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Day 538: MHT-CET Maths

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

  1. Question 1

    Vectors. Asked once: 12 May 2024 S2

    121
    A, B, C, D are four points in a plane with position vectors a⃗,b⃗,c⃗,d⃗\vec{a}, \vec{b}, \vec{c}, \vec{d} respectively such that (a⃗−d⃗)⋅(b⃗−c⃗)=(b⃗−d⃗)⋅(c⃗−a⃗)=0(\vec{a}-\vec{d})\cdot(\vec{b}-\vec{c}) = (\vec{b}-\vec{d})\cdot(\vec{c}-\vec{a}) = 0. The point D, then is the ___ of △ABC\triangle ABC.

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  2. Question 2

    Indefinite Integration. Asked once: 11 May 2024 S2

    141
    ∫x2sin⁡(x2+1)−sin⁡2(x2+1)2sin⁡(x2+1)+sin⁡2(x2+1) dx=\int\frac{x^2\sin(x^2+1)-\sin 2(x^2+1)}{2\sin(x^2+1)+\sin 2(x^2+1)}\,dx =

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  3. Question 3

    Line and Plane. Asked once: 11 May 2023 S2

    118
    A variable plane passes through the fixed point (3,2,1)(3,2,1) and meets X, Y and Z axes at points A, B and C respectively. A plane is drawn parallel to YZ-plane through A, a second plane parallel to ZX-plane through B, a third plane parallel to XY-plane through C. Then locus of the point of intersection of these three planes, is

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  4. Question 4

    Trigonometric Functions. Asked once: 10 May 2024 S2

    107
    If x,y,zx,y,z are in A.P. and tan⁡−1x,tan⁡−1y\tan^{-1}x,\tan^{-1}y and tan⁡−1z\tan^{-1}z are also in A.P., then

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  5. Question 5

    Vectors. Asked once: 12 May 2024 S2

    133
    If ∣u⃗∣=8|\vec{u}| = 8, ∣v⃗∣=12|\vec{v}| = 12 and the angle between them is 150∘150^\circ, then ∣u⃗×v⃗∣|\vec{u} \times \vec{v}| is

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