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Day 508: JEE Mains Maths

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

  1. Question 1

    Trigonometric Equations. Asked once: 2021 Paper 18

    61
    The sum of solutions of the equation cos⁡x1+sin⁡x=∣tan⁡2x∣,x∈(−π2,π2)−{π4,−π4}\frac{\cos x}{1 + \sin x}= |\tan2x|,x\in\left( -\frac{\pi}{2},\frac{\pi}{2} \right)-\left\{ \frac{\pi}{4}, -\frac{\pi}{4} \right\} is :

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  2. Question 2

    Trigonometric Identities. Asked once: 6 Apr 2023

    172
    The value of tan⁡9∘−tan⁡27∘−tan⁡63∘+tan⁡81∘\tan9^{\circ}- \tan27^{\circ}- \tan63^{\circ}+ \tan81^{\circ} is

  3. Question 3

    Vector Algebra. Asked once: 27 Jan 2024

    170
    Let the position vectors of the vertices A,BA,B and CC of a triangle be 2i^+2j^+k^, i^+2j^+2k^2\widehat{i}+ 2\widehat{j}+\widehat{k},\ \widehat{i}+ 2\widehat{j}+ 2\widehat{k} and 2i^+j^+2k^2\widehat{i}+\widehat{j}+ 2\widehat{k} respectively. Let l1,l2l_{1},l_{2} and l3l_{3} be the lengths of perpendiculars drawn from the ortho center of the triangle on the sides AB,BCAB,BC and CACA respectively, then l12+l22+l32l_{1}^{2}+l_{2}^{2}+l_{3}^{2} equals :

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  4. Question 4

    Application of Derivatives. Asked once: 4 Apr 2024

    65
    Let the sum of the maximum and the minimum values of the function f(x)=2x2−3x+82x2+3x+8f(x) =\frac{2x^{2}- 3x + 8}{2x^{2}+ 3x + 8} be mn\frac{m}{n}, where gcd(m,n)=1gcd(m,n) = 1. Then m+nm + n is equal to:

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  5. Question 5

    Application of Integrals. Asked once: 22 Jan 2025

    71
    Let the function,
    f(x)={−3ax2−2,x<1a2+bx,x≥1f(x) =\left\{ \begin{matrix} - 3ax^{2}- 2, & x < 1 \\ a^{2}+ bx, & x \geq 1 \end{matrix} \right.
    Be differentiable for all x∈Rx \in R, where a>1, b∈Ra > 1,\text{ }b \in R. If the area of the region enclosed by y=f(x)y = f(x) and the line y=−20y = - 20 is α+β3,α,β,∈Z\alpha + \beta\sqrt{3},\alpha,\beta, \in Z, then the value of α+β\alpha + \beta is ________\_\_\_\_\_\_\_\_ .