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Day 235: MHT-CET Maths

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

  1. Question 1

    Determinants and Matrices. Asked once: 15 Apr 2026 S2 (same type asked 3 times) See all 3 of this type

    68
    The element in the third row and the second column in the inverse matrix of a matrix [133313334]\begin{bmatrix} 1 & 3 & 3 \\ 3 & 1 & 3 \\ 3 & 3 & 4 \end{bmatrix} is

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  2. Question 2

    Trigonometric Functions. Asked once: 9 May 2024 S2 (same type asked 3 times) See all 3 of this type

    103
    The value of tan⁡−1 ⁣ ⁣(1+x2+1−x21+x2−1−x2),  ∣x∣<12,  x≠0\tan^{-1}\!\!\left(\dfrac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}\right),\;|x| < \frac{1}{\sqrt{2}},\; x \neq 0

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  3. Question 3

    Applications of Derivative. Asked once: 15 Apr 2026 S2 (same type asked 3 times) See all 3 of this type

    75
    The maximum value of (1x)x,x>0\left(\dfrac{1}{x}\right)^x, x > 0 is

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  4. Question 4

    Line and Plane. Asked once: 26 Apr 2025 S2 (same type asked 3 times) See all 3 of this type

    131
    The lines 6x−618=y+13=z−15\frac{6x- 6}{18}=\frac{y+ 1}{3}=\frac{z- 1}{5} and 3x+612=y−13=z+12\frac{3x+ 6}{12}=\frac{y- 1}{3}=\frac{z+ 1}{2} are...

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  5. Question 5

    Sets, Relations and Functions. Asked once: 10 May 2023 S2 (same type asked 3 times) See all 3 of this type

    147
    Let f(x)=αxx+1, x≠−1f(x) = \frac{\alpha x}{x+1},\, x \neq -1, then for α= ?\alpha = \,?, f(f(x))=xf(f(x)) = x.

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