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Day 541: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 27 Jul 2022

    83
    Let the line x−37=y−2−1=z−3−4\frac{x - 3}{7}=\frac{y - 2}{- 1}=\frac{z - 3}{- 4} intersect the plane containing the lines x−41=y+1−2=z1\frac{x - 4}{1}=\frac{y + 1}{- 2}=\frac{z}{1} and 4ax−y+5z−7a=0=2x−5y−z−3,a∈R4ax - y + 5z - 7a = 0 = 2x - 5y - z - 3,a \in R at the point P(α,β,γ)P(\alpha,\beta,\gamma). Then the value of α+β+γ\alpha + \beta + \gamma equals

  2. Question 2

    Vector Algebra. Asked once: 1 Feb 2023

    153
    Let a→=5i^−j^−3k^\overrightarrow{a}= 5\widehat{i}-\widehat{j}- 3\widehat{k} and b→=i^+3j^+5k^\overrightarrow{b}=\widehat{i}+ 3\widehat{j}+ 5\widehat{k} be two vectors. Then which one of the following statements is TRUE?

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  3. Question 3

    Application of Derivatives. Asked once: 30 Jan 2023

    160
    If the functions f(x)=x33+2bx+ax22f(x) =\frac{x^{3}}{3}+ 2bx +\frac{ax^{2}}{2} and g(x)=x33+ax+bx2,a≠2bg(x) =\frac{x^{3}}{3}+ ax + bx^{2},a \neq 2b have a common extreme point, then a+2b+7a + 2b + 7 is equal to:

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  4. Question 4

    Application of Integrals. Asked once: 1 Feb 2024

    177
    Three points O(0,0),P(a,a2),Q(−b,b2),a>0, b>0O(0,0),P\left( a,a^{2} \right),Q\left( - b,b^{2} \right),a > 0,\text{ }b > 0, are on the parabola y=x2y=x^{2}. Let S1S_{1} be the area of the region bounded by the line PQPQ and the parabola, and S2S_{2} be the area of the triangle OPQ. If the minimum value of S1 S2\frac{S_{1}}{{\text{ }S}_{2}} is mn,gcd(m,n)=1\frac{m}{n},gcd(m,n) = 1, then m+nm + n is equal to:

  5. Question 5

    Binomial Theorem. Asked once: 28 Jul 2022

    171
    Let the coefficients of the middle terms in the expansion of (16+βx)4,(1−3βx)2\left( \frac{1}{\sqrt{6}}+ \beta x \right)^{4},(1 - 3\beta x)^{2} and (1−β2x)6,β>0\left( 1 -\frac{\beta}{2}x \right)^{6},\beta > 0, respectively form the first three terms of an A.P. If dd is the common difference of this A.P., then 50−2 dβ250 -\frac{2\text{ }d}{\beta^{2}} is equal to