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Day 272: JEE Mains Maths

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

  1. Question 1

    Determinants. Asked once: 12 Apr 2023 (same type asked 3 times) See all 3 of this type

    86
    Let Dk=∣12k2k−1nn2+n+2n2nn2+nn2+n+2∣D_{k}=\left| \begin{matrix} 1 & 2k & 2k - 1 \\ n & n^{2}+ n + 2 & n^{2} \\ n & n^{2}+ n & n^{2}+ n + 2 \end{matrix} \right|. If ∑k=1nDk=96\sum_{k = 1}^{n} D_{k}= 96, then nn is equal to

  2. Question 2

    Differential Equations. Asked once: 2021 Paper 11 (same type asked 3 times) See all 3 of this type

    51
    Let y=y(x)y=y(x) be the solution of the differential equation xtan(yx)dy=(ytan(yx)−x)dxxtan\left( \frac{y}{x} \right)dy=\left( ytan\left( \frac{y}{x} \right)-x \right)dx, −1≤x≤1,y(12)=π6- 1 \leq x \leq 1,y\left( \frac{1}{2} \right)=\frac{\pi}{6}. Then the area of the region bounded by the curves x=0,x=12x= 0,x=\frac{1}{\sqrt{2}} and y=y(x)y=y(x) in the upper half plane is:

    Tap an option to check your answer.

  3. Question 3

    Limits and Continuity. Asked once: 8 Apr 2024 (same type asked 3 times) See all 3 of this type

    90
    The value of lim⁡x→02(1−cos⁡xcos⁡2xcos⁡3x3…..cos⁡10x10x2)\lim_{x\rightarrow 0} 2\left( \frac{1 - \cos x\sqrt{\cos2x}\sqrt[3]{\cos3x}\ldots..\sqrt[10]{\cos10x}}{x^{2}} \right) is

  4. Question 4

    Quadratic Equations. Asked once: 2 Apr 2025 (same type asked 3 times) See all 3 of this type

    150
    If the set of all a∈R−{1}a \in R - \left\{ 1 \right\}, for which the roots of the equation (1−a)x2+2(a−3)x+9=0(1 - a)x^{2} + 2(a - 3)x + 9 = 0 are positive is (−∞,−α]∪[β,γ)( - \infty, - \alpha\rbrack \cup \lbrack\beta,\gamma), then 2α+β+γ2\alpha + \beta + \gamma is equal to

  5. Question 5

    Matrices. Asked once: 2021 Paper 23 (same type asked 3 times) See all 3 of this type

    87
    The number of elements in the set
    {A=[ab0 d]:a,b,d∈{−1,0,1} and (I−A)3=I−A3},\left\{ A =\begin{bmatrix} a & b \\ 0 & \text{ }d \end{bmatrix}\mathbf{:a,b,d \in \{ - 1,0,1\}}\text{~and~}(I - A)^{3}= I -A^{3} \right\},
    where I is 2×22 \times 2 identity matrix, is: