JEE Main 2019 Question Paper (11-Jan-2019) (Shift-1)

Question 1

Let $f : R	o R$, $f(x) = \frac{x}{1+x^2}$, $x \in R$ be defined, then the range of $f$ is

Accepted Answer

$\left[ -\frac{1}{2}, \frac{1}{2} \right]$

Answer

$R - \left[ -\frac{1}{2}, \frac{1}{2} \right]$

Answer

$R - [-1,1]$

Answer

$(-1, 1)-\{0\}$

Question 2

If one real root of the quadratic equation $81x^2+kx+256 = 0$ is cube of the other root, then a value of $k$ is

Accepted Answer

-300

Answer

100

Answer

144

Answer

-81

Question 3

Let $\left(-2-\frac{1}{3}i\right)^3 = \frac{x+iy}{27}$ $(i=\sqrt{-1})$, where $x$ and $y$ are real numbers, then $y-x$ equals

Accepted Answer

91

Answer

85

Answer

-91

Answer

-85

Question 4

Let $A= \begin{pmatrix} 0 & 2q & r \ p & q & -r \ p & -q & r \end{pmatrix}$. If $AA^T = I_3$, then |$p$| is :

Accepted Answer

$\frac{1}{\sqrt{2}}$

Answer

$\frac{1}{\sqrt{3}}$

Answer

$\frac{1}{\sqrt{5}}$

Answer

$\frac{1}{\sqrt{6}}$

Question 5

If the system of linear equations $2x+2y+3z = a$$3x-y+5z=b$ $x-3y+2z=c$where $a, b, c$ are non-zero real numbers, has more than one solution, then :

Accepted Answer

$b-c-a=0$

Answer

$b+c-a=0$

Answer

$b-c+a=0$

Answer

$a+b+c=0$