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Day 55: JEE Mains Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Trigonometric Equations. This type asked 3 times: 29 Jan 2024, 5 Apr 2024, 6 Apr 2026 S1. This one: 6 Apr 2026 S1 See all 3 of this type

    64
    Let S={θ∈(−2π,2π):cos⁡θ+1=3sin⁡θ}S = \{\theta\in ( - 2\pi,2\pi):\cos\theta+ 1 =\sqrt{3}\sin\theta\}. Then ∑θ∈Sθ\sum_{\theta\in S} \theta is equal to:

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  2. Question 2

    Complex Numbers. This type asked 3 times: 28 Jan 2025, 3 Apr 2025, 5 Apr 2026 S2. This one: 5 Apr 2026 S2 See all 3 of this type

    52
    Let z1,z2∈Cz_{1},z_{2}\in C be the distinct solutions of the equation z2+4z−(1+12i)=0z^{2}+ 4z- (1 + 12i) = 0. Then ∣z1∣2+∣z2∣2\left| z_{1} \right|^{2}+\left| z_{2} \right|^{2} is equal to :

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  3. Question 3

    Determinants. This type asked 3 times: 12 Apr 2023, 6 Apr 2024, 5 Apr 2026 S2. This one: 5 Apr 2026 S2 See all 3 of this type

    53
    If f:N→Zf:N \rightarrow Z is defined by f(n)=∣n−1−5−2n23(2k+1)2k+1−3n33k(2k+1)3k(k+2)+1∣,k∈Nf(n) =\left| \begin{matrix} n & - 1 & - 5 \\ - 2n^{2} & 3(2k+ 1) & 2k+ 1 \\ - 3n^{3} & 3k(2k+ 1) & 3k(k+ 2) + 1 \end{matrix} \right|,k\in N, and ∑n=1kf(n)=98\sum_{n= 1}^{k} f(n) = 98, then kk is equal to:

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  4. Question 4

    Differential Equations. This type asked 3 times: 2021 Paper 11, 29 Jan 2024, 5 Apr 2026 S1. This one: 5 Apr 2026 S1 See all 3 of this type

    75
    Let y=y(x)y = y(x) be the solution of the differential equation x sin⁡(yx)dy=(ysin⁡(yx)−x)dx,y(1)=π2x\ \sin\left( \frac{y}{x} \right)dy = \left( y\sin\left( \frac{y}{x} \right) - x \right)dx,y(1) = \frac{\pi}{2} and let α=cos⁡(y(e12)e12)\alpha = \cos\left( \frac{y\left( e^{12} \right)}{e^{12}} \right). Then the number of integral value of pp, for which the equation x2+y2−2px+2py+α+2=0x^{2} + y^{2} - 2px + 2py + \alpha + 2 = 0 represents a circle of radius r≤6r \leq 6, is ____\_\_\_\_ .

  5. Question 5

    Limits and Continuity. This type asked 3 times: 8 Apr 2024, 28 Jan 2026 S1, 5 Apr 2026 S1. This one: 5 Apr 2026 S1 See all 3 of this type

    67
    The product of all possible values of α\alpha, for which lim⁡x→0(1−cos⁡(αx)cos⁡((α+1)x)cos⁡((α+2)x)sin⁡2((α+1)x))=2\lim_{x\rightarrow 0} \left( \frac{1 - \cos(\alpha x)\cos((\alpha+ 1)x)\cos((\alpha+ 2)x)}{\sin^{2}((\alpha+ 1)x)} \right)= 2, is :

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