JEE Main 2013 (Online) 22nd AprilQuestion 5491
Mean of $5$ observations is $7$. If four of these observations are $6,7,8,10$ and one is missing then the variance of all the five observations is :
Statistics
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JEE Main 2013 (Online) 25th AprilQuestion 5492
A point on the ellipse, $4x^{2}+9y^{2}=36$, where the normal is parallel to the line, $4x-2y-5=0$, is :
Ellipse
JEE Main 2013 (Online) 23rd AprilQuestion 5493
If two lines $L_1$ and $L_2$ in space, are defined by $L_1=\left\{x=\sqrt\lambda\,y+\left(\sqrt\lambda-1\right),\ z=\left(\sqrt\lambda-1\right)y+\sqrt\lambda\right\}$ and $L_2=\left\{x=\sqrt\mu\,y+\left(1-\sqrt\mu\right),\ z=\left(1-\sqrt\mu\right)y+\sqrt\mu\right\}$, then $L_1$ is perpendicular to $L_2$, for all non-negative reals $\lambda$ and $\mu$, such that :
3D Geometry
JEE Main 2013 (Online) 23rd AprilQuestion 5494
Statement-1: The system of linear equations $x+(\sin\alpha)y+(\cos\alpha)z=0$, $x+(\cos\alpha)y+(\sin\alpha)z=0$, $x-(\sin\alpha)y-(\cos\alpha)z=0$ has a non-trivial solution for only one value of $\alpha$ lying in the interval $\left(0,\frac\pi2\right)$. Statement-2: The equation in $\alpha$ $\begin{vmatrix}\cos\alpha&\sin\alpha&\cos\alpha\\\sin\alpha&\cos\alpha&\sin\alpha\\\cos\alpha&-\sin\alpha&-\cos\alpha\end{vmatrix}=0$ has only one solution lying in the interval $\left(0,\frac\pi2\right)$.
Determinant
JEE Main 2013 (Online) 23rd AprilQuestion 5495
The least integral value $\alpha$ of $x$ such that $\frac{x-5}{x^{2}+5x-14}>0$, satisfies :
Quadratic Equation · Sign, Range and Inequalities of Quadratic Expressions