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Day 451: JEE Mains Maths

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

  1. Question 1

    Trigonometric Identities. Asked once: 28 Jan 2026 S2

    65
    The sum of all the elements in the range of f(x)=Sgn(sin⁡x)+Sgn(cos⁡x)+Sgn(tan⁡x)+Sgn(cot⁡x)f(x) = Sgn(\sin x) + Sgn(\cos x) + Sgn(\tan x) + Sgn(\cot x), x≠nπ2,n∈Zx \neq\frac{n\pi}{2},n \in Z, where Sgn(t)={1, if t>0−1 if t<0Sgn(t) =\left\{ \begin{matrix} 1, & \text{~if~} & t> 0 \\ - 1 & \text{~if~} & t< 0 \end{matrix} \right., is

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  2. Question 2

    Vector Algebra. Asked once: 2 Apr 2026 S2

    66
    Two adjacent sides of a parallelogram PQRS are given by PQ→=j^+k^\overrightarrow{PQ}=\widehat{j}+\widehat{k} and PS→=i^−j^\overrightarrow{PS}=\widehat{i}-\widehat{j}. If the side PS is rotated about the point P by an acute angle α\alpha in the plane of the parallelogram so that it becomes perpendicular to the side PQ , then sin⁡2(5α2)−sin⁡2(α2)\sin^{2}\left( \frac{5\alpha}{2} \right)-\sin^{2}\left( \frac{\alpha}{2} \right) is equal to :

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  3. Question 3

    Application of Derivatives. Asked once: 24 Jan 2026 S1

    74
    Let (2α,α)(2\alpha,\alpha) be the largest interval in which the function f(t)=∣t+1∣t2,t<0f(t) = \frac{|t + 1|}{t^{2}},t < 0, is strictly decreasing. Then the local maximum value of the function g(x)=2log⁡e(x−2)+αx2+4x−α,x>2g(x) = 2\log_{e}(x - 2) + \alpha x^{2} + 4x - \alpha,x > 2, is ____\_\_\_\_

  4. Question 4

    Application of Integrals. Asked once: 4 Apr 2026 S1

    68
    The area of the region {(x,y):y≤π−∣x∣, y≤∣xsin⁡x∣, y≥0}\{(x,y):y \leq\pi- |x|,\ y \leq |x\sin x|,\ y \geq 0\} is :

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  5. Question 5

    Binomial Theorem. Asked once: 2 Apr 2026 S2

    56
    If for 3≤r≤303 \leq r \leq 30, ( 30C30−r)+3( 30C31−r)+3( 30C32−r)+( 30C33−r)= mCr,\left( \ ^{30}C_{30 - r} \right)+ 3\left( \ ^{30}C_{31 - r} \right)+ 3\left( \ ^{30}C_{32 - r} \right)+\left( \ ^{30}C_{33 - r} \right)=\ ^{m}C_{r}, then mm equals :

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