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Day 44: JEE Mains Maths

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

  1. Question 1

    Matrices. This type asked 4 times: 29 Jun 2022, 31 Jan 2023, 29 Jan 2025, 2 Apr 2025. This one: 2 Apr 2025 See all 4 of this type

    55
    Let A=[α−16β],α>0A=\begin{bmatrix} \alpha & - 1 \\ 6 & \beta \end{bmatrix},\alpha> 0, such that det(A)=0det(A) = 0 and α+β=1\alpha+\beta= 1. If I denotes 2×22 \times 2 identity matrix, then the matrix (1+A)8(1 +A)^{8} is:

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  2. Question 2

    Vector Algebra. This type asked 4 times: 2021 Paper 6, 2021 Paper 14, 10 Apr 2023, 29 Jan 2025. This one: 29 Jan 2025 See all 4 of this type

    144
    Let â be a unit vector perpendicular to the vectors b→=i^−2j^+3k^\overrightarrow{b}=\widehat{i}- 2\widehat{j}+ 3\widehat{k} and c→=2i^+3j^−k^\overrightarrow{c}= 2\widehat{i}+ 3\widehat{j}-\widehat{k}, and makes an angle of cos⁡−1(−13)\cos^{- 1}\left( -\frac{1}{3} \right) with the vector i^+j^+k^\widehat{i}+\widehat{j}+\widehat{k}. If a^\widehat{a} makes an angle of π3\frac{\pi}{3} with the vector i^+αj^+k^\widehat{i}+ \alpha\widehat{j}+\widehat{k}, then the value of α\alpha is :

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  3. Question 3

    Definite Integration. This type asked 4 times: 27 Jun 2022, 10 Apr 2023, 1 Feb 2024, 28 Jan 2025. This one: 28 Jan 2025 See all 4 of this type

    132
    Let ff be a real valued continuous function defined on the positive real axis such that g(x)=∫0xtf(t)dtg(x) =\int_{0}^{x} tf(t)dt. If g(x3)=x6+x7g\left( x^{3} \right)=x^{6}+x^{7}, then value of ∑r=115f(r3)\sum_{r = 1}^{15} f\left( r^{3} \right) is :

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  4. Question 4

    Matrices. This type asked 4 times: 2021 Paper 18, 25 Jan 2023, 8 Apr 2023, 28 Jan 2025. This one: 28 Jan 2025 See all 4 of this type

    135
    Let A=[12−201]A =\begin{bmatrix} \frac{1}{\sqrt{2}} & - 2 \\ 0 & 1 \end{bmatrix} and P=[cos⁡θ−sin⁡θsin⁡θcos⁡θ],θ>0P =\begin{bmatrix} \cos\theta & - \sin\theta \\ \sin\theta & \cos\theta \end{bmatrix},\theta > 0. If B=PAPT,C=PTB10PB = PAP^{T},C =P^{T}B^{10}P and the sum of the diagonal elements of C is mn\frac{m}{n}, where gcd(m,n)=gcd(m,n) = 1 , then m+nm + n is :

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  5. Question 5

    Permutations and Combinations. This type asked 4 times: 2021 Paper 13, 24 Jan 2023, 25 Jan 2023, 28 Jan 2025. This one: 28 Jan 2025 See all 4 of this type

    51
    The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0,1 , 2,3,4,5,6,72,3,4,5,6,7, such that the sum of their first and last digits should not be more than 8 , is

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