PYQ Vault

Least n for which a trig equation has exactly k solutions in [0, n pi/2]

This type of question, asked 2 times: 27 Jan 2024, 30 Jan 2024. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    27 Jan 2024

    165
    If 2tan⁡2θ−5sec⁡θ=12\tan^{2}\theta - 5\sec\theta = 1 has exactly 7 solutions in the interval [0,nπ2]\left\lbrack 0,\frac{n\pi}{2} \right\rbrack, for the least value of n∈Nn \in N then ∑k=1nk2k\sum_{k = 1}^{n} \frac{k}{2^{k}} is equal to :

    Tap an option to check your answer.

  2. Question 2

    30 Jan 2024

    79
    If 2sin⁡3x+sin⁡2xcos⁡x+4sin⁡x−4=02\sin^{3}x+ \sin2x\cos x+ 4\sin x- 4 = 0 has exactly 3 solutions in the interval [0,nπ2],n∈N\left\lbrack 0,\frac{n\pi}{2} \right\rbrack,n \in N, then the roots of the equation x2+nx+(n−3)=0x^{2}+nx+ (n- 3) = 0 belong to :

    Tap an option to check your answer.