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Day 318: MHT-CET Maths

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

  1. Question 1

    Sets, Relations and Functions. Asked once: 4 May 2023 S2 (same type asked 3 times) See all 3 of this type

    134
    If f(x)=x2−xf(x)=\dfrac{x}{2-x}, g(x)=x+1x+2g(x)=\dfrac{x+1}{x+2}, then (g∘g∘f)(x)=(g\circ g\circ f)(x)=

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  2. Question 2

    Probability Distribution. Asked once: 11 May 2024 S1 (same type asked 3 times) See all 3 of this type

    104
    From a lot of 20 baskets, which includes 6 defective baskets, a sample of 2 baskets is drawn at random one by one without replacement. The expected value of number of defective baskets is

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  3. Question 3

    Vectors. Asked once: 16 May 2023 S2 (same type asked 3 times) See all 3 of this type

    117
    If a⃗\vec{a} is perpendicular to b⃗\vec{b} and c⃗\vec{c}, ∣a⃗∣=2|\vec{a}|=2, ∣b⃗∣=3|\vec{b}|=3, ∣c⃗∣=4|\vec{c}|=4 and the angle between b⃗\vec{b} and c⃗\vec{c} is π3\frac{\pi}{3}, then [a⃗ b⃗ c⃗]=[\vec{a}\,\vec{b}\,\vec{c}] =

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  4. Question 4

    Determinants and Matrices. Asked once: 13 Apr 2026 S2 (same type asked 3 times) See all 3 of this type

    65
    The element in 1st row and 2nd column of the inverse of the matrix [13−2−30−5250]\begin{bmatrix} 1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 0 \end{bmatrix} is ...

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  5. Question 5

    Trigonometric Functions. Asked once: 11 May 2023 S1 (same type asked 3 times) See all 3 of this type

    126
    The value of tan⁡−1(1+x−1−x1+x+1−x)+12cos⁡−1x\tan^{-1}\left(\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\right) + \frac{1}{2}\cos^{-1}x is

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