JEE Main 12th January 2019 Shift 1
For the following questions answer them individually
JEE Main 12th January 2019 Shift 1 - Question 81
For $$x \gt 1$$, if $$(2x)^{2y} = 4e^{2x-2y}$$, then $$(1 + \log_e 2x)^2 \frac{dy}{dx}$$ is equal to
JEE Main 12th January 2019 Shift 1 - Question 82
The maximum area (in sq. units) of a rectangle having its base on the x-axis and its other two vertices on the parabola, $$y = 12 - x^2$$ such that the rectangle lies inside the parabola, is:
JEE Main 12th January 2019 Shift 1 - Question 83
The integral $$\int \cos(\ln x) dx$$, is equal to
JEE Main 12th January 2019 Shift 1 - Question 84
Let f and g be continuous functions on [0, a] such that $$f(x) = f(a-x)$$ and $$g(x) + g(a-x) = 4$$, then $$\int_0^a f(x)g(x)dx$$ is equal to
JEE Main 12th January 2019 Shift 1 - Question 85
The area (in sq. units) of the region bounded by the parabola, $$y = x^2 + 2$$ and the lines, $$y = x + 1$$, $$x = 0$$ and $$x = 3$$, is
JEE Main 12th January 2019 Shift 1 - Question 86
Let $$y = y(x)$$ be the solution of the differential equation, $$x\frac{dy}{dx} + y = x\log_e x$$, $$(x > 1)$$. If $$2y(2) = \log_e 4 - 1$$, then $$y(e)$$ is equal to
JEE Main 12th January 2019 Shift 1 - Question 87
The sum of the distinct real values of $$\mu$$ for which the vectors $$\mu\hat{i} + \hat{j} + \hat{k}$$, $$\hat{i} + \mu\hat{j} + \hat{k}$$, $$\hat{i} + \hat{j} + \mu\hat{k}$$ are co-planar, is
JEE Main 12th January 2019 Shift 1 - Question 88
A tetrahedron has vertices P(1, 2, 1), Q(2, 1, 3), R(-1, 1, 2) and O(0, 0, 0). The angle between the faces OPQ and PQR is
JEE Main 12th January 2019 Shift 1 - Question 89
The perpendicular distance from the origin to the plane containing the two lines, $$\frac{x+2}{3} = \frac{y-2}{5} = \frac{z+5}{7}$$ and $$\frac{x-1}{1} = \frac{y-4}{4} = \frac{z+4}{7}$$, is
JEE Main 12th January 2019 Shift 1 - Question 90
In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to:
