PYQ Vault
EbooksTutor

Day 159: JEE Mains Maths

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

  1. Question 1

    Inverse Trigonometric Functions. Asked once: 24 Jan 2025 (same type asked 4 times) See all 4 of this type

    72
    If for some α,β;α≤β,α+β=8\alpha,\beta;\alpha \leq \beta,\alpha + \beta = 8 and sec⁡2(tan⁡−1α)+csc⁡2(cot⁡−1β)=36\sec^{2}\left( \tan^{- 1}\alpha \right)+\csc^{2}\left( \cot^{- 1}\beta \right)= 36, then α2+β\alpha^{2}+ \beta is  ____\ \_\_\_\_ .

  2. Question 2

    Sequences and Series. Asked once: 2 Apr 2026 S2 (same type asked 4 times) See all 4 of this type

    55
    The sum 131+13+231+3+13+23+331+3+5+…\frac{1^{3}}{1}+\frac{1^{3}+2^{3}}{1 + 3}+\frac{1^{3}+2^{3}+3^{3}}{1 + 3 + 5}+ \ldots up to 8 terms, is :

    Tap an option to check your answer.

  3. Question 3

    Vector Algebra. Asked once: 13 Apr 2023 (same type asked 4 times) See all 4 of this type

    157
    Let ∣a→∣=2,∣b→∣=3|\overrightarrow{a}| = 2,|\overrightarrow{b}| = 3 and the angle between the vectors a→\overrightarrow{a} and b→\overrightarrow{b} be π4\frac{\pi}{4}. Then ∣(a→+2b→)×(2a→−3b→)∣2|(\overrightarrow{a}+ 2\overrightarrow{b}) \times (2\overrightarrow{a}- 3\overrightarrow{b})|^{2} is equal to

    Tap an option to check your answer.

  4. Question 4

    Conic Sections. Asked once: 2 Apr 2026 S2 (same type asked 4 times) See all 4 of this type

    60
    Let a circle pass through the origin and its center be the point of intersection of two mutually perpendicular lines x+(k−1)y+3=0x + (k - 1)y + 3 = 0 and 2x+k2y−4=02x +k^{2}y - 4 = 0. If the line x−y+2=0x - y + 2 = 0 intersects the circle at the points A and B , then (AB)2(AB)^{2} is equal to :

    Tap an option to check your answer.

  5. Question 5

    Conic Sections. Asked once: 2 Apr 2025 (same type asked 4 times) See all 4 of this type

    52
    Let one focus of the hyperbola H:x2a2−y2b2=1H:\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}= 1 be at (10,0)(\sqrt{10},0) and the corresponding directrix be  x=910\ ^{x=\frac{9}{\sqrt{10}}}. If e and  l\ ^{l} respectively are the eccentricity and the length of the latus rectum of HH, then 9(e2+l)9\left( e^{2}+l \right) is equal to:

    Tap an option to check your answer.