for some…MediumNumerical value
  4. 8 Apr 2023, Shift 2 · Q3Let S be the set of all values of θ∈[−π,π]\theta \in [-\pi, \pi] for which the system of linear equations x+y+3z=0x + y + \sqrt{3}z = 0…MediumSingle correct
  5. 3 Aug 2021, Shift 2 · Q65For the system of linear equations (k−3)x+y+z=0(k-3)x + y + z = 0 x+(k−3)y+z=0x + (k-3)y + z = 0 x+y+(k−3)z=0x + y + (k-3)z = 0 the number of distinct values of kk,…MediumSingle correct
  6. 18 Mar 2021, Shift 1 · Q64Let α,β,γ\alpha,\beta,\gamma be the real roots of the equation, x3+ax2+bx+c=0x^3+ax^2+bx+c=0, (a,b,c∈Ra,b,c\in\mathbf{R} and a,b≠0a,b\ne0). If the system of…HardSingle correct
  7. 18 Mar 2021, Shift 2 · Q75Let the system of linear equations 4x+λy+2z=04x+\lambda y+2z=0 2x−y+z=02x-y+z=0 μx+2y+3z=0\mu x+2y+3z=0, λ,μ∈R\lambda, \mu\in\mathbb{R}. has a non-trivial…EasySingle correct
  8. 6 Sep 2020, Shift 2 · Q71The sum of distinct values of λ\lambda for which the system of equations (λ−1)x+(3λ+1)y+2λz=0(\lambda-1)x+(3\lambda+1)y+2\lambda z=0…MediumNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.