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Day 342: MHT-CET Maths

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

  1. Question 1

    Trigonometric Functions. Asked once: 9 May 2024 S1 (same type asked 6 times) See all 6 of this type

    146
    If sin⁡−1x+cos⁡−1y=3π10\sin^{-1}x+\cos^{-1}y=\frac{3\pi}{10}, then the value of cos⁡−1x+sin⁡−1y\cos^{-1}x+\sin^{-1}y is

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  2. Question 2

    Vectors. Asked once: 10 May 2023 S1 (same type asked 6 times) See all 6 of this type

    135
    If ∣a⃗∣=2,∣b⃗∣=3|\vec{a}|=2,|\vec{b}|=3 and a⃗,b⃗\vec{a},\vec{b} are mutually perpendicular vectors, then the area of the triangle whose vertices are 0⃗, a⃗+2b⃗, a⃗−2b⃗\vec{0},\,\vec{a}+2\vec{b},\,\vec{a}-2\vec{b} is

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  3. Question 3

    Limits. Asked once: 3 May 2023 S2 (same type asked 6 times) See all 6 of this type

    138
    For each x∈Rx\in\mathbb{R}, let [x][x] represent greatest integer function, then lim⁡x→0−x([x]+∣x∣)sin⁡[x]∣x∣\lim_{x\to0^{-}}\frac{x([x]+|x|)\sin[x]}{|x|} is equal to

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  4. Question 4

    Trigonometric Functions. Asked once: 20 Apr 2025 S1 (same type asked 6 times) See all 6 of this type

    144
    In a triangle ABC with usual notations, if a,b,ca,b,c are in arithmetic progression, then, tan⁡A2⋅tan⁡C2=\tan\frac{A}{2}\cdot \tan\frac{C}{2}=

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  5. Question 5

    Determinants and Matrices. Asked once: 10 May 2023 S2 (same type asked 6 times) See all 6 of this type

    127
    Inverse of the matrix (0.8−0.60.60.8)\begin{pmatrix}0.8&-0.6\\0.6&0.8\end{pmatrix} is

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