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Day 285: MHT-CET Maths

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

  1. Question 1

    Trigonometric Functions. Asked once: 12 May 2024 S1 (same type asked 6 times) See all 6 of this type

    130
    The solution set of 8cos⁡2θ+14cos⁡θ+5=08\cos^{2}\theta+14\cos\theta+5=0, in the interval [0,2π][0,2\pi] is

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  2. Question 2

    Vectors. Asked once: 21 Apr 2025 S1 (same type asked 6 times) See all 6 of this type

    115
    If a‾\overline{a} and b‾\overline{b} are unit vectors such that ∣a‾+b‾∣=3|\overline{a}+\overline{b}| =\sqrt{3}, then the angle between a‾\overline{a} and b‾\overline{b} is

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  3. Question 3

    Limits. Asked once: 13 May 2024 S2 (same type asked 6 times) See all 6 of this type

    116
    lim⁡x→01+xsin⁡x−cos⁡xtan⁡2(x/2)=\lim_{x\to0}\dfrac{\sqrt{1+x\sin x}-\sqrt{\cos x}}{\tan^2(x/2)}=

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  4. Question 4

    Trigonometric Functions. Asked once: 19 Apr 2025 S1 (same type asked 6 times) See all 6 of this type

    123
    If 4sin⁡−1x+cos⁡−1x=π4\sin^{- 1}x+\cos^{- 1}x=\pi then x=x=

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  5. Question 5

    Vectors. Asked once: 22 Apr 2025 S1 (same type asked 6 times) See all 6 of this type

    133
    The area of a parallelogram whose diagonals are the vectors 2aˉ−bˉ2\bar{a}-\bar{b} and 4aˉ−5bˉ4\bar{a}- 5\bar{b}, where aˉ\bar{a} and bˉ\bar{b} are unit vectors forming an angle of 45∘45^{\circ} is

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