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Day 123: JEE Mains Maths

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

  1. Question 1

    Trigonometric Equations. This type asked 2 times: 2021 Paper 9, 25 Jul 2022. This one: 25 Jul 2022 See all 2 of this type

    78
    The number of solutions of ∣cos⁡x∣=sin⁡x|\cos x| = \sin x, such that −4π≤x≤4π- 4\pi \leq x \leq 4\pi is:

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  2. Question 2

    Matrices. This type asked 2 times: 25 Jun 2022, 29 Jun 2022. This one: 29 Jun 2022 See all 2 of this type

    179
    Let M=[0−αα0]M =\begin{bmatrix} 0 & - \alpha \\ \alpha & 0 \end{bmatrix}, where α\alpha is a non-zero real number an N=∑k=149M2kN =\sum_{k = 1}^{49} M^{2k}. If (I−M2)N=−2I\left( I -M^{2} \right)N = - 2I, then the positive integral value of α\alpha is

  3. Question 3

    Three Dimensional Geometry. This type asked 2 times: 2021 Paper 23, 29 Jun 2022. This one: 29 Jun 2022 See all 2 of this type

    162
    Let the line x−23=y+1−2=z+3−1\frac{x - 2}{3}=\frac{y + 1}{- 2}=\frac{z + 3}{- 1} lie on the plane px−qy+px - qy + z=5z = 5, for some p,q∈Rp,q \in R. The shortest distance of the plane from the origin is:

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  4. Question 4

    Application of Derivatives. This type asked 2 times: 14 Jun 2022, 28 Jun 2022. This one: 28 Jun 2022 See all 2 of this type

    86
    Let l\mathcal{l} be a line which is normal to the curve y=2x2+x+2y = 2x^{2}+ x + 2 at a point PP on the curve. If the point Q(6,4)Q(6,4) lies on the line l\mathcal{l} and OO is origin, then the area of the triangle OPQ is equal to

  5. Question 5

    Probability. This type asked 2 times: 2021 Paper 23, 28 Jun 2022. This one: 28 Jun 2022 See all 2 of this type

    167
    The probability that a randomly chosen one-one function from the set {a,b,c,d}\mathbf{\{ a,b,c,d\}} to the set {1,2,3,4,5}\mathbf{\{ 1,2,3,4,5\}} satisfies f(a)+2f(b)−f(c)=f(d)f(a) + 2f(b) - f(c) = f(d) is :

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