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Day 391: JEE Mains Maths

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

  1. Question 1

    Quadratic Equations. Asked once: 30 Jan 2024 (same type asked 10 times) See all 10 of this type

    178
    The number of real solutions of the equation x(x2+3∣x∣+5∣x−1∣+6∣x−2∣)=0x\left( x^{2}+ 3|x| + 5|x- 1| + 6|x- 2| \right)= 0 is

  2. Question 2

    Vector Algebra. Asked once: 2021 Paper 23 (same type asked 10 times) See all 10 of this type

    62
    Let a→,b→,c→\overrightarrow{a},\overrightarrow{b},\overrightarrow{c} be three vectors mutually perpendicular to each other and have same magnitude. If a vector r→\overrightarrow{r} satisfies a→×{(r→−b→)×a→}+b→×{(r→−c→)×b→}+c→×{(r→−a→)×c→}=0→\overrightarrow{a}\times\{(\overrightarrow{r}-\overrightarrow{b})\times\overrightarrow{a}\}+\overrightarrow{b}\times\{(\overrightarrow{r}-\overrightarrow{c})\times\overrightarrow{b}\}+\overrightarrow{c}\times\{(\overrightarrow{r}-\overrightarrow{a})\times\overrightarrow{c}\}=\overrightarrow{0}, then r→\overrightarrow{r} is equal to:

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  3. Question 3

    Sequences and Series. Asked once: 28 Jun 2022 (same type asked 10 times) See all 10 of this type

    66
    Let A1, A2, A3A_{1},{\text{ }A}_{2},{\text{ }A}_{3}, be an increasing geometric progression of positive real numbers. If A1A3A5A7=11296A_{1}A_{3}A_{5}A_{7}=\frac{1}{1296} and A2+A4=736A_{2}+A_{4}=\frac{7}{36}, then, the value of A6+A8+A10A_{6}+A_{8}+A_{10} is equal to

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  4. Question 4

    Matrices. Asked once: 29 Jun 2022 (same type asked 9 times) See all 9 of this type

    153
    Let A=(2−102)A =\begin{pmatrix} 2 & - 1 \\ 0 & 2 \end{pmatrix}. If B=I− 5C1(adjA)+ 5C2B = I -\ ^{5}C_{1}(adjA) +\ ^{5}C_{2} (adjA)2−…− 5C5(adjA)5(adjA)^{2}- \ldots -\ ^{5}C_{5}(adjA)^{5}, then the sum of all elements of the matrix BB is:

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  5. Question 5

    Application of Integrals. Asked once: 25 Jun 2022 (same type asked 9 times) See all 9 of this type

    156
    The area of the region enclosed between the parabolas y2=2x−1y^{2}= 2x - 1 and y2=4x−3y^{2}= 4x - 3 is

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