JEE Main 2019 (Online) 10th January Evening Slot | Differential Equations Question 116 | Mathematics

JEE Main 2019 (Online) 10th January Evening Slot

MCQ (Single Correct Answer)

-1

The curve amongst the family of curves represented by the differential equation, (x² – y²)dx + 2xy dy = 0 which passes through (1, 1) is

a circle with centre on the y-axis

an ellipse with major axis along the y-axis

a circle with centre on the x-axis

a hyperbola with transverse axis along the x-axis

JEE Main 2019 (Online) 10th January Evening Slot

MCQ (Single Correct Answer)

-1

Let f be a differentiable function such that f '(x) = 7 - $${3 \over 4}{{f\left( x \right)} \over x},$$ (x > 0) and f(1) $$ \ne $$ 4. Then $$\mathop {\lim }\limits_{x \to 0'} \,$$ xf$$\left( {{1 \over x}} \right)$$

does not exist

exists and equals $${4 \over 7}$$

exists and equals 4

exists and equals 0

JEE Main 2019 (Online) 10th January Evening Slot

MCQ (Single Correct Answer)

-1

A helicopter is flying along the curve given by y – x^3/2 = 7, (x $$ \ge $$ 0). A soldier positioned at the point $$\left( {{1 \over 2},7} \right)$$ wants to shoot down the helicopter when it is nearest to him. Then this nearest distance is -

$${1 \over 6}\sqrt {{7 \over 3}} $$

$${{\sqrt 5 } \over 6}$$

$${1 \over 2}$$

$${1 \over 3}$$$$\sqrt {{7 \over 3}} $$

JEE Main 2019 (Online) 9th January Evening Slot

MCQ (Single Correct Answer)

-1

Let f : [0,1] $$ \to $$ R be such that f(xy) = f(x).f(y), for all x, y $$ \in $$ [0, 1], and f(0) $$ \ne $$ 0. If y = y(x) satiesfies the differential equation, $${{dy} \over {dx}}$$ = f(x) with y(0) = 1, then y$$\left( {{1 \over 4}} \right)$$ + y$$\left( {{3 \over 4}} \right)$$ is equal to :