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Day 289: JEE Mains Maths

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

  1. Question 1

    Matrices. Asked once: 2021 Paper 14 (same type asked 3 times) See all 3 of this type

    56
    Let S={n∈N,[0ii0]n[abcd]=[abcd]∀a,b,c,d∈R]S=\left\{ n\in N,\begin{bmatrix} 0 & i \\ i & 0 \end{bmatrix}^{n}\begin{bmatrix} a & b \\ c & d \end{bmatrix}=\begin{bmatrix} a & b \\ c & d \end{bmatrix}\forall a,b,c,d\in R \right\rbrack. Find number of 2-digit numbers in 5

  2. Question 2

    Differential Equations. Asked once: 2021 Paper 22 (same type asked 3 times) See all 3 of this type

    76
    If dydx=2x+y−2x2y,y(0)=1\frac{dy}{dx}=\frac{2^{x+y}-2^{x}}{2^{y}},y(0) = 1, then y(1)y(1) is equal to :

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  3. Question 3

    Limits and Continuity. Asked once: 2021 Paper 16 (same type asked 3 times) See all 3 of this type

    42
    lim⁡x→2x2f(2)−4f(x)(x−2)\lim_{x\rightarrow 2} \frac{x^{2}f(2) - 4f(x)}{(x- 2)}, where f(2)=4f(2) = 4 and f′(2)=1f^{'}(2) = 1, is equal to

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  4. Question 4

    Determinants. Asked once: 2021 Paper 7 (same type asked 2 times) See all 2 of this type

    64
    The system of equations kx+y+z=1kx + y + z = 1, x+ky+z=kx + ky + z = k and x+y+zk=k2x + y + zk =k^{2} has no solution if kk is equal to:

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  5. Question 5

    Conic Sections. Asked once: 29 Jul 2022 (same type asked 2 times) See all 2 of this type

    178
    Let ABAB be a chord of length 12 of the circle (x−2)2+(y+1)2=1694(x - 2)^{2}+ (y + 1)^{2}=\frac{169}{4}. If tangents drawn to the circle at points AA and BB intersect at the point PP, then five times the distance of point PP from chord ABAB is equal to