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Day 422: JEE Mains Maths

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

  1. Question 1

    Determinants. Asked once: 28 Jun 2022 (same type asked 19 times) See all 19 of this type

    64
    Let AA be a matrix of order 3×33 \times 3 and det(A)=2det(A) = 2. Then det(det(A)adj(5adj(A3)))det\left( det(A)adj\left( 5adj\left( A^{3} \right) \right) \right) is equal to

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  2. Question 2

    Vector Algebra. Asked once: 31 Jan 2023 (same type asked 18 times) See all 18 of this type

    164
    Let: a→=ı^+2ȷ^+3k^,b→=ı^−ȷ^+2k^\overrightarrow{a}=\widehat{\imath}+ 2\widehat{\jmath}+ 3\widehat{k},\overrightarrow{b}=\widehat{\imath}-\widehat{\jmath}+ 2\widehat{k} and c→=5ı^−3ȷ^+3k^\overrightarrow{c}= 5\widehat{\imath}- 3\widehat{\jmath}+ 3\widehat{k} be there vectors. If r→\overrightarrow{r} is a vector such that, r→×b→=c→×b→\overrightarrow{r}\times\overrightarrow{b}=\overrightarrow{c}\times\overrightarrow{b} and r→⋅a→=0\overrightarrow{r}\cdot\overrightarrow{a}= 0, then 25∣r→∣225|\overrightarrow{r}|^{2} is equal to

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  3. Question 3

    Limits and Continuity. Asked once: 2021 Paper 10 (same type asked 16 times) See all 16 of this type

    80
    Let f:R→Rf:\mathbb{R}\to\mathbb{R} be a function defined as f(x)={sin⁡(a+1)x+sin⁡2x2x,x<0b,x=0x+bx3−xbx5/2,x>0f(x)=\begin{cases}\dfrac{\sin(a+1)x+\sin 2x}{2x}, & x<0 \\ b, & x=0 \\ \dfrac{\sqrt{x+bx^{3}}-\sqrt{x}}{bx^{5/2}}, & x>0\end{cases}. If ff is continuous at x=0x=0, then the value of a+ba+b is equal to:

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  4. Question 4

    Three Dimensional Geometry. Asked once: 2021 Paper 2 (same type asked 15 times) See all 15 of this type

    65
    The vector equation of the plane passing through the intersection of the planes r→⋅(i^+j^+k^)=1\overrightarrow{r}\cdot (\widehat{i}+\widehat{j}+\widehat{k}) = 1 and r→⋅(i^−2j^)=−2\overrightarrow{r}\cdot (\widehat{i}- 2\widehat{j}) = - 2, and the point (1,0,2)(1,0,2) is :

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  5. Question 5

    Differential Equations. Asked once: 4 Apr 2024 (same type asked 41 times) See all 41 of this type

    83
    Let the solution y=y(x)y = y(x) of the differential equation dydx−y=1+4sin⁡x\frac{dy}{dx}- y = 1 + 4\sin x satisfy y(π)=1y(\pi) = 1. Then y(π2)+10y\left( \frac{\pi}{2} \right)+ 10 is equal to