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Day 532: JEE Mains Maths

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

  1. Question 1

    Matrices. Asked once: 27 Jan 2024

    173
    Let A be a 2×22 \times 2 real matrix and I be the identity matrix of order 2 . If the roots of the equation ∣A−xI∣=0|A-xI| = 0 be -1 and 3 , then the sum of the diagonal elements of the matrix A2A^{2} is.........

  2. Question 2

    Permutations and Combinations. Asked once: 10 Apr 2023

    85
    The number of permutations, of the digits 1,2,31,2,3, ..... 7 without repetition, which neither contain the string 153 nor the string 2467, is

  3. Question 3

    Probability. Asked once: 30 Jan 2023

    63
    If an unbiased die, marked with −2,−1,0,1,2,3- 2, - 1,0,1,2,3 on its faces, is thrown five times, then the probability that the product of the outcomes is positive, is :

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  4. Question 4

    Quadratic Equations. Asked once: 10 Apr 2023

    86
    Let a,b,ca,b,c be three distinct positive real numbers such that (2a)log⁡ea=(bc)log⁡eb(2a)^{\log_{e}a}= (bc)^{\log_{e}b} and blog⁡e2=alog⁡ecb^{\log_{e}2}=a^{\log_{e}c}. Then 6a+5bc6a + 5bc is equal to

  5. Question 5

    Relations and Functions. Asked once: 12 Apr 2023

    68
    Let DD be the domain of the function f(x)=sin⁡−1f(x) =\sin^{- 1} (log⁡3x(6+2log⁡3x−5x))\left( \log_{3x}\left( \frac{6 + 2\log_{3}x}{- 5x} \right) \right). If the range of the function g:D→Rg:D \rightarrow R defined by g(x)=x−[x],([x]g(x) = x - \lbrack x\rbrack,(\lbrack x\rbrack is the greatest integer function), is (α,β)(\alpha,\beta), then α2+5β\alpha^{2}+\frac{5}{\beta} is equal to

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