Let A={X=(x,y,z)ᵀ: PX=0 and... | Matrices | JEE Main 2020

Competishun Header

JEE MAIN 2020

02-09-2020 S2

Question

Let $A=\left\{X=(x, y, z)^{\top}: P X=0\right.$ and $\left.x^2+y^2+z^2=1\right\}$, where $P=\left[\begin{array}{ccc}1 & 2 & 1 \\ -2 & 3 & -4 \\ 1 & 9 & -1\end{array}\right]$, then the set $A$ :

Select the correct option:

A

is an empty set

B

contains more than two elements.

C

contains exactly two elements.

D

is a singleton

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Hard

Start Preparing for JEE with Competishun

Filters 0

Showing 18 questions

QJEE Main 20242024

Let z be a complex number such that the real part of $\frac{z-2 i}{z+2 i}$ is zero. Then, the maximum...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

Let $\int_0^x \sqrt{1-\left(y^{\prime}(t)\right)^2} \mathrm{dt}=\int_0^{\mathrm{x}} \mathrm{y}(\mathrm{t}) \mathrm{dt}, 0 \leq \mathrm{x} \leq 3, \mathrm{y} \geq 0, y(0)=0$. Then at $x=2, y^{\prime \prime}+y+1$...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

Consider the line L passing through the points $(1,2,3)$ and $(2,3,5)$. The distance of the point $\left(\frac{11}{3}, \frac{11}{3}, \frac{19}{3}\right)$ from...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

$\operatorname{Lim}_{x \rightarrow 0} \frac{e-(1+2 x)^{\frac{1}{2 x}}}{x}$ is equal to :

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

When $\Delta \mathrm{H}_{\text {vap }}=30 \mathrm{~kJ} / \mathrm{mol}$ and $\Delta \mathrm{S}_{\text {vap }}=75 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$, then the temperature of...

JEE MainChemistryEasy

View Solution→

QJEE Main 20242024

Total number of electron present in $\left(\pi^*\right)$ molecular orbitals of $\mathrm{O}_2, \mathrm{O}_2^{+}$and $\mathrm{O}_2^{-}$is $\_\_\_\_$ .

JEE MainPhysicsEasy

View Solution→

QJEE Main 20242024

Number of compounds from the following which cannot undergo Friedel-Crafts reactions is :____ toluene, nitrobenzene, xylene, cumene, aniline, chlorobenzene, m-nitroaniline,...

JEE MainPhysicsEasy

View Solution→

QJEE Main 20242024

Based on Heisenberg's uncertainty principle, the uncertainty in the velocity of the electron to be found within an atomic nucleus...

JEE MainChemistryEasy

View Solution→

QJEE Main 20242024

Consider the following first order gas phase reaction at constant temperature
$ \mathrm{A}(\mathrm{~g}) \rightarrow 2 \mathrm{~B}(\mathrm{~g})+\mathrm{C}(\mathrm{~g}) $
If...

JEE MainChemistryEasy

View Solution→

QJEE Main 20242024

Consider the following test for a group-IV cation.
$\mathrm{M}^{2+}+\mathrm{H}_2 \mathrm{~S} \rightarrow \mathrm{~A}$ (Black precipitate) + byproduct $\mathrm{A}+$ aqua regia...

JEE MainChemistryEasy

View Solution→

QJEE Main 20242024

The vapour pressure of pure benzene and methyl benzene at $27^{\circ} \mathrm{C}$ is given as 80 Torr and 24 Torr...

JEE MainChemistryEasy

View Solution→

QJEE Main 20242024

A transition metal 'M' among Sc, Ti, V , Cr, Mn and Fe has the highest second ionisation enthalpy. The...

JEE MainPhysicsEasy

View Solution→

QJEE Main 20242024

Number of oxygen atoms present in chemical formula of fuming sulphuric acid is

JEE MainPhysicsEasy

View Solution→

QJEE Main 20242024

The electronic configuration of Einsteinium is : (Given atomic number of Einsteinium = 99)

JEE MainPhysicsEasy

View Solution→

QJEE Main 20242024

Which out of the following is a correct equation to show change in molar conductivity with respect to concentration for...

JEE MainChemistryEasy

View Solution→

QJEE Main 20242024

Which of the following compounds will give silver mirror with ammoniacal silver nitrate?
(A) Formic acid
(B) Formaldehyde...

JEE MainChemistryEasy

View Solution→

QJEE Main 20242024

The incorrect statement regarding ethyne is

JEE MainChemistryEasy

View Solution→

QJEE Main 20242024

Given below are two statements :
Statement I : The higher oxidation states are more stable down the group...

JEE MainChemistryEasy

View Solution→