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Day 137: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 21 Jan 2026 S2 (same type asked 7 times) See all 7 of this type

    58
    Let the line L1L_{1} be parallel to the vector −3i^+2j^+4k^- 3\widehat{i}+ 2\widehat{j}+ 4\widehat{k} and pass through the point (2,6,7)(2,6,7) and the line L2L_{2} be parallel to the vector 2i^+j^+3k^2\widehat{i}+\widehat{j}+ 3\widehat{k} and pass through the point (4,3,5)(4,3,5). If the line L3L_{3} is parallel to the vector −3i^+5j^+16k^- 3\widehat{i}+ 5\widehat{j}+ 16\widehat{k} and intersects the lines L1L_{1} and L2L_{2} at the points C and D , respectively, then ∣CD→∣2|\overrightarrow{CD}|^{2} is equal to :

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  2. Question 2

    Limits and Continuity. Asked once: 22 Jan 2026 S2 (same type asked 7 times) See all 7 of this type

    65
    Let [∙]\lbrack \bullet \rbrack denote the greatest integer function, and let f(x)=min{2x,x2}f(x) = min\left\{ \sqrt{2}x,x^{2} \right\}. Let S={x∈(−2,2):\mathbf{S = \{ x \in ( - 2,2):} the function g(x)=∣x∣[x2]g(x) = |x|\left\lbrack x^{2} \right\rbrack is discontinuous at x}\}. Then ∑x∈Sf(x)\sum_{x \in S} f(x) equals :

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  3. Question 3

    Sequences and Series. Asked once: 4 Apr 2025 (same type asked 7 times) See all 7 of this type

    53
    Let A={1,6,11,16,…}A\mathbf{= \{ 1,6,11,16,\ldots\}} and B={9,16,23,30,…}B\mathbf{= \{ 9,16,23,30,\ldots\}} be the sets consisting of the first 2025 terms of two arithmetic progressions. Then n(A∪B)n(A\cup B) is.

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  4. Question 4

    Trigonometric Identities. Asked once: 24 Jan 2026 S1 (same type asked 7 times) See all 7 of this type

    58
    The value of 3csc⁡20∘−sec⁡20∘cos⁡20∘cos⁡40∘cos⁡60∘cos⁡80∘\frac{\sqrt{3}\csc20^{\circ}- \sec20^{\circ}}{\cos20^{\circ}\cos40^{\circ}\cos60^{\circ}\cos80^{\circ}} is equal to

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  5. Question 5

    Differential Equations. Asked once: 4 Apr 2025 (same type asked 7 times) See all 7 of this type

    141
    If a curve y=y(x)y = y(x) passes through the point (1,π2)\left( 1,\frac{\pi}{2} \right) and satisfies the differential equation (7x4cot⁡y−excsc⁡y)dxdy=x5,x≥1\left( 7x^{4}\cot y-e^{x}\csc y \right)\frac{dx}{dy}=x^{5},x\geq 1, then at x=2x= 2, the value of cosy is:

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