NTA JEE Main 9th April 2014 Online
For the following questions answer them individually
NTA JEE Main 9th April 2014 Online - Question 81
If $$f(x) = \left(\frac{3}{5}\right)^x + \left(\frac{4}{5}\right)^x - 1$$, $$x \in R$$, then the equation $$f(x) = 0$$ has:
NTA JEE Main 9th April 2014 Online - Question 82
If the Rolle's theorem holds for the function $$f(x) = 2x^3 + ax^2 + bx$$ in the interval $$[-1, 1]$$ for the point $$c = \frac{1}{2}$$, then the value of $$2a + b$$ is:
NTA JEE Main 9th April 2014 Online - Question 83
$$\int \frac{\sin^8 x - \cos^8 x}{1 - 2\sin^2 x \cos^2 x} dx$$ is equal to:
NTA JEE Main 9th April 2014 Online - Question 84
The integral $$\int_0^{\frac{1}{2}} \frac{\ln(1+2x)}{1+4x^2} dx$$ equals:
NTA JEE Main 9th April 2014 Online - Question 85
Let $$A = \{(x, y) : y^2 \leq 4x, y - 2x \geq -4\}$$. The area of the region $$A$$ in square units is:
NTA JEE Main 9th April 2014 Online - Question 86
If the differential equation representing the family of all circles touching $$x$$-axis at the origin is $$(x^2 - y^2)\frac{dy}{dx} = g(x)y$$, then $$g(x)$$ equals:
NTA JEE Main 9th April 2014 Online - Question 87
If $$|\vec{a}| = 2$$, $$|\vec{b}| = 3$$ and $$|2\vec{a} - \vec{b}| = 5$$, then $$|2\vec{a} + \vec{b}|$$ equals:
NTA JEE Main 9th April 2014 Online - Question 88
Equation of the plane which passes through the point of intersection of lines $$\frac{x-1}{3} = \frac{y-2}{1} = \frac{z-3}{2}$$ and $$\frac{x-3}{1} = \frac{y-1}{-2} = \frac{z-2}{3}$$ and has the largest distance from the origin is:
NTA JEE Main 9th April 2014 Online - Question 89
A line in the 3-dimensional space makes an angle $$\theta$$ ($$0 < \theta \leq \frac{\pi}{2}$$) with both the X and Y-axes. Then, the set of all values of $$\theta$$ is in the interval:
NTA JEE Main 9th April 2014 Online - Question 90
If $$A$$ and $$B$$ are two events such that $$P(A \cup B) = P(A \cap B)$$, then the incorrect statement amongst the following statements is:
