1

JEE Advanced 2022 Paper 1 Online

MCQ (More than One Correct Answer)

+4

-2

Let $$S$$ be the reflection of a point $$Q$$ with respect to the plane given by

$$ \vec{r}=-(t+p) \hat{\imath}+t \hat{\jmath}+(1+p) \hat{k} $$

where $$t, p$$ are real parameters and $$\hat{\imath}, \hat{\jmath}, \hat{k}$$ are the unit vectors along the three positive coordinate axes. If the position vectors of $$Q$$ and $$S$$ are $$10 \hat{\imath}+15 \hat{\jmath}+20 \hat{k}$$ and $$\alpha \hat{\imath}+\beta \hat{\jmath}+\gamma \hat{k}$$ respectively, then which of the following is/are TRUE ?

$$ \vec{r}=-(t+p) \hat{\imath}+t \hat{\jmath}+(1+p) \hat{k} $$

where $$t, p$$ are real parameters and $$\hat{\imath}, \hat{\jmath}, \hat{k}$$ are the unit vectors along the three positive coordinate axes. If the position vectors of $$Q$$ and $$S$$ are $$10 \hat{\imath}+15 \hat{\jmath}+20 \hat{k}$$ and $$\alpha \hat{\imath}+\beta \hat{\jmath}+\gamma \hat{k}$$ respectively, then which of the following is/are TRUE ?

2

JEE Advanced 2021 Paper 2 Online

MCQ (More than One Correct Answer)

+4

-2

Let O be the origin and $$\overrightarrow {OA} = 2\widehat i + 2\widehat j + \widehat k$$ and $$\overrightarrow {OB} = \widehat i - 2\widehat j + 2\widehat k$$ and $$\overrightarrow {OC} = {1 \over 2}\left( {\overrightarrow {OB} - \lambda \overrightarrow {OA} } \right)$$ for some $$\lambda$$ > 0. If $$\left| {\overrightarrow {OB} \times \overrightarrow {OC} } \right| = {9 \over 2}$$, then which of the following statements is (are) TRUE?

3

JEE Advanced 2020 Paper 2 Offline

MCQ (More than One Correct Answer)

+4

-2

Let $$\alpha $$

^{2}+ $$\beta $$^{2}+ $$\gamma $$^{2}$$ \ne $$ 0 and $$\alpha $$ + $$\gamma $$ = 1. Suppose the point (3, 2, $$-$$1) is the mirror image of the point (1, 0, $$-$$1) with respect to the plane $$\alpha $$x + $$\beta $$y + $$\gamma $$z = $$\delta $$. Then which of the following statements is/are TRUE?4

JEE Advanced 2020 Paper 2 Offline

MCQ (More than One Correct Answer)

+4

-2

Let a and b be positive real numbers. Suppose $$PQ = a\widehat i + b\widehat j$$ and $$PS = a\widehat i - b\widehat j$$ are adjacent sides of a parallelogram PQRS. Let u and v be the projection vectors of $$w = \widehat i + \widehat j$$ along PQ and PS, respectively. If |u| + |v| = |w| and if the area of the parallelogram PQRS is 8, then which of the following statements is/are TRUE?

Questions Asked from Vector Algebra and 3D Geometry (MCQ (Multiple Correct Answer))

Number in Brackets after Paper Indicates No. of Questions

JEE Advanced 2022 Paper 2 Online (1)
JEE Advanced 2022 Paper 1 Online (2)
JEE Advanced 2021 Paper 2 Online (1)
JEE Advanced 2020 Paper 2 Offline (2)
JEE Advanced 2020 Paper 1 Offline (1)
JEE Advanced 2019 Paper 2 Offline (1)
JEE Advanced 2019 Paper 1 Offline (1)
JEE Advanced 2018 Paper 1 Offline (1)
JEE Advanced 2016 Paper 2 Offline (1)
JEE Advanced 2016 Paper 1 Offline (1)
JEE Advanced 2015 Paper 1 Offline (3)
JEE Advanced 2014 Paper 1 Offline (1)
JEE Advanced 2013 Paper 2 Offline (1)
JEE Advanced 2013 Paper 1 Offline (1)
IIT-JEE 2012 Paper 2 Offline (1)
IIT-JEE 2011 Paper 1 Offline (1)
IIT-JEE 2006 (1)
IIT-JEE 1999 (1)
IIT-JEE 1998 (1)
IIT-JEE 1994 (1)
IIT-JEE 1993 (1)

JEE Advanced Subjects

Physics

Mechanics

Units & Measurements
Motion
Laws of Motion
Work Power & Energy
Impulse & Momentum
Rotational Motion
Properties of Matter
Heat and Thermodynamics
Simple Harmonic Motion
Waves
Gravitation

Electricity

Optics

Modern Physics

Chemistry

Physical Chemistry

Some Basic Concepts of Chemistry
Structure of Atom
Redox Reactions
Gaseous State
Equilibrium
Solutions
States of Matter
Thermodynamics
Chemical Kinetics and Nuclear Chemistry
Electrochemistry
Solid State & Surface Chemistry

Inorganic Chemistry

Periodic Table & Periodicity
Chemical Bonding & Molecular Structure
Isolation of Elements
Hydrogen
s-Block Elements
p-Block Elements
d and f Block Elements
Coordination Compounds
Salt Analysis

Organic Chemistry

Mathematics

Algebra

Quadratic Equation and Inequalities
Sequences and Series
Mathematical Induction and Binomial Theorem
Matrices and Determinants
Permutations and Combinations
Probability
Vector Algebra and 3D Geometry
Statistics
Complex Numbers

Trigonometry

Coordinate Geometry

Calculus