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Day 220: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 2021 Paper 10 (same type asked 2 times) See all 2 of this type

    83
    If ∑r=110r!(r3+6r2+2r+5)=α(11!)\sum_{r = 1}^{10} r!\left( r^{3}+ 6r^{2}+ 2r + 5 \right)=\alpha(11!), then the value of α\alpha is equal to

  2. Question 2

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

    46
    If f(x)={5x+1,x<2∫0x(5+∣1−t∣) dt,x≥2f(x)=\begin{cases} 5x+1, & x<2 \\ \int_{0}^{x} (5+|1-t|)\,dt, & x\ge 2 \end{cases} then

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  3. Question 3

    Matrices. Asked once: 2021 Paper 25 (same type asked 2 times) See all 2 of this type

    71
    Let AA be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of A2A^{2} is 1 , then the possible number of such matrices is:

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  4. Question 4

    Vector Algebra. Asked once: 29 Jun 2022 (same type asked 2 times) See all 2 of this type

    65
    Let  a→=αi^+3j^−k^,b→=3i^−βj^+4k^\ \overrightarrow{a}= \alpha\widehat{i}+ 3\widehat{j}-\widehat{k},\overrightarrow{b}= 3\widehat{i}- \beta\widehat{j}+ 4\widehat{k} and c→=i^+2j^−2k^\overrightarrow{c}=\widehat{i}+ 2\widehat{j}- 2\widehat{k} where α,β∈R\alpha,\beta \in R, be three vectors. If the projection of a→\overrightarrow{a} on c→\overrightarrow{c} is 103\frac{10}{3} and b→×c→=−6i^+10j^+7k^\overrightarrow{b}\times\overrightarrow{c}= - 6\widehat{i}+ 10\widehat{j}+ 7\widehat{k}, then the value of α+β\alpha + \beta equal to:

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  5. Question 5

    Conic Sections. Asked once: 2021 Paper 18 (same type asked 2 times) See all 2 of this type

    87
    The locus of a point, which moves such that the sum of squares of its distances from the points (0,0),(1,0),(0,1)(1,1)(0,0),(1,0),(0,1)(1,1) is 18 units, is a circle of diameter dd. Then d2d^{2} is equal to