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Day 309: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 25 Jun 2022 (same type asked 6 times) See all 6 of this type

    76
    If y=m1x+c1y =m_{1}x +c_{1} and y=m2x+c2, m1≠m2y =m_{2}x +c_{2},{\text{ }m}_{1}\neq m_{2} are two common tangents of circle x2+y2=2x^{2}+y^{2}= 2 and parabola y2=xy^{2}= x, then the value of 8∣ m1 m2∣8\left| {\text{ }m}_{1}{\text{ }m}_{2} \right| is equal to

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  2. Question 2

    Limits and Continuity. Asked once: 2021 Paper 18 (same type asked 6 times) See all 6 of this type

    78
    The value of lim⁡n→∞1n∑r=02n−1n2n2+4r2\lim_{n\rightarrow \infty} \frac{1}{n}\sum_{r= 0}^{2n- 1} \frac{n^{2}}{n^{2}+ 4r^{2}} is:

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  3. Question 3

    Definite Integration. Asked once: 2021 Paper 11 (same type asked 6 times) See all 6 of this type

    43
    Let aa be a positive real number such that ∫0aex−[x]dx=10e−9\int_{0}^{a} e^{x- \lbrack x\rbrack}dx= 10e- 9 where [x]\lbrack x\rbrack is the greatest integer less than or equal to xx. Then a is equal to:

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  4. Question 4

    Application of Integrals. Asked once: 2021 Paper 18 (same type asked 5 times) See all 5 of this type

    86
    The area of the region S={(x,y):3x2≤4y≤6x+24}S=\left\{ (x,y):3x^{2}\leq 4y\leq 6x+ 24 \right\} is

  5. Question 5

    Limits and Continuity. Asked once: 25 Jun 2022 (same type asked 5 times) See all 5 of this type

    172
    Let f(x)=[2x2+1]f(x) =\left\lbrack 2x^{2}+ 1 \right\rbrack and g(x)={2x−3,x<02x+3,x≥0g(x) =\left\{ \begin{matrix} 2x - 3, & x < 0 \\ 2x + 3, & x \geq 0 \end{matrix} \right., where [t]\lbrack t\rbrack is the greatest integer ≤t\leq t. Then, in the open interval (−1,1)( - 1,1), the number of points where fog is discontinuous is equal to