PYQ Vault
EbooksTutor

Day 460: JEE Mains Maths

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

  1. Question 1

    Straight Lines. Asked once: 23 Jan 2026 S2

    54
    Let A(1,2)A(1,2) and C(−3,−6)C( - 3, - 6) be two diagonally opposite vertices of a rhombus, whose sides AD an BC are parallel to the line 7x−y=147x - y = 14. If B(α,β)B(\alpha,\beta) and D(γ,δ)D(\gamma,\delta) are the other two vertices, then ∣α+β+γ+δ∣|\alpha + \beta + \gamma + \delta| is equal to :

    Tap an option to check your answer.

  2. Question 2

    Three Dimensional Geometry. Asked once: 29 Jan 2025

    64
    Let a→=i^+2j^+k^\overrightarrow{a}=\widehat{i}+ 2\widehat{j}+\widehat{k} and b→=2i^+7j^+3k^\overrightarrow{b}= 2\widehat{i}+ 7\widehat{j}+ 3\widehat{k}. Let L1:r→=(−i^+2j^+k^)+λa→,λ∈RL_{1}:\overrightarrow{r}= ( -\widehat{i}+ 2\widehat{j}+\widehat{k}) + \lambda\overrightarrow{a},\lambda \in R and L2:r→=(j^+k^)+μb→,μ∈RL_{2}:\overrightarrow{r}= (\widehat{j}+\widehat{k}) + \mu\overrightarrow{b},\mu \in R be two lines. If the line L3L_{3} passes through the point of intersection of L1L_{1} and L2L_{2}, and is parallel to a→+b→\overrightarrow{a}+\overrightarrow{b}, then L3L_{3} passes through the point:

    Tap an option to check your answer.

  3. Question 3

    Trigonometric Equations. Asked once: 30 Jan 2023

    71
    If the solution of the equation log⁡cos⁡xcot⁡x+4log⁡sin⁡xtan⁡x=1,x∈(0,π2)\log_{\cos x}\cot x + 4\log_{\sin x}\tan x = 1,x \in\left( 0,\frac{\pi}{2} \right), is sin⁡−1(α+β2)\sin^{- 1}\left( \frac{\alpha +\sqrt{\beta}}{2} \right), where α\alpha and β\beta are integers, then α+β\alpha + \beta is equal to:

    Tap an option to check your answer.

  4. Question 4

    Trigonometric Identities. Asked once: 23 Jan 2026 S1

    68
    Let α\alpha and β\beta respectively be the maximum and the minimum values of the function f(θ)=4(sin⁡4(7π2−θ)+sin⁡4(11π+θ))f(\theta) = 4\left( \sin^{4}\left( \frac{7\pi}{2}- \theta \right)+\sin^{4}(11\pi + \theta) \right) −2(sin⁡6(3π2−θ)+sin⁡6(9π−θ)),θ∈R.- 2\left( \sin^{6}\left( \frac{3\pi}{2}- \theta \right)+\sin^{6}(9\pi - \theta) \right),\theta \in R. Then α+2β\alpha + 2\beta is equal to :

    Tap an option to check your answer.

  5. Question 5

    Vector Algebra. Asked once: 23 Jan 2026 S2

    53
    Let a→=i^−2j^+3k^,b→=2i^+j^−k^,c→=λi^+j^+k^\overrightarrow{a}=\widehat{i}- 2\widehat{j}+ 3\widehat{k},\overrightarrow{b}= 2\widehat{i}+\widehat{j}-\widehat{k},\overrightarrow{c}= \lambda\widehat{i}+\widehat{j}+\widehat{k} and v→=a→×b→\overrightarrow{v}=\overrightarrow{a}\times\overrightarrow{b}. If v→⋅c→=11\overrightarrow{v}\cdot\overrightarrow{c}= 11 and the length of the projection of b→\overrightarrow{b} on c→\overrightarrow{c} is pp, then 9p29p^{2} is equal to :

    Tap an option to check your answer.