NTA JEE Main 6th April 2014 Offline
For the following questions answer them individually
NTA JEE Main 6th April 2014 Offline - Question 71
The locus of the foot of perpendicular drawn from the centre of the ellipse $$x^2 + 3y^2 = 6$$ on any tangent to it is:
NTA JEE Main 6th April 2014 Offline - Question 72
$$\lim_{x \to 0} \frac{\sin(\pi \cos^2 x)}{x^2}$$ is equal to:
NTA JEE Main 6th April 2014 Offline - Question 73
The statement $$\sim(p \leftrightarrow \sim q)$$ is:
NTA JEE Main 6th April 2014 Offline - Question 74
The variance of the first 50 even natural numbers is:
NTA JEE Main 6th April 2014 Offline - Question 75
A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45°. It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to 30°. Then the speed (in m/s) of the bird is:
NTA JEE Main 6th April 2014 Offline - Question 76
If $$X = \{4^n - 3n - 1 : n \in N\}$$ and $$Y = \{9(n-1) : n \in N\}$$, where $$N$$ is the set of natural numbers, then $$X \cup Y$$ is equal to:
NTA JEE Main 6th April 2014 Offline - Question 77
If $$A$$ is a $$3 \times 3$$ non-singular matrix such that $$AA' = A'A$$ and $$B = A^{-1}A'$$, then $$BB'$$ equals, where $$X'$$ denotes the transpose of the matrix $$X$$.
NTA JEE Main 6th April 2014 Offline - Question 78
If $$\alpha$$, $$\beta \neq 0$$, $$f(n) = \alpha^n + \beta^n$$ and $$\begin{vmatrix} 3 & 1+f(1) & 1+f(2) \\ 1+f(1) & 1+f(2) & 1+f(3) \\ 1+f(2) & 1+f(3) & 1+f(4) \end{vmatrix} = K(1-\alpha)^2(1-\beta)^2(\alpha - \beta)^2$$, then K is equal to:
NTA JEE Main 6th April 2014 Offline - Question 79
If $$g$$ is the inverse of a function $$f$$ and $$f'(x) = \frac{1}{1+x^5}$$, then $$g'(x)$$ is equal to:
NTA JEE Main 6th April 2014 Offline - Question 80
If $$f$$ & $$g$$ are differentiable functions in $$[0, 1]$$ satisfying $$f(0) = 2 = g(1)$$, $$g(0) = 0$$ & $$f(1) = 6$$, then for some $$c \in ]0, 1[$$:
