JEE Maths PYQ Practice, chapter-wise

JEE Advanced 2025 Paper 1Question 331

Let $L_1$ be the line of intersection of the planes given by the equations $$2x+3y+z=4\quad\text{and}\quad x+2y+z=5.$$ Let $L_2$ be the line passing through the point $P(2,-1,3)$ and parallel to $L_1$. Let $M$ denote the plane given by the equation $$2x+y-2z=6.$$ Suppose that the line $L_2$ meets the plane $M$ at the point $Q$. Let $R$ be the foot of the perpendicular drawn from $P$ to the plane $M$. Then which of the following statements is (are) TRUE?

3D Geometry

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The length of the line segment $PQ$ is $9\sqrt3$The length of the line segment $QR$ is $15$The area of $\Delta PQR$ is $\frac32\sqrt{234}$The acute angle between the line segments $PQ$ and $PR$ is $\cos^{-1}\left(\frac1{2\sqrt3}\right)$

JEE Advanced 2026 Paper 2Question 332

Let $L$ be the straight line joining the points $P(1,2,-1)$ and $Q(2,3,1)$. Let $S$ be the foot of the perpendicular drawn from the point $R(4,-1,5)$ to the line $L$. Another line passing through $R$ intersects $L$ at a point $T$ such that the point $S$ divides the line segment $PT$ internally in the ratio $|PS|:|ST| = 1:2$, where $|PS|$ and $|ST|$ are the lengths of the line segments $PS$ and $ST$, respectively. Then which of the following statements is (are) TRUE ?

3D Geometry

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The orthocentre of the triangle $PRT$ is $\left(\frac{23}{5}, -4, \frac{31}{5}\right)$The orthocentre of the triangle $PRT$ is $(4,3,5)$The area of the triangle $PRT$ is $6\sqrt{5}$The area of the triangle $PRT$ is $18\sqrt{5}$

JEE Advanced 2026 Paper 1Question 333

Let $P$ be the plane such that it contains the straight line $\frac{x-1}{2}=\frac{y-3}{3}=\frac{z+2}{1}$ and is perpendicular to the plane $x+2y+3z=4$. Let $P_1$ be the plane which passes through the point $(4,2,2)$ and is parallel to $P$. Then which of the following statements is (are) TRUE ?

3D Geometry

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The equation of the plane $P$ is $7x-5y+z=-10$The distance between the planes $P$ and $P_1$ is $30$The distance of the plane $P$ from the origin is $2\sqrt3$The acute angle between the plane $P$ and the plane $2x+2y+z=3$ is $\cos^{-1}\left(\frac{1}{3\sqrt3}\right)$

JEE Main 2023 (Online) 29th January Morning ShiftQuestion 334

Let the equation of the plane $P$ containing the line $x+10=\frac{8-y}{2}=z$ be $ax+by+3z=2(a+b)$ and the distance of the plane $P$ from the point $(1,27,7)$ be $c$. Then $a^{2}+b^{2}+c^{2}$ is equal to ______.

3D Geometry

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JEE Main 2021 (Online) 20th July Morning ShiftQuestion 335

Let $P$ be a plane passing through the points $(1,0,1)$, $(1,-2,1)$ and $(0,1,-2)$. Let a vector $\vec a=\alpha\hat i+\beta\hat j+\gamma\hat k$ be such that $\vec a$ is parallel to the plane $P$, perpendicular to $\left(\hat i+2\hat j+3\hat k\right)$ and $\vec a\cdot\left(\hat i+\hat j+2\hat k\right)=2$, then $(\alpha-\beta+\gamma)^{2}$ equals

3D Geometry

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