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Day 352: MHT-CET Maths

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

  1. Question 1

    Permutations and Combinations. Asked once: 11 May 2023 S1 (same type asked 4 times) See all 4 of this type

    103
    How many numbers greater than a million can be formed with the digits 2, 3, 0, 3, 4, 2, 3?

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  2. Question 2

    Vectors. Asked once: 14 May 2024 S1 (same type asked 4 times) See all 4 of this type

    115
    If a⃗,b⃗,c⃗\vec{a},\vec{b},\vec{c} are unit vectors and θ\theta is angle between a⃗\vec{a} and c⃗\vec{c} and a⃗+2b⃗+2c⃗=0⃗\vec{a}+2\vec{b}+2\vec{c}=\vec{0}, then ∣a⃗×c⃗∣=|\vec{a}\times\vec{c}|=

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  3. Question 3

    Complex Numbers. Asked once: 9 May 2024 S1 (same type asked 4 times) See all 4 of this type

    110
    If Z1=4i40−5i35+6i17+2Z_1=4i^{40}-5i^{35}+6i^{17}+2, Z2=−1+iZ_2=-1+i, where i=−1i=\sqrt{-1}, then ∣Z1+Z2∣=|Z_1+Z_2|=

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  4. Question 4

    Linear Programming. Asked once: 2 May 2023 S1 (same type asked 4 times) See all 4 of this type

    143
    The point, at which the maximum value of 10x+6y10x + 6y subject to the constraints x+y≤12x+y \le 12, 2x+y≤202x+y \le 20, x≥0x \ge 0, y≥0y \ge 0 occurs, is

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  5. Question 5

    Vectors. Asked once: 16 May 2023 S1 (same type asked 4 times) See all 4 of this type

    115
    If [a⃗×b⃗    b⃗×c⃗    c⃗×a⃗]=λ[a⃗  b⃗  c⃗]2[\vec{a}\times\vec{b}\;\; \vec{b}\times\vec{c}\;\; \vec{c}\times\vec{a}] = \lambda[\vec{a}\;\vec{b}\;\vec{c}]^2, then λ\lambda is equal to

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