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QJEE MAIN
Let $\lambda, \mu \in R$. If the system of equations $3 x+5 y+\lambda z=3$ 7x+11y-9z=2 $97 x+155 y-189 z=\mu$ has infinitely many solutions, then $...
JEE MainMathematicsEasy
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QJEE MAIN 2024
If the line (2-x)/3=(3y-2)/(4λ+1)=4-z makes a right angle with the line (x+3)/3μ=(1-2y)/6=(5-z)/7, then 4λ+9μ is equal to :
JEE MainMathematicsEasy
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QJEE MAINS 2024
An artillery piece of mass M_1 fires a shell of mass M_2 horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery...
JEE MainPhysicsEasy
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QJEE MAIN 2024
Let $\mathrm{H}: \frac{-\mathrm{x}^2}{\mathrm{a}^2}+\frac{\mathrm{y}^2}{\mathrm{~b}^2}=1$ be the hyperbola, whose eccentricity is $\sqrt{3}$ and the length of the latus rectum is $4 \sqrt{3}$. Suppose the point $...
JEE MainMathematicsMedium
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QJEE MAIN 2024
Let $\alpha \in(0, \infty)$ and $A=\left[\begin{array}{lll}1 & 2 & \alpha \\ 1 & 0 & 1 \\ 0 & 1 & 2\end{array}\right]$. If $...
JEE MainMathematicsHard
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QJEE MAIN
A ray of light coming from the point P(1,2) gets reflected from the point Q on the x-axis and then passes through the point R(4,3)....
JEE MainMathematicsMedium
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QJEE MAIN 2024
Let $y=y(x)$ be the solution of the differential equation $\left(1+y^2\right) e^{\tan x} d x+\cos ^2 x\left(1+e^{2 \tan x}\right) d y=0$, $y(0)=1$. Then $y\left(\frac{\pi}{4}\right)$ is equal...
JEE MainMathematicsEasy
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QJEE MAIN 2024
The value of ∫_(-π)^π (2y(1+siny))/(1+〖cos〗^2y) dy is :
JEE MainMathematicsEasy
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QJEE MAINS 2024
Two conductors have the same resistances at but their temperature coefficients of resistance are and . The respective temperature coefficients for their series and parallel...
JEE MainPhysicsHard
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QJEE MAIN 2024
Let $f(\mathrm{x})=\mathrm{x}^5+2 \mathrm{e}^{\mathrm{x} / 4}$ for all $\mathrm{x} \in \mathrm{R}$. Consider a function $g(x)$ such that (gof) $(x)=x$ for all $x \in R$. Then the...
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