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Day 517: JEE Mains Maths

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

  1. Question 1

    Trigonometric Identities. Asked once: 27 Jun 2022

    78
    The value of cos⁡(2π7)+cos⁡(4π7)+cos⁡(6π7)\cos\left( \frac{2\pi}{7} \right)+ \cos\left( \frac{4\pi}{7} \right)+ \cos\left( \frac{6\pi}{7} \right) is equal to :

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  2. Question 2

    Vector Algebra. Asked once: 13 Apr 2023

    89
    Let a=3i^+j^−k^a = 3\widehat{i}+\widehat{j}-\widehat{k} and c=2i^−3j^+3k^c = 2\widehat{i}- 3\widehat{j}+ 3\widehat{k}. If bb is aa vector such that a→=b→×c→\overrightarrow{a}=\overrightarrow{b}\times\overrightarrow{c} and ∣b→∣2=50|\overrightarrow{b}|^{2}= 50, then ∣72−∣b→+ c→∣2∣|72 - |\overrightarrow{b}+\left. \ \overrightarrow{c} \right|^{2}\mid is equal to

  3. Question 3

    Application of Derivatives. Asked once: 30 Jan 2024

    159
    Let y=f(x)y = f(x) be a thrice differentiable function in (−5,5)( - 5,5). Let the tangents to the curve y=f(x)y = f(x) at (1,f(1))(1,f(1)) and (3,f(3))(3,f(3)) make angles π6\frac{\pi}{6} and π4\frac{\pi}{4}, respectively with positive x-axis. If 27∫13((f′(t))2+1)f′′(t)dt=α+β327\int_{1}^{3} \left( \left( f^{'}(t) \right)^{2}+ 1 \right)f^{''}(t)dt = \alpha + \beta\sqrt{3} where  α, β\ \alpha,\ \beta are integers, then the value of α+β\alpha + \beta equals

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  4. Question 4

    Application of Integrals. Asked once: 9 Apr 2024

    155
    The area (in square units) of the region enclosed by the ellipse x2+3y2=18x^{2}+ 3y^{2}= 18 in the first quadrant below the line y=xy = x is :

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  5. Question 5

    Binomial Theorem. Asked once: 11 Apr 2023

    81
    The mean of the coefficients of x,x2,…….x7x,x^{2},\ldots\ldots.x^{7} in the binomial expansion of (2+x)9(2 + x)^{9} is