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Day 269: JEE Mains Maths

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

  1. Question 1

    Trigonometric Equations. Asked once: 2021 Paper 23 (same type asked 4 times) See all 4 of this type

    77
    The number of solutions of the equation 32tan⁡2x+32sec⁡2x=81,0≤x≤π432^{\tan^{2}x}+32^{\sec^{2}x}= 81,0 \leq x\leq\frac{\pi}{4} is:

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  2. Question 2

    Conic Sections. Asked once: 2021 Paper 23 (same type asked 4 times) See all 4 of this type

    71
    The angle of intersection of the curves x2a2+y2b2=1\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 and x2+y2=ab, a>b,x^{2}+y^{2}=ab,\ a>b, is:

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  3. Question 3

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

    152
    If the four points, whose position vectors are 3i^−4j^+2k^,i^+2j^−k^,−2i^−j^+3k^3\widehat{i}- 4\widehat{j}+ 2\widehat{k},\widehat{i}+ 2\widehat{j}-\widehat{k}, - 2\widehat{i}-\widehat{j}+ 3\widehat{k} and 5i^−2αj^+4k^5\widehat{i}- 2\alpha\widehat{j}+ 4\widehat{k} are coplanar, then α\alpha is equal to

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  4. Question 4

    Application of Derivatives. Asked once: 2021 Paper 20 (same type asked 4 times) See all 4 of this type

    80
    A wire of length 20 m20\text{ }m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a regular hexagon. Then the length of the side (in meters) of the hexagon, so that the combined area of the square and the hexagon is minimum, is:

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  5. Question 5

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

    71
    The area, enclosed by the curves y=sin⁡x+cos⁡xy= \sin x+ \cos x and y=∣cos⁡x−sin⁡x∣y= |\cos x- \sin x| and the lines x=0,x=π2x= 0,x=\frac{\pi}{2}, is:

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