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Day 272: MHT-CET Maths

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

  1. Question 1

    Mathematical Logic. Asked once: 17 Apr 2026 S2 (same type asked 9 times) See all 9 of this type

    60
    The statement pattern [(p∧q)→(∼p∨r)]∨[(∼p∨r)→(p∧q)][(p \wedge q) \to (\sim p \vee r)] \vee [(\sim p \vee r) \to (p \wedge q)] is

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  2. Question 2

    Definite Integration. Asked once: 26 Apr 2025 S2 (same type asked 9 times) See all 9 of this type

    105
    ∫01x∣x−12∣dx=\int_{0}^{1} x\left| x-\frac{1}{2} \right|dx=

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  3. Question 3

    Mathematical Logic. Asked once: 26 Apr 2025 S2 (same type asked 9 times) See all 9 of this type

    107
    If p,q,r,sp, q, r, s are statements where p:A2−B2=(A−B)(A+B)p: A^{2}-B^{2}=(A-B)(A+B) for matrices A,BA, B with AB≠BAAB \neq BA; q:5≤5q: 5 \leq 5; r:8C1+8C2+8C3+⋯+8C8=256r: {}^{8}C_{1}+{}^{8}C_{2}+{}^{8}C_{3}+\cdots+{}^{8}C_{8}=256; s:s: the maximum value of 8Cr{}^{8}C_{r} is 70, then the statement from the following having truth value true is

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  4. Question 4

    Differentiation. Asked once: 13 May 2024 S2 (same type asked 9 times) See all 9 of this type

    127
    If slope of the tangent to the curve xy+ax+by=0xy+ax+by=0 at the point (1,1)(1,1) on it is 2, then the value of 3a+b3a+b is

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  5. Question 5

    Vectors. Asked once: 13 May 2024 S2 (same type asked 9 times) See all 9 of this type

    147
    a⃗=2i^+3j^+4k^,b⃗=i^−2j^+k^,c⃗=i^+j^−k^\vec{a}=2\hat{i}+3\hat{j}+4\hat{k},\vec{b}=\hat{i}-2\hat{j}+\hat{k},\vec{c}=\hat{i}+\hat{j}-\hat{k} are three vectors. For a vector r⃗\vec{r} with r⃗×a⃗=b⃗\vec{r}\times\vec{a}=\vec{b} and r⃗⋅c⃗=3\vec{r}\cdot\vec{c}=3, ∣r⃗∣|\vec{r}| is

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