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Day 420: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked once: 2021 Paper 6 (same type asked 19 times) See all 19 of this type

    79
    Let C1C_{1} be the curve obtained by the solution of differential equation 2xydydx=y2−x2,x>02xy\frac{dy}{dx}=y^{2}-x^{2},x> 0. Let the curve C2C_{2} be the solution of 2xyx2−y2=dydx\frac{2xy}{x^{2}-y^{2}}=\frac{dy}{dx}. If both the curves pass through (1,1)(1,1), then the area enclosed by the curves C1C_{1} and C2C_{2} is equal to:

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  2. Question 2

    Determinants. Asked once: 27 Jul 2022 (same type asked 19 times) See all 19 of this type

    171
    Consider a matrix A=[αβγα2β2γ2β+γγ+αα+β]A =\begin{bmatrix} \alpha & \beta & \gamma \\ \alpha^{2} & \beta^{2} & \gamma^{2} \\ \beta + \gamma & \gamma + \alpha & \alpha + \beta \end{bmatrix}, where α,β,γ\alpha,\beta,\gamma are three distinct natural numbers. If det(adj(adj(adj(adjA))))(α−β)16(β−γ)16(γ−α)16=232×316\frac{det(adj(adj(adj(adjA))))}{(\alpha - \beta)^{16}(\beta - \gamma)^{16}(\gamma - \alpha)^{16}}=2^{32}\times3^{16}, then the number of such 3 - tuples (α,β,γ)(\alpha,\beta,\gamma) is

  3. Question 3

    Vector Algebra. Asked once: 1 Feb 2023 (same type asked 18 times) See all 18 of this type

    154
    Let a→=2i^−7j^+5k^,b→=i^+k^\overrightarrow{a}= 2\widehat{i}- 7\widehat{j}+ 5\widehat{k},\overrightarrow{b}=\widehat{i}+\widehat{k} and c→=i^+2j^−3k^\overrightarrow{c}=\widehat{i}+ 2\widehat{j}- 3\widehat{k} be three given vectors. If r→\overrightarrow{r} is a vector such that r→×a→=c→×a→\overrightarrow{r}\times\overrightarrow{a}=\overrightarrow{c}\times\overrightarrow{a} and r→⋅b→=0\overrightarrow{r}\cdot\overrightarrow{b}= 0, then ∣r→∣|\overrightarrow{r}| is equal to:

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  4. Question 4

    Limits and Continuity. Asked once: 2021 Paper 14 (same type asked 16 times) See all 16 of this type

    62
    Let f(x)={μ,x=2etan⁡(x−2)x−[x],x<2∣x2−5x+6∣λ(−x2+5x−6)μ,x>2f\left( x \right)=\left\{ \begin{matrix} \mu, & x= 2 \\ e^{\frac{\tan\left( x- 2 \right)}{x-\left\lbrack x \right\rbrack}}, & x< 2 \\ \frac{\left| x^{2}- 5x+ 6 \right|\lambda}{\left( -x^{2}+ 5x- 6 \right)\mu}, & x> 2 \end{matrix} \right. If ff is continuous at x=2x = 2, then μ+λ\mu+\lambda is equal to

  5. Question 5

    Three Dimensional Geometry. Asked once: 2021 Paper 7 (same type asked 15 times) See all 15 of this type

    89
    If the equation of the plane passing through the line of intersection of the planes 2x−7y+4z−3=0,3x−5y+4z+11=02x - 7y + 4z - 3 = 0,3x - 5y + 4z + 11 = 0 and the point (−2,1,3)( - 2,1,3) is ax + by +cz−7=0+ cz - 7 = 0, then the value of 2a+b+c−72a + b + c - 7 is