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Day 628: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 11 Apr 2023

    177
    Let the tangent to the parabola y2=12xy^{2}=12x at the point (3,α)(3,\alpha) be perpendicular to the line 2x+2y=32x+2y=3. Then the square of distance of the point (6,−4)(6,-4) from the normal to the hyperbola α2x2−9y2=9α2\alpha^{2}x^{2}-9y^{2}=9\alpha^{2} at its point (α−1,α+2)(\alpha-1,\alpha+2) is equal to

  2. Question 2

    Definite Integration. Asked once: 29 Jun 2022

    77
    ∫05cos⁡(π(x−[x2]))dx\int_{0}^{5} \cos\left( \pi\left( x -\left\lbrack \frac{x}{2} \right\rbrack \right) \right)dx, Where [t] denotes greatest integer less than or equal to tt, is equal to:

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  3. Question 3

    Sequences and Series. Asked once: 2021 Paper 22

    85
    The mean of 10 numbers 7×8,10×10,13×12,16×14,…7 \times 8,10 \times 10,13 \times 12,16 \times 14,\ldots. Is

  4. Question 4

    Conic Sections. Asked once: 11 Apr 2023

    88
    Let Hn=x21+n−y23+n=1,n∈NH_{n}=\frac{x^{2}}{1 + n}-\frac{y^{2}}{3 + n}= 1,n \in N. Let kk be the smallest even value of nn such that the eccentricity of HkH_{k} is a rational number. If ll is length of the latus return of HkH_{k}, then 21l21l is equal to

  5. Question 5

    Definite Integration. Asked once: 28 Jun 2022

    157
    Let f:R→Rf:R \rightarrow R be a differentiable function such that f(π4)=2,f(π2)=0f\left( \frac{\pi}{4} \right)=\sqrt{2},f\left( \frac{\pi}{2} \right)= 0 and f′(π2)=1f^{'}\left( \frac{\pi}{2} \right)= 1 and let g(x)=∫xπ/4(f′(t)sect+tan⁡tsectf(t))dtg(x) =\int_{x}^{\pi/4} \left( f^{'}(t)sect + \tan tsectf(t) \right)dt for x∈[π4,π2)x \in\left\lbrack \frac{\pi}{4},\frac{\pi}{2} \right). Then lim⁡x→(π2)−g(x)\lim_{x \rightarrow\left( \frac{\pi}{2} \right)^{-}} g(x) is equal to

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