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Day 614: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 29 Jan 2023

    68
    Let [x]\lbrack x\rbrack denote the greatest integer ≤x\leq x. Consider the function f(x)=max{x2,1+[x]}f(x) = max\left\{ x^{2},1 + \lbrack x\rbrack \right\}. Then the value of the integral ∫02f(x)dx\int_{0}^{2} f(x)dx is

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  2. Question 2

    Matrices. Asked once: 2021 Paper 1

    81
    Let P=[3−1−220α3−50]P=\begin{bmatrix} 3 & - 1 & - 2 \\ 2 & 0 & \alpha \\ 3 & - 5 & 0 \end{bmatrix}, where α∈R\alpha\in R. Suppose Q=[qij]Q=\left\lbrack q_{ij} \right\rbrack is a matrix satisfying PQ=kI3PQ=kI_{3} for some non-zero k∈Rk\in R. If q23=−k8q_{23}= -\frac{k}{8} and ∣Q∣=k22|Q| =\frac{k^{2}}{2}, then α2+k2\alpha^{2}+k^{2} is equal to

  3. Question 3

    Sequences and Series. Asked once: 24 Jan 2023

    88
    The 4th 4^{\text{th~}} term of GP is 500 and its common ratio is 1m,m∈\frac{1}{m},m \in N. Let SnS_{n} denote the sum of the first n terms of this GP. If S6>S5+1S_{6}>S_{5}+ 1 and S7<S6+12S_{7}<S_{6}+\frac{1}{2}, then the number of possible values of mm is

  4. Question 4

    Straight Lines. Asked once: 2021 Paper 6

    74
    Let A(−1,1),B(3,4)A( - 1,1),B(3,4) and C(2,0)C(2,0) be given three points. A line y=mx,m>0y = mx,m > 0, intersects lines ACAC and BCBC at point PP and QQ respectively. Let A1A_{1} and A2A_{2} be the areas of △ABC\bigtriangleup ABC and △PQC\bigtriangleup PQC respectively, such that A1=3A2A_{1}= 3A_{2}, then the value of mm is equal to:

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  5. Question 5

    Application of Derivatives. Asked once: 2021 Paper 7

    81
    The maximum value of zz in the following equation z=6xy+y2z= 6xy+y^{2}, where 3x+4y≤1003x+ 4y\leq 100 and 4x+3y≤754x+ 3y\leq 75 for x≥0x\geq 0 and y≥0y\geq 0 is