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Day 220: MHT-CET Maths

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

  1. Question 1

    Vectors. Asked once: 12 May 2024 S1 (same type asked 4 times) See all 4 of this type

    112
    If the area of the triangle with vertices (1,2,0)(1,2,0), (1,0,2)(1,0,2) and (0,x,1)(0,x,1) is 6\sqrt{6} square units, then the value of xx is

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  2. Question 2

    Applications of Derivative. Asked once: 26 Apr 2025 S1 (same type asked 4 times) See all 4 of this type

    135
    The equation of the tangent to the curve (1+x2)y=2−x\left( 1 +x^{2} \right)y= 2 -x, where it crosses the X -axis, is

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  3. Question 3

    Vectors. Asked once: 11 May 2024 S2 (same type asked 4 times) See all 4 of this type

    150
    The unit vector perpendicular to each of the vectors a⃗+b⃗\vec{a}+\vec{b} and a⃗−b⃗\vec{a}-\vec{b}, where a⃗=i^+j^+k^\vec{a}=\hat{i}+\hat{j}+\hat{k} and b⃗=3i^−2j^+5k^\vec{b}=3\hat{i}-2\hat{j}+5\hat{k} is:

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  4. Question 4

    Vectors. Asked once: 25 Apr 2025 S2 (same type asked 4 times) See all 4 of this type

    127
    If the vectors a‾=c(log⁡7x)i^+2j^+3k^\overline{a}= c\left( \log_{7}x \right)\widehat{i}+ 2\widehat{j}+ 3\widehat{k} and b‾=(log⁡7x)i^+3c(log⁡7x)j^−4k^\overline{b}=\left( \log_{7}x \right)\widehat{i}+ 3c\left( \log_{7}x \right)\widehat{j}- 4\widehat{k} make obtuse angle for any x>0x> 0, then c belongs to

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  5. Question 5

    Probability Distribution. Asked once: 19 Apr 2025 S1 (same type asked 4 times) See all 4 of this type

    116
    If a random variable X has the p.d.f. f(x)={kx2+1, if 0<x<∞0, otherwise f(x) =\left\{ \begin{matrix} \frac{k}{x^{2}+ 1} & ,\text{~if~}0 <x< \infty \\ 0 & ,\text{~otherwise~} \end{matrix} \right. then c.d.f. of X is

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