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Day 323: MHT-CET Maths

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

  1. Question 1

    Vectors. Asked once: 10 May 2023 S2 (same type asked 3 times) See all 3 of this type

    124
    Given a⃗=i^+j^+k^\vec{a} = \hat{i}+\hat{j}+\hat{k}, b⃗=4i^−2j^+3k^\vec{b} = 4\hat{i}-2\hat{j}+3\hat{k}, c⃗=i^−2j^+k^\vec{c} = \hat{i}-2\hat{j}+\hat{k}, then a vector of magnitude 6 units, which is parallel to the vector 2a⃗−b⃗+3c⃗2\vec{a}-\vec{b}+3\vec{c}, is

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  2. Question 2

    Mathematical Logic. Asked once: May 2021 S1 (same type asked 3 times) See all 3 of this type

    114
    Consider the following statements: r: If a number is a multiple of 9, then it is a multiple of 3. Let pp: A number is a multiple of 9, and qq: A number is a multiple of 3. Then, 'if p then q' is the same as

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  3. Question 3

    Straight Line. Asked once: May 2021 S1 (same type asked 2 times) See all 2 of this type

    106
    A line through the point A(2,0)A(2,0) which makes an angle of 30∘30^\circ with the positive direction of X-axis is rotated about AA in clockwise direction through an angle of 15∘15^\circ. Then, the equation of the straight line in the new position is

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  4. Question 4

    Mathematical Logic. Asked once: 14 May 2026 S2 (same type asked 19 times) See all 19 of this type

    64
    [(p∧q)∨(∼r∨∼s∨∼t)]∧[(p∧q)∨(r∧s∧t)]≡[(p \wedge q) \vee (\sim r \vee \sim s \vee \sim t)] \wedge [(p \wedge q) \vee (r \wedge s \wedge t)] \equiv

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  5. Question 5

    Differential Equations. Asked once: 21 Apr 2025 S2 (same type asked 15 times) See all 15 of this type

    102
    A particular solution of 3extan⁡y dx+(1−ex)sec⁡2y dy=03e^{x}\tan y\text{ }dx+\left( 1 -e^{x} \right)\sec^{2}y\text{ }dy= 0 with y(1)=π4y(1) =\frac{\pi}{4} is

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