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Day 423: MHT-CET Maths

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

  1. Question 1

    Line and Plane. Asked once: 15 May 2026 S2

    94
    If the direction cosines of the line 2x+53=2−3z−1; 3y=−2\dfrac{2x + 5}{3} = \dfrac{2 - 3z}{-1};\ 3y = -2 are 985, m, 285\dfrac{9}{\sqrt{85}},\ m,\ \dfrac{2}{\sqrt{85}} then the value of mm is:

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  2. Question 2

    Linear Programming. Asked once: 11 May 2023 S2

    122
    A production unit makes special type of metal chips by combining copper and brass. The standard weight of the chip must be at least 5 gms. The basic ingredients i.e. copper and brass cost ₹8 and ₹5 per gm. The durability considerations dictate that the metal chip must not contain more than 4 gms of brass and should contain minimum 2 gms of copper. Then the minimum cost of the metal chip satisfying the above conditions is

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  3. Question 3

    Mathematical Logic. Asked once: 14 May 2026 S1

    64
    The truth values of logical statements p,q,rp, q, r are T, T and F respectively. If ∗* and #\# are symbolic logical connectives such that (p#r)→(∼q#r)(p \# r) \to (\sim q \# r) is false and (∼p∗q)↔(∼q#r)(\sim p * q) \leftrightarrow (\sim q \# r) is true, then ∗* and #\# are respectively ____

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  4. Question 4

    Measures of Dispersion. Asked once: 10 May 2024 S1

    141
    Variance for first six prime numbers greater than 5 is

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  5. Question 5

    Pair of Straight Lines. Asked once: 12 May 2026 S1

    60
    If the sum of the slopes of the line represented by x2+kxy−3y2=0x^2 + kxy - 3y^2 = 0 is twice their product, then the acute angle between the lines x2+k xycsc⁡α+y2=0x^2 + k\,xy\csc\alpha + y^2 = 0 is ...

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