PYQ Vault

Day 522: MHT-CET Maths

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

  1. Question 1

    Differentiation. Asked once: 19 Apr 2025 S1

    134
    f(x)=(cos⁡x+isinx).(cos⁡3x+isin3x)⋯f(x) = (\cos x+ isinx).(\cos3x+ isin3x)\cdots, [cos⁡(2n−1)x+isin(2n−1)x]n∈N\lbrack \cos(2n - 1)x+ isin(2n - 1)x\rbrack n \in\mathbb{N}Then f′′(x)=f^{''}(x) = ____\_\_\_\_ , (Where i=−1i =\sqrt{- 1} )

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  2. Question 2

    Indefinite Integration. Asked once: 22 Apr 2025 S1

    131
    ∫cos⁡2x−cos⁡2αcos⁡x−cos⁡αdx=\int\frac{\cos2x- \cos2\alpha}{\cos x- \cos\alpha}dx=

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  3. Question 3

    Line and Plane. Asked once: 21 Apr 2025 S2

    137
    The length of the altitude through the point D of tetrahedron where the vertices of the tetrahedron are A(2,3,1),B(4,1,−2),C(6,3,7),D(−5,−4,8)A(2,3,1),B(4,1, - 2),C(6,3,7),D( - 5, - 4,8), is

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  4. Question 4

    Trigonometric Functions. Asked once: 21 Apr 2025 S1

    121
    If sin⁡−113+sin⁡−135+sin⁡−1x=π2\sin^{- 1}\frac{1}{3}+\sin^{- 1}\frac{3}{5}+\sin^{- 1}x=\frac{\pi}{2} then x=x=

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  5. Question 5

    Vectors. Asked once: 23 Apr 2025 S1

    120
    The area of the rectangle having vertices P,Q,R,SP,Q,R,S with position vectors −i^+j^+k^,i^+j^+k^,i^−j^+k^,−i^−j^+k^-\widehat{i}+\widehat{j}+\widehat{k},\widehat{i}+\widehat{j}+\widehat{k},\widehat{i}-\widehat{j}+\widehat{k}, -\widehat{i}-\widehat{j}+\widehat{k} respectively is

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