NTA JEE Main 8th April 2017 Online
For the following questions answer them individually
NTA JEE Main 8th April 2017 Online - Question 81
The tangent at the point $$(2, -2)$$ to the curve, $$x^2y^2 - 2x = 4(1-y)$$ does not pass through the point:
NTA JEE Main 8th April 2017 Online - Question 82
The integral $$\displaystyle\int \sqrt{1 + 2\cot x(\csc x + \cot x)}\,dx$$, $$\left(0 \lt x \lt \frac{\pi}{2}\right)$$ is equal to:
NTA JEE Main 8th April 2017 Online - Question 83
The integral $$\displaystyle\int_{\pi/12}^{\pi/4} \frac{8\cos 2x}{(\tan x + \cot x)^3}\,dx$$ equals:
NTA JEE Main 8th April 2017 Online - Question 84
The area (in sq. units) of the smaller portion enclosed between the curves, $$x^2 + y^2 = 4$$ and $$y^2 = 3x$$, is:
NTA JEE Main 8th April 2017 Online - Question 85
The curve satisfying the differential equation, $$ydx - (x + 3y^2)dy = 0$$ and passing through the point $$(1, 1)$$ also passes through the point:
NTA JEE Main 8th April 2017 Online - Question 86
The area (in sq. units) of the parallelogram whose diagonals are along the vectors $$8\hat{i} - 6\hat{j}$$ and $$3\hat{i} + 4\hat{j} - 12\hat{k}$$, is:
NTA JEE Main 8th April 2017 Online - Question 87
The coordinates of the foot of the perpendicular from the point $$(1, -2, 1)$$ on the plane containing the lines $$\frac{x+1}{6} = \frac{y-1}{7} = \frac{z-3}{8}$$ and $$\frac{x-1}{3} = \frac{y-2}{5} = \frac{z-3}{7}$$, is:
NTA JEE Main 8th April 2017 Online - Question 88
The line of intersection of the planes $$\vec{r} \cdot (3\hat{i} - \hat{j} + \hat{k}) = 1$$ and $$\vec{r} \cdot (\hat{i} + 4\hat{j} - 2\hat{k}) = 2$$, is:
NTA JEE Main 8th April 2017 Online - Question 89
An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is:
NTA JEE Main 8th April 2017 Online - Question 90
Three persons P, Q and R independently try to hit a target. If the probabilities of their hitting the target are $$\frac{3}{4}$$, $$\frac{1}{2}$$ and $$\frac{5}{8}$$ respectively, then the probability that the target is hit by P or Q but not by R is:
