WB JEE 2020 | Application of Derivatives Question 39 | Mathematics

WB JEE 2020

MCQ (More than One Correct Answer)

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Tangent is drawn at any point P(x, y) on a curve, which passes through (1, 1). The tangent cuts X-axis and Y-axis at A and B respectively. If AP : BP = 3 : 1, then

The differential equation of the curve is $$3x{{dy} \over {dx}} + y = 0$$

the differential equation of the curve is $$3x{{dy} \over {dx}} - y = 0$$

the curve passes through $$\left( {{1 \over 8},2} \right)$$

the normal at (1, 1) is x + 3y = 4

WB JEE 2019

MCQ (More than One Correct Answer)

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Two particles A and B move from rest along a straight line with constant accelerations f and h, respectively. If A takes m seconds more than B and describes n units more than that of B acquiring the same speed, then

$$(f + h){m^2} = fhn$$

$$(f - h){m^2} = fhn$$

$$(h - f)n = {1 \over 2}fh{m^2}$$

$${1 \over 2}(f + h)n = fh{m^2}$$

WB JEE 2018

MCQ (More than One Correct Answer)

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A particle is in motion along a curve 12y = x³. The rate of change of its ordinate exceeds that of abscissa in

$$-$$ 2 < x < 2

x = $$ \pm $$ 2

x < $$-$$2

x > 2

WB JEE 2018

MCQ (More than One Correct Answer)

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Let $$f(x) = \cos \left( {{\pi \over x}} \right),x \ne 0$$, then assuming k as an integer,

f(x) increases in the interval $$\left( {{1 \over {2k + 1}},{1 \over {2k}}} \right)$$

f(x) decreases in the interval $$\left( {{1 \over {2k + 1}},{1 \over {2k}}} \right)$$

f(x) decreases in the interval $$\left( {{1 \over {2k + 2}},{1 \over {2k + 1}}} \right)$$

f(x) increases in the interval $$\left( {{1 \over {2k + 2}},{1 \over {2k + 1}}} \right)$$

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