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Day 469: JEE Mains Maths

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

  1. Question 1

    Relations and Functions. Asked once: 2 Apr 2025

    137
    If the domain of the function f(x)=110+3x−x2+1x+∣x∣f(x) =\frac{1}{\sqrt{10 + 3x -x^{2}}}+\frac{1}{\sqrt{x + |x|}} is (a,b)(a,b), then (1+a)2+b2(1 +a)^{2}+b^{2} is equal to :

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  2. Question 2

    Sequences and Series. Asked once: 2 Apr 2026 S2

    54
    Let a1,a2,a3,……a_{1},a_{2},a_{3},\ldots\ldots be an A.P. and g1=a1, g2, g3,……g_{1}=a_{1},{\text{ }g}_{2},{\text{ }g}_{3},\ldots\ldots be an increasing G.P. If a1=a2+g2=1a_{1}=a_{2}+g_{2}= 1 and a3+g3=4a_{3}+g_{3}= 4, then a10+g5a_{10}+g_{5} is equal to :

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  3. Question 3

    Statistics. Asked once: 28 Jul 2022

    88
    Let x1,x2,x3,……,x20x_{1},x_{2},x_{3},\ldots\ldots,x_{20} be in geometric progression with x1=3x_{1}= 3 and the common ratio 12\frac{1}{2}. A new data is constructed replacing each xix_{i} by (xi−i)2\left( x_{i}- i \right)^{2}. If xˉ\bar{x} is the mean of new data, then the greatest integer less than or equal to xˉ\bar{x} is

  4. Question 4

    Straight Lines. Asked once: 7 Apr 2025

    126
    If the orthocenter of the triangle formed by the lines y=x+1,y=4x−8y = x + 1,y = 4x - 8 and y=mx+cy = mx + c is at (3,−1)(3, - 1), then m−cm-c is :

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  5. Question 5

    Three Dimensional Geometry. Asked once: 23 Jan 2025

    67
    Let the position vectors of the vertices A,BA,B and C of a tetrahedron ABCD be i^+2j^+k^,i^+3j^−2k^\widehat{i}+ 2\widehat{j}+\widehat{k},\widehat{i}+ 3\widehat{j}- 2\widehat{k} and 2i^+j^−k^2\widehat{i}+\widehat{j}-\widehat{k} respectively. The altitude from the vertex DD to the opposite face ABCABC meets the median line segment through AA of the triangle ABCABC at the point EE. If the length of ADAD is 1103\frac{\sqrt{110}}{3} and the volume of the tetrahedron is 80562\frac{\sqrt{805}}{6\sqrt{2}}, then the position vector of EE is

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