NTA JEE Main 2nd April 2017 Offline
For the following questions answer them individually
NTA JEE Main 2nd April 2017 Offline - Question 71
$$\lim_{x \to \frac{\pi}{2}} \frac{\cot x - \cos x}{(\pi - 2x)^{3}}$$ equals
NTA JEE Main 2nd April 2017 Offline - Question 72
The statement $$p \to q \to (\sim p \to q \to q)$$ is
NTA JEE Main 2nd April 2017 Offline - Question 73
A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is:
NTA JEE Main 2nd April 2017 Offline - Question 74
Let a vertical tower $$AB$$ have its end $$A$$ on the level ground. Let $$C$$ be the mid-point of $$AB$$ and $$P$$ be a point on the ground such that $$AP = 2AB$$. If $$\angle BPC = \beta$$, then $$\tan\beta$$ is equal to:
NTA JEE Main 2nd April 2017 Offline - Question 75
If $$A = \begin{pmatrix} 2 & -3 \\ -4 & 1 \end{pmatrix}$$, then Adj$$(3A^{2} + 12A)$$ is equal to:
NTA JEE Main 2nd April 2017 Offline - Question 76
If $$S$$ is the set of distinct values of $$b$$ for which the following system of linear equations
$$x + y + z = 1$$
$$x + ay + z = 1$$
$$ax + by + z = 0$$
has no solution, then $$S$$ is:
NTA JEE Main 2nd April 2017 Offline - Question 77
The function $$f : R \to \left(-\frac{1}{2}, \frac{1}{2}\right)$$ defined as $$f(x) = \frac{x}{1+x^{2}}$$, is:
NTA JEE Main 2nd April 2017 Offline - Question 78
Let $$a, b, c \in R$$. If $$f(x) = ax^{2} + bx + c$$ is such that $$a + b + c = 3$$ and $$f(x + y) = f(x) + f(y) + xy$$, $$\forall$$ $$x, y \in R$$, then $$\sum_{n=1}^{10} f(n)$$ is equal to:
NTA JEE Main 2nd April 2017 Offline - Question 79
If for $$x \in \left(0, \frac{1}{4}\right)$$, the derivative of $$\tan^{-1}\left(\frac{6x\sqrt{x}}{1-9x^{3}}\right)$$ is $$\sqrt{x} \cdot g(x)$$, then $$g(x)$$ equals:
NTA JEE Main 2nd April 2017 Offline - Question 80
Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is:
