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Day 239: MHT-CET Maths

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

  1. Question 1

    Applications of Derivative. Asked once: 12 May 2024 S1 (same type asked 3 times) See all 3 of this type

    107
    The approximate value of sin⁡60∘0′10′′\sin 60^{\circ}0'10'' is (given that 3=1.732\sqrt{3}=1.732, 1∘=0.0175∘1^{\circ}=0.0175^{\circ})

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  2. Question 2

    Line and Plane. Asked once: 2 May 2023 S2 (same type asked 3 times) See all 3 of this type

    109
    Distance between the parallel lines x3=y−1−2=z1\frac{x}{3} = \frac{y-1}{-2} = \frac{z}{1} and x+43=y−3−2=z+21\frac{x+4}{3} = \frac{y-3}{-2} = \frac{z+2}{1} is

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  3. Question 3

    Trigonometric Functions. Asked once: 15 May 2023 S2 (same type asked 3 times) See all 3 of this type

    143
    In a triangle ABC, with usual notations, cos⁡B+cos⁡Cb+c+cos⁡Aa\frac{\cos B+\cos C}{b+c}+\frac{\cos A}{a} has the value

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  4. Question 4

    Binomial Distribution. Asked once: 9 May 2023 S2 (same type asked 3 times) See all 3 of this type

    144
    A bag contains 4 red and 3 black balls. One ball is drawn and then replaced in the bag and the process is repeated. Let X denote the number of times black ball is drawn in 3 draws. Assuming that at each draw each ball is equally likely to be selected, then probability distribution of X is given by

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  5. Question 5

    Definite Integration. Asked once: 11 May 2024 S1 (same type asked 3 times) See all 3 of this type

    115
    Let f(x)f(x) be positive for all real xx. If I1=∫1−hhxf(x(1−x)) dxI_1 = \int_{1-h}^{h} xf(x(1-x))\,dx and I2=∫1−hhf(x(1−x)) dxI_2 = \int_{1-h}^{h} f(x(1-x))\,dx, where (2h−1)>0(2h-1) > 0, then I1I2\frac{I_1}{I_2} is

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