JEE Main 11th January 2019 Shift 2
For the following questions answer them individually
JEE Main 11th January 2019 Shift 2 - Question 71
$$\lim_{x \to 0} \frac{x \cot(4x)}{\sin^2 x \cot^2(2x)}$$ is equal to:
JEE Main 11th January 2019 Shift 2 - Question 72
Contrapositive of the statement "If two numbers are not equal, then their squares are not equal" is:
JEE Main 11th January 2019 Shift 2 - Question 73
Given $$\frac{b+c}{11} = \frac{c+a}{12} = \frac{a+b}{13}$$ for a $$\Delta ABC$$ with usual notation. If $$\frac{\cos A}{a} = \frac{\cos B}{\beta} = \frac{\cos C}{\gamma}$$, then the ordered triad $$(\alpha, \beta, \gamma)$$ has a value:
JEE Main 11th January 2019 Shift 2 - Question 74
If $$\begin{vmatrix} a-b-c & 2a & 2a \\ 2b & b-c-a & 2b \\ 2c & 2c & c-a-b \end{vmatrix} = (a + b + c)(x + a + b + c)^2$$, $$x \neq 0$$ and $$a + b + c \neq 0$$, then x is equal to
JEE Main 11th January 2019 Shift 2 - Question 75
Let A and B be two invertible matrices of order $$3 \times 3$$. If $$\det(ABA^T) = 8$$ and $$\det(AB^{-1}) = 8$$, then $$\det(BA^{-1}B^T)$$ is equal to
JEE Main 11th January 2019 Shift 2 - Question 76
All $$x$$ satisfying the inequality $$(\cot^{-1} x)^2 - 7(\cot^{-1} x) + 10 > 0$$, lie in the interval:
JEE Main 11th January 2019 Shift 2 - Question 77
Let a function $$f : (0, \infty) \to (0, \infty)$$ be defined by $$f(x) = \left|1 - \frac{1}{x}\right|$$. Then f is:
JEE Main 11th January 2019 Shift 2 - Question 78
The number of functions f from $$\{1, 2, 3, \ldots, 20\}$$ onto $$\{1, 2, 3, \ldots, 20\}$$ such that $$f(k)$$ is a multiple of 3, whenever k is a multiple of 4 is:
JEE Main 11th January 2019 Shift 2 - Question 79
Let K be the set of all real values of x where the function $$f(x) = \sin|x| - |x| + 2(x - \pi)\cos|x|$$ is not differentiable. Then the set K is equal to:
JEE Main 11th January 2019 Shift 2 - Question 80
Let $$f(x) = \frac{x}{\sqrt{a^2 + x^2}} - \frac{d - x}{\sqrt{b^2 + (d-x)^2}}$$, $$x \in \mathbb{R}$$ where a, b and d are non-zero real constants. Then:
