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Day 357: JEE Mains Maths

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

  1. Question 1

    Relations and Functions. Asked once: 27 Jul 2022 (same type asked 4 times) See all 4 of this type

    151
    The domain of the function f(x)=sin⁡−1[2x2−3]+log⁡2(log⁡12(x2−5x+5))f(x) =\sin^{- 1}\left\lbrack 2x^{2}- 3 \right\rbrack+\log_{2}\left( \log_{\frac{1}{2}}\left( x^{2}- 5x + 5 \right) \right), where [t]\lbrack t\rbrack is the greatest integer function, is:

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  2. Question 2

    Vector Algebra. Asked once: 2021 Paper 6 (same type asked 4 times) See all 4 of this type

    89
    Let c→\overrightarrow{c} be a vector perpendicular to the vectors a→=i^+j^−k^\overrightarrow{a}=\widehat{i}+\widehat{j}-\widehat{k} and b→=i^+2j^+k^\overrightarrow{b}=\widehat{i}+ 2\widehat{j}+\widehat{k}. If c→⋅(i^+j^+3k^)=8\overrightarrow{c}\cdot (\widehat{i}+\widehat{j}+ 3\widehat{k}) = 8 then the value of c→⋅(a→×b→)\overrightarrow{c}\cdot (\overrightarrow{a}\times\overrightarrow{b}) is equal to

  3. Question 3

    Matrices. Asked once: 2021 Paper 16 (same type asked 4 times) See all 4 of this type

    56
    If A=[12−14]A−1=αI+βAA=\begin{bmatrix} 1 & 2 \\ - 1 & 4 \end{bmatrix}A^{- 1}=\alpha I+\beta A, find 5(α−β)=5(\alpha-\beta) = ?

  4. Question 4

    Three Dimensional Geometry. Asked once: 2021 Paper 25 (same type asked 4 times) See all 4 of this type

    78
    If (1,5,35),(7,5,5),(1,λ,7)(1,5,35),(7,5,5),(1,\lambda,7) and (2λ,1,2)(2\lambda,1,2) are coplanar, then the sum of all possible values of λ\lambda is:

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  5. Question 5

    Differential Equations. Asked once: 23 Jan 2026 S1 (same type asked 41 times) See all 41 of this type

    57
    Let y=y(x)y = y(x) be the solution of the differential equation x4dy+(4x3y+2sin⁡x)dx=0,x>0,y(π2)=0x^{4}dy +\left( 4x^{3}y + 2\sin x \right)dx = 0,x > 0,y\left( \frac{\pi}{2} \right)= 0. Then π4y(π3)\pi^{4}y\left( \frac{\pi}{3} \right) is equal to :

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