If the system of equations $2x+3y-z=0,\ x+ky-2z=0$ and $2x-y+z=0$ has a non-trivial solution $(x,y,z)$, then $\dfrac{x}{y}+\dfrac{y}{z}+\dfrac{z}{x}+k$ is equal to:
Previous 10 Questions — JEE Main 2019 (9 April Evening Shift)
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If $f:\mathbb{R}\to\mathbb{R}$ is a differentiable function and $f(2)=6$, then
$\displaystyle \lim_{x\to 2}\dfrac{\int_…
Topic: JEE Main 2019 (9 April Evening Shift)
A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is $\tan^{-1}\left(\dfrac{1}{2…
Topic: JEE Main 2019 (9 April Evening Shift)
If the two lines $x+(a-1)y=1$ and $2x+a^{2}y=1$ $(a\in\mathbb{R}\setminus{0,1})$ are perpendicular, then the distance o…
Topic: JEE Main 2019 (9 April Evening Shift)
The vertices $B$ and $C$ of a $\triangle ABC$ lie on the line $\dfrac{x+2}{3}=\dfrac{y-1}{0}=\dfrac{z}{4}$ such that $B…
Topic: JEE Main 2019 (9 April Evening Shift)
The total number of matrices
$A = \left( {\matrix{
0 & {2y} & 1 \cr
{2x} & y & { - 1} \cr
…
Topic: JEE Main 2019 (9 April Evening Shift)
If $f(x)=[x]-\left[\dfrac{x}{4}\right],\ x\in\mathbb{R}$, where $[\cdot]$ denotes the greatest integer function, then
Topic: JEE Main 2019 (9 April Evening Shift)
$\displaystyle \int e^{\sec x},\big(\sec x\tan x,f(x)+\sec x\tan x+\sec^{2}x\big),dx ;=; e^{\sec x}f(x)+C$
Then a possi…
Topic: JEE Main 2019 (9 April Evening Shift)
If $m$ is chosen in the quadratic equation
$(m^{2}+1)x^{2}-3x+(m^{2}+1)^{2}=0$
such that the sum of its roots is greate…
Topic: JEE Main 2019 (9 April Evening Shift)
Two newspapers $A$ and $B$ are published in a city. It is known that $25%$ of the city population reads $A$ and $20%$ r…
Topic: JEE Main 2019 (9 April Evening Shift)
The domain of the function $f(x)=\dfrac{1}{4-x^{2}}+\log_{10}(x^{3}-x)$ is:
Topic: JEE Main 2019 (9 April Evening Shift)
