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Day 494: MHT-CET Maths

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

  1. Question 1

    Sets, Relations and Functions. Asked once: May 2021 S1

    126
    If f(x)=sin⁡2x+sin⁡2 ⁣(x+π3)+cos⁡xcos⁡ ⁣(x+π3)f(x) = \sin^2 x + \sin^2\!\left(x+\frac{\pi}{3}\right) + \cos x\cos\!\left(x+\frac{\pi}{3}\right) and g ⁣(54)=1g\!\left(\frac{5}{4}\right) = 1, then g(f(x))g(f(x)) is equal to

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  2. Question 2

    Straight Line. Asked once: 16 May 2023 S1

    140
    Suppose that the points (h,k)(h,k), (1,2)(1,2) and (−3,4)(-3,4) lie on the line l1l_1. If a line l2l_2 passing through the points (h,k)(h,k) and (4,3)(4,3) is perpendicular to l1l_1, then kh\frac{k}{h} equals

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  3. Question 3

    Trigonometric Functions. Asked once: 15 Apr 2026 S2

    57
    If sec⁡4θ−sec⁡2θ=2\sec 4\theta - \sec 2\theta = 2, then θ=\theta =

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  4. Question 4

    Trigonometry - II. Asked once: 19 Apr 2025 S2

    112
    If tan⁡A=1x(x2+x+1),tan⁡B=xx2+x+1\tan A =\frac{1}{\sqrt{x\left( x^{2}+x+ 1 \right)}},\tan B =\frac{\sqrt{x}}{\sqrt{x^{2}+x+ 1}} and tan⁡C=x−1+x−2+x−3\tan C =\sqrt{x^{- 1}+x^{- 2}+x^{- 3}} then

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  5. Question 5

    Vectors. Asked once: 20 Apr 2026 S1

    90
    Let OD‾=i^+2j^+6k^,CB‾=−3i^−2k^\overline{OD} = \hat{i} + 2\hat{j} + 6\hat{k}, \overline{CB} = -3\hat{i} - 2\hat{k} be the diagonals of the parallelogram OBDC and OA‾=i^+2j^+3k^\overline{OA} = \hat{i} + 2\hat{j} + 3\hat{k} be another vector. Then the volume of a parallelopiped determined by vectors OA‾\overline{OA}, OB‾\overline{OB}, and OC‾\overline{OC} (in cubic units), is

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