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Day 370: MHT-CET Maths

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

  1. Question 1

    Mathematical Logic. Asked once: 2 May 2023 S2 (same type asked 7 times) See all 7 of this type

    142
    The negation of contrapositive of the statement p→(¬q∧r)p\to(\neg q \wedge r) is

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  2. Question 2

    Indefinite Integration. Asked once: 2 May 2023 S2 (same type asked 7 times) See all 7 of this type

    106
    If ∫x+12x−1 dx=f(x)2x−1+c\int \frac{x+1}{\sqrt{2x-1}}\,dx = f(x)\sqrt{2x-1} + c, then f(x)f(x) is equal to

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  3. Question 3

    Limits. Asked once: 10 May 2023 S2 (same type asked 7 times) See all 7 of this type

    129
    If f(x)=(1+tan⁡x1+sin⁡x)csc⁡xf(x) = \left(\frac{1+\tan x}{1+\sin x}\right)^{\csc x} is continuous at x=0x=0, then f(0)f(0) is equal to

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  4. Question 4

    Line and Plane. Asked once: 13 May 2024 S2 (same type asked 7 times) See all 7 of this type

    130
    The foot of the perpendicular from the point (1,2,3)(1,2,3) on the line r⃗=(6i^+7j^+7k^)+λ(3i^+2j^−2k^)\vec{r}=(6\hat{i}+7\hat{j}+7\hat{k})+\lambda(3\hat{i}+2\hat{j}-2\hat{k}) has the co-ordinates.

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  5. Question 5

    Differentiation. Asked once: 22 Apr 2025 S1 (same type asked 7 times) See all 7 of this type

    147
    If x=acos3θy=asin3θx=acos^{3}\theta y=asin^{3}\theta Then 1+(dy dx)2=\sqrt{1 +\left( \frac{dy}{\text{ }dx} \right)^{2}}=

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