JEE Maths PYQ Practice, chapter-wise

JEE Main 2026 (Online) 21st January Morning ShiftQuestion 361

Let $(\alpha,\beta,\gamma)$ be the coordinates of the foot of the perpendicular drawn from the point $(5,4,2)$ on the line $\vec r=(-\hat i+3\hat j+\hat k)+\lambda(2\hat i+3\hat j-\hat k)$. Then the length of the projection of the vector $\alpha\hat i+\beta\hat j+\gamma\hat k$ on the vector $6\hat i+2\hat j+3\hat k$ is :

3D Geometry

$3$$4$$\frac{18}{7}$$\frac{15}{7}$

JEE Main 2026 (Online) 24th January Morning ShiftQuestion 362

Let a line $L$ passing through the point $P(1,1,1)$ be perpendicular to the lines $\frac{x-4}{4}=\frac{y-1}{1}=\frac{z-1}{1}$ and $\frac{x-17}{1}=\frac{y-71}{1}=\frac z0$. Let the line $L$ intersect the $yz$ plane at the point $Q$. Another line parallel to $L$ and passing through the point $S(1,0,-1)$ intersects the $yz$-plane at the point $R$. Then the square of the area of the parallelogram $PQRS$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2026 (Online) 28th January Evening ShiftQuestion 363

If the distance of the point $P(43,\alpha,\beta)$, $\beta<0$, from the line $\vec r=4\hat i-\hat k+\mu(2\hat i+3\hat k)$, $\mu\in\mathbf{R}$ along a line with direction ratios $3,-1,0$ is $13\sqrt{10}$, then $\alpha^2+\beta^2$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2026 (Online) 4th April Morning ShiftQuestion 364

A line with direction ratios $1,-1,2$ intersects the lines $\frac{x}{2}=\frac{y}{3}=\frac{z+1}{3}$ and $\frac{x+1}{-1}=\frac{y-2}{1}=\frac{z}{4}$ at the points $P$ and $Q$, respectively. If the length of the line segment $PQ$ is $\alpha$, then $225\alpha^{2}$ is equal to :

3D Geometry

$1024$$1014$$1104$$1204$

JEE Main 2026 (Online) 5th April Morning ShiftQuestion 365

The square of the distance of the point $P(5,6,7)$ from the line $\frac{x-2}{2}=\frac{y-5}{3}=\frac{z-2}{4}$ is equal to :

3D Geometry

$3$$5$$6$$8$