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QJEE MAIN 2023
Suppose $a_1, a_2, 2, a_3, a_4$ be in an arithmetico-geometric progression. If the common ratio of the corresponding geometric progression is 2 and the sum...
JEE MainMathematicsEasy
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QJEE MAIN 2023
Let the tangent at any point P on a curve passing through the points $(1,1)$ and $\left(\frac{1}{10}, 100\right)$, intersect positive $x$-axis and $y$-axis at the...
JEE MainMathematicsHard
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QJEE-Main 2023
For $\mathrm{a}, \mathrm{b} \in \mathrm{Z}$ and $|\mathrm{a}-\mathrm{b}| \leq 10$, let the angle between the plane $\mathrm{P}: \mathrm{ax}+\mathrm{y}-\mathrm{z}=\mathrm{b}$ and the line $l: \mathrm{x}-1=\mathrm{a} -y=z+1$ be $...
JEE MainMathematicsHard
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QJEE MAIN 2023
Let quadratic curve passing through the point $(-1,0)$ and touching the line $y=x$ at $(1,1)$ be $y=f(x)$. Then the x-intercept of the normal to the...
JEE MainMathematicsMedium
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QJEE MAIN 2023
Let the foot of perpendicular from the point $\mathrm{A}(4,3,1)$ on the plane $\mathrm{P}: \mathrm{x}-\mathrm{y}+2 \mathrm{z}+3=0$ be N . If $\mathrm{B}(5, \alpha$, $\beta$ ), $...
JEE MainMathematicsMedium
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QJEE MAIN 2023
Let S be the set of values of $\lambda$, for which the system of equations $$ \begin{aligned} & 6 \lambda x-3 y+3 z=4 \lambda^2 \\...
JEE MainMathematicsMedium
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QJEE-Main 2023
The area of the quadrilateral ABCD with vertices A(2, 1, 1), B(1, 2, 5), C(–2, –3, 5) and D(1, –6, –7) is equal to
JEE MainMathematicsEasy
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QJEE MAIN 2023
Let the equations of two adjacent sides of a parallelogram ABCD be $2 \mathrm{x}-3 \mathrm{y}=-23$ and $5 \mathrm{x}+4 \mathrm{y}=23$. If the equation of its one...
JEE MainMathematicsMedium
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QJEE MAIN 2023
The remainder, when $7^{103}$ is divided by 17 is $\_\_\_\_$ $-$
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