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Day 384: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 14 Jun 2022 (same type asked 7 times) See all 7 of this type

    84
    Let a line having direction ratios 1, -4, 2 intersect the lines x−73=y−1−1=z+21\frac{x - 7}{3}=\frac{y - 1}{- 1}=\frac{z + 2}{1} and x2=y−73=z1\frac{x}{2}=\frac{y - 7}{3}=\frac{z}{1} at the point AA and BB. Then (AB)2(AB)^{2} is equal to

  2. Question 2

    Limits and Continuity. Asked once: 14 Jun 2022 (same type asked 7 times) See all 7 of this type

    85
    The number of points where the function
    f(x)={∣2x2−3x−7∣ if x≤−1[4x2−1] if −1<x<1∣x+1∣+∣x−2∣ if x≥1f(x) =\left\{ \begin{matrix} \left| 2x^{2}- 3x- 7 \right| & \text{~if~} & x\leq - 1 \\ \left\lbrack 4x^{2}- 1 \right\rbrack & \text{~if~} & - 1 <x< 1 \\ |x+ 1| + |x- 2| & \text{~if~} & x\geq 1 \end{matrix} \right.
    [t] denotes the greatest integer ≤t\leq t, is discontinuous is

  3. Question 3

    Sequences and Series. Asked once: 29 Jun 2022 (same type asked 7 times) See all 7 of this type

    173
    Let 3,6,9,12,…3,6,9,12,\ldots upto 78 terms and 5,9,13,17,…5,9,13,17,\ldots upto 59 terms be two series. Then, the sum of the terms common to both the series is equal to

  4. Question 4

    Trigonometric Identities. Asked once: 2021 Paper 19 (same type asked 7 times) See all 7 of this type

    73
    The value of 2sin⁡(π8)sin⁡(2π8)sin⁡(3π8)sin⁡(5π8)sin⁡(6π8)sin⁡(7π8)2\sin\left( \frac{\pi}{8} \right)\sin\left( \frac{2\pi}{8} \right)\sin\left( \frac{3\pi}{8} \right)\sin\left( \frac{5\pi}{8} \right)\sin\left( \frac{6\pi}{8} \right)\sin\left( \frac{7\pi}{8} \right) is :

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  5. Question 5

    Differential Equations. Asked once: 2021 Paper 19 (same type asked 7 times) See all 7 of this type

    66
    Let y(x)y(x) be the solution of the differential equation 2x2dy+(ey−2x)dx=0,x>02x^{2}dy+\left( e^{y}- 2x \right)dx= 0,x> 0. If y(e)=1y(e) = 1, then y(1)y(1) is equal to:

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