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Day 586: JEE Mains Maths

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

  1. Question 1

    Relations and Functions. Asked once: 2021 Paper 26

    75
    Let A={1,2,3,…,10}A = \{1,2,3,\ldots,10\} and f:A→Af:A \rightarrow A be defined as f(k)={k+1,if k is oddk,if k is evenf(k) =\left\{ \begin{matrix} k + 1, & \text{if } k \text{ is odd} \\ k, & \text{if } k \text{ is even} \end{matrix} \right. Then the number of possible functions g:A→Ag:A \rightarrow A such that g∘f=fg \circ f = f is:

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  2. Question 2

    Sequences and Series. Asked once: 27 Jan 2024

    155
    The 20th 20^{\text{th~}} term from the end of the progression 20,1914,1812,1734,….,−1291420,19\frac{1}{4},18\frac{1}{2},17\frac{3}{4},\ldots., - 129\frac{1}{4} is :-

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  3. Question 3

    Straight Lines. Asked once: 29 Jul 2022

    161
    Let m1, m2m_{1},{\text{ }m}_{2} be the slopes of two adjacent sides of a square of side a such that a2+11a+3(m12+m22)=220a^{2}+ 11a + 3\left( m_{1}^{2}+m_{2}^{2} \right)= 220. If one vertex of the square is (10(cos⁡α−sin⁡α),10(sin⁡α+cos⁡α))(10(\cos\alpha - \sin\alpha),10(\sin\alpha + \cos\alpha)), where α∈(0,π2)\alpha \in\left( 0,\frac{\pi}{2} \right) and the equation of one diagonal is (cos⁡α−sin⁡α)x+(sin⁡α+cos⁡α)y=10(\cos\alpha - \sin\alpha)x + (\sin\alpha + \cos\alpha)y = 10, then 72 (sin⁡4α+cos⁡4α)+a2−3a+13\left( \sin^{4}\alpha +\cos^{4}\alpha \right)+a^{2}- 3a + 13 is equal to:

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  4. Question 4

    Three Dimensional Geometry. Asked once: 2021 Paper 3

    66
    The equation of the line through the point (0,1,2)(0,1,2) and perpendicular to the line x−12=y+13=z−1−2\frac{x - 1}{2}=\frac{y + 1}{3}=\frac{z - 1}{- 2} is:

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  5. Question 5

    Vector Algebra. Asked once: 2021 Paper 5

    68
    Let the position vectors of two points PP and QQ be 3i^−j^+2k^3\widehat{i}-\widehat{j}+ 2\widehat{k} and i^+2j^−4k^\widehat{i}+ 2\widehat{j}- 4\widehat{k}, respectively. Let RR and SS be two points such that the direction ratios of lines PRPR and QSQS are (4,−1,2)(4, - 1,2) and (−2,1,−2)( - 2,1, - 2), respectively. Let lines PRPR and QSQS intersect at TT. If the vector TA→\overrightarrow{TA} is perpendicular to both PR→\overrightarrow{PR} and QS→\overrightarrow{QS} and the length of vector TA→\overrightarrow{TA} is 5\sqrt{5} units, then the modulus of a position vector of AA is :

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