PYQ Vault
EbooksTutor

Day 211: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 2021 Paper 3 (same type asked 2 times) See all 2 of this type

    69
    A tangent is drawn to the parabola y2=6xy^{2}= 6x which is perpendicular to the line 2x+y=12x+y= 1. Which of the following points does NOT lie on it?

    Tap an option to check your answer.

  2. Question 2

    Conic Sections. Asked once: 30 Jan 2024 (same type asked 2 times) See all 2 of this type

    173
    Consider two circles C1:x2+y2=25C_{1}:x^{2}+y^{2}= 25 and C2:(x−C_{2}:(x - α)2+y2=16\alpha)^{2}+y^{2}= 16, where α∈(5,9)\alpha \in (5,9). Let the angle between the two radii (one to each circle) drawn from one of the intersection points of C1C_{1} and C2C_{2} be sin⁡−1(638)\sin^{- 1}\left( \frac{\sqrt{63}}{8} \right). If the length of common chord of C1C_{1} and C2C_{2} is β\beta, then the value of (αβ)2(\alpha\beta)^{2} equals

  3. Question 3

    Straight Lines. Asked once: 2021 Paper 23 (same type asked 2 times) See all 2 of this type

    76
    Let AA be the set of all points (α,β)(\alpha,\beta) such that the area of triangle formed by the points (5,6),(3,2)(5,6),(3,2) and (α,β)(\alpha,\beta) is 12 square units. Then the least possible length of a line segment joining the origin to a point in AA, is:

    Tap an option to check your answer.

  4. Question 4

    Three Dimensional Geometry. Asked once: 26 Jun 2022 (same type asked 2 times) See all 2 of this type

    74
    If the two lines l1:x−23=y+1−2,z=2l_{1}:\frac{x - 2}{3}=\frac{y + 1}{- 2},z = 2 and l2:x−11=2y+3α=z+52l_{2}:\frac{x - 1}{1}=\frac{2y + 3}{\alpha}=\frac{z + 5}{2} are perpendicular, then an angle between the lines l2l_{2} and l3:1−x3=2y−1−4=z4l_{3}:\frac{1 - x}{3}=\frac{2y - 1}{- 4}=\frac{z}{4} is :

    Tap an option to check your answer.

  5. Question 5

    Limits and Continuity. Asked once: 27 Jan 2024 (same type asked 2 times) See all 2 of this type

    78
    If a=lim⁡x→01+1+x4−2x4a =\lim_{x \rightarrow 0} \frac{\sqrt{1 +\sqrt{1 +x^{4}}}-\sqrt{2}}{x^{4}} and b=lim⁡x→0sin⁡2x2−1+cos⁡xb =\lim_{x \rightarrow 0} \frac{\sin^{2}x}{\sqrt{2}-\sqrt{1 + \cos x}}, then the value of ab3ab^{3} is :

    Tap an option to check your answer.