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Day 173: JEE Mains Maths

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

  1. Question 1

    Relations and Functions. Asked once: 27 Jul 2022 (same type asked 4 times) See all 4 of this type

    62
    Let f,g:N−{1}→N\mathbf{f,g:N - \{ 1\} \rightarrow N} be functions defined by f(a)=αf(a) = \alpha, where α\alpha is the maximum of the powers of those primes pp such that pαp^{\alpha} divides aa, and g(a)=a+1g(a) = a + 1, for all a∈N−{1}\mathbf{a \in N - \{ 1\}}. Then, the function f+gf + g is

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  2. Question 2

    Binomial Theorem. Asked once: 25 Jan 2023 (same type asked 4 times) See all 4 of this type

    81
    The constant term in the expansion of (2x+1x7+3x2)5\left( 2x +\frac{1}{x^{7}}+ 3x^{2} \right)^{5} is

  3. Question 3

    Three Dimensional Geometry. Asked once: 2021 Paper 22 (same type asked 4 times) See all 4 of this type

    83
    The square of the distance of the point of intersection of the line x−12=y−23=z+16\frac{x- 1}{2}=\frac{y- 2}{3}=\frac{z+ 1}{6} and the plane 2x−y+z=62x - y + z = 6 from the point (−1,−1,2)( - 1, - 1,2) is

  4. Question 4

    Trigonometric Equations. Asked once: 26 Jul 2022 (same type asked 4 times) See all 4 of this type

    78
    Let S={θ∈[0,2π]:82sin⁡2θ+82cos⁡2θ=16}S =\left\{ \theta \in \lbrack 0,2\pi\rbrack:8^{2\sin^{2}\theta}+8^{2\cos^{2}\theta}= 16 \right\}. Then n(S)+∑θ∈S(sec(π4+2θ)csc⁡(π4+2θ))n(S) +\sum_{\theta \in S} \left( sec\left( \frac{\pi}{4}+ 2\theta \right)\csc\left( \frac{\pi}{4}+ 2\theta \right) \right) is equal to:

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  5. Question 5

    Conic Sections. Asked once: 2021 Paper 24 (same type asked 4 times) See all 4 of this type

    80
    Let θ\theta be the acute angle between the tangents to the ellipse x29+y21=1\frac{x^{2}}{9}+\frac{y^{2}}{1}= 1 and the circle x2+y2=3x^{2}+y^{2}= 3 at their point of intersection in the first quadrant. Then tan⁡θ\tan\theta is equal to:

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