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Day 571: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 1 Feb 2024

    171
    If three successive terms of a G.P. with common ratio r(r>1)r(r> 1) are the lengths of the sides of a triangle and [r]\lbrack r\rbrack denotes the greatest integer less than or equal to rr, then 3[r]+[−r]3\lbrack r\rbrack + \lbrack -r\rbrack is equal to:

  2. Question 2

    Straight Lines. Asked once: 25 Jan 2023

    180
    A triangle is formed by the XX-axis, YY-axis and the line 3x+4y=603x+4y=60. Then the number of points P(a,b)P(a,b) which lie strictly inside the triangle, where aa is an integer and bb is a multiple of aa, is

  3. Question 3

    Three Dimensional Geometry. Asked once: 2021 Paper 9

    86
    The equation of the planes parallel to the plane xx −2y+2z−3=0- 2y+ 2z- 3 = 0 which are at unit distance from the point (1,2,3)(1,2,3) is ax+by+cz+d=0ax+by+cz+d= 0. If (b−d)=K(c−a)(b-d) =K(c-a), then the positive value of KK is

  4. Question 4

    Vector Algebra. Asked once: 27 Jun 2022

    75
    Let a→=i^+j^−k^\overrightarrow{a}=\widehat{i}+\widehat{j}-\widehat{k} and c→=2i^−3j^+2k^\overrightarrow{c}= 2\widehat{i}- 3\widehat{j}+ 2\widehat{k}. Then the number of vectors b→\overrightarrow{b} such that b→×c→=a→\overrightarrow{b}\times\overrightarrow{c}=\overrightarrow{a} and ∣b→∣∈{1,2,……,10}|\overrightarrow{b}\mathbf{| \in \{ 1,2,\ldots\ldots,10\}} is:

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  5. Question 5

    Application of Derivatives. Asked once: 27 Jul 2022

    86
    Let MM and NN be the number of points on the curve y5−9xy+2x=0y^{5}- 9xy + 2x = 0, where the tangents to the curve are parallel to xx-axis and yy-axis, respectively. Then the value of M+NM + N equals