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Day 415: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked once: 2021 Paper 23 (same type asked 19 times) See all 19 of this type

    72
    If ydydx=x[y2x2+ϕ(y2x2)ϕ′(y2x2)],x>0,ϕ>0y\frac{dy}{dx}=x\left\lbrack \frac{y^{2}}{x^{2}}+\frac{\phi\left( \frac{y^{2}}{x^{2}} \right)}{\phi^{'}\left( \frac{y^{2}}{x^{2}} \right)} \right\rbrack,x> 0,\phi> 0, and y(1)=−1y(1) = - 1, then ϕ(y24)\phi\left( \frac{y^{2}}{4} \right) is equal to:

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  2. Question 2

    Determinants. Asked once: 25 Jan 2023 (same type asked 19 times) See all 19 of this type

    78
    Let x,y,z>1x,y,z > 1 and A=[1log⁡xylog⁡xzlog⁡yx2log⁡yzlog⁡zxlog⁡zy3]A =\begin{bmatrix} 1 & \log_{x}y & \log_{x}z \\ \log_{y}x & 2 & \log_{y}z \\ \log_{z}x & \log_{z}y & 3 \end{bmatrix}. Then ∣adj(adjA2)∣\left| adj\left( adjA^{2} \right) \right| is equal to

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  3. Question 3

    Vector Algebra. Asked once: 13 Apr 2023 (same type asked 18 times) See all 18 of this type

    76
    Let a=i^+4j^+2k^,b=3i^−2j^+7k^a =\widehat{i}+ 4\widehat{j}+ 2\widehat{k},b = 3\widehat{i}- 2\widehat{j}+ 7\widehat{k} and c→=2i^−j^+4k^\overrightarrow{c}= 2\widehat{i}-\widehat{j}+ 4\widehat{k}. If a vector d→\overrightarrow{d} satisfies d→×b→=c→×b→\overrightarrow{d}\times\overrightarrow{b}=\overrightarrow{c}\times\overrightarrow{b} and d→.a→=24\overrightarrow{d}.\overrightarrow{a}= 24, then ∣d→∣2|\overrightarrow{d}|^{2} is equal to

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  4. Question 4

    Limits and Continuity. Asked once: 2021 Paper 22 (same type asked 16 times) See all 16 of this type

    75
    If the function f(x)={1xlog⁡e(1+xa1−xb), x<0k, x=0cos⁡2x−sin⁡2x−1x2+1−1, x>0f(x)=\left\{\begin{matrix}\frac{1}{x}\log_{e}\left(\frac{1+\frac{x}{a}}{1-\frac{x}{b}}\right) & ,\ x<0 \\ k & ,\ x=0 \\ \frac{\cos^{2}x-\sin^{2}x-1}{\sqrt{x^{2}+1}-1} & ,\ x>0\end{matrix}\right. is continuous at x=0x=0, then 1a+1b+4k\frac{1}{a}+\frac{1}{b}+\frac{4}{k} is equal to:

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  5. Question 5

    Three Dimensional Geometry. Asked once: 2021 Paper 19 (same type asked 15 times) See all 15 of this type

    76
    Let PP be the plane passing through the point (1,2,3)(1,2,3) and the line of intersection of the planes r→⋅(i^+j^+4k^)=16\overrightarrow{r}\cdot (\widehat{i}+\widehat{j}+ 4\widehat{k}) = 16 and r→⋅(−i^+j^+k^)=6\overrightarrow{r}\cdot ( -\widehat{i}+\widehat{j}+\widehat{k}) = 6. Then which of the following points does NOT lie on P?

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