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Day 236: MHT-CET Maths

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

  1. Question 1

    Trigonometric Functions. Asked once: 11 May 2023 S2 (same type asked 3 times) See all 3 of this type

    139
    If the sides of a triangle a,b,ca,b,c are in A.P., then with usual notations, acos⁡2C2+ccos⁡2A2a\cos^2\frac{C}{2}+c\cos^2\frac{A}{2} is

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  2. Question 2

    Pair of Straight Lines. Asked once: 14 May 2024 S2 (same type asked 3 times) See all 3 of this type

    129
    The centroid of the triangle formed by the lines x+3y=10x+3y=10 and 6x2+xy−y2=06x^2+xy-y^2=0 is

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  3. Question 3

    Probability Distribution. Asked once: 11 Apr 2026 S2 (same type asked 3 times) See all 3 of this type

    100
    If events A and B are such that P(A)=14,P(A∩B)=110P(A) = \dfrac{1}{4}, P(A \cap B) = \dfrac{1}{10} and P(A/B)=2P(B/A)P(A/B) = 2P(B/A) then P(B)=P(B) =...........

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  4. Question 4

    Applications of Derivative. Asked once: 21 Apr 2025 S2 (same type asked 3 times) See all 3 of this type

    145
    A wire of length 8 units is cut into two parts which are bent respectively in the form of a square and a circle. The least value of the sum of the areas so formed is

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  5. Question 5

    Line and Plane. Asked once: 21 Apr 2025 S1 (same type asked 3 times) See all 3 of this type

    140
    If the distance of the point P(1,−2,1)P(1, - 2,1) from the plane x+2y−2z=αx+ 2y- 2z=\alpha, where α>0\alpha> 0 is 5 units, then the foot of the perpendicular from P to the plane is

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