jee-advanced

Papers (53)
2025
paper1 16 paper2 16
2024
paper1 17 paper2 17
2023
paper1 17 paper2 17
2022
paper1 18 paper2 18
2021
paper1 23 paper2 19
2020
paper1 18 paper2 18
2019
paper1 18 paper2 18
2018
paper1 18 paper2 18
2017
paper1 18 paper2 18
2016
paper1 18 paper2 18
2015
paper1 20 paper2 20
2014
paper1 20 paper2 20
2013
paper1 20 paper2 20
2012
paper1 1 paper2 2
2011
paper1 6 paper2 9
2010
paper1 28 paper2 19
2009
paper1 19 paper2 17
2008
paper1 23 paper2 22
2007
paper1 27 paper2 5
2006
jee-advanced_2006.pdf 26
2005
mains 10 screening 16
2004
mains 18 screening 17
2003
mains 20 screening 17
2002
mains 4 screening 27
2001
mains 12 screening 28
2000
mains 5 screening 30
1999
jee-advanced_1999.pdf 33
1998
jee-advanced_1998.pdf 25
2005 mains

10 maths questions

Q9 Vectors Introduction & 2D Expressing a Vector as a Linear Combination View
9. Incident ray is along the unit vector v and the reflected ray is along the unit vector w . The normal is along unit vector a outwards. Express vector $w$ in terms of vector $a$ and $v$.
Q10 Circles Circle-Related Locus Problems View
10. Tangents are drawn from any point on the hyperbola $x ^ { 2 } / 9 - y ^ { 2 } / 4 = 1$ to the circle $x ^ { 2 } + y ^ { 2 } = 9$. Find the locus of mid-point of the chord of contact.
Q11 Circles Tangent Lines and Tangent Lengths View
11. Find the equation of the common tangent in 1st quadrant to the circle $x ^ { 2 } + y ^ { 2 } = 16$ and the ellipse $x ^ { 2 } / 25 + y ^ { 2 } / 4 = 1$. Also find the length of the intercept of the tangent between the coordinate axes.
Q12 Differential equations Solving Separable DEs with Initial Conditions View
12. If length of tangent at any point on the curve $y = f ( x )$ intercepted between the point and the $x$-axis is of length 1 . Find the equation of the curve.
Q13 Areas Between Curves Area Involving Conic Sections or Circles View
13. Find the area bounded by the curves $x ^ { 2 } = y , x ^ { 2 } = - y$ and $y ^ { 2 } = 4 x - 3$.
Q14 Complex Numbers Argand & Loci Similarity, Rotation, and Geometric Transformations in the Complex Plane View
14. If one of the vertices of the square circumscribing the circle $| z - 1 | = \sqrt { } 2$ is $2 + \sqrt { } 3 \mathrm { i }$. Find the other vertices of square.
Q15 Chain Rule Limit Involving Derivative Definition of Composed Functions View
15. If $f ( x - y ) = f ( x ) \cdot g ( y ) - f ( y ) \cdot g ( x )$ and $g ( x - y ) = g ( x ) \cdot g ( y ) + f ( x ) \cdot f ( y )$ for all $x$, $y \hat { I } R$. If right hand derivative at $x = 0$ exists for $f ( x )$. Find derivative of $g ( x )$ at $x = 0$.
Q16 Stationary points and optimisation Determine parameters from given extremum conditions View
16. If $p ( x )$ be a polynomial of degree 3 satisfying $p ( - 1 ) = 10 , p ( 1 ) = - 6$ and $p ( x )$ has maximum at $x = - 1$ and $p ^ { \prime } ( x )$ has minima at $x = 1$. Find the distance between the local maximum and local minimum of the curve.
Q17 Proof Existence or properties of extrema via abstract/theoretical argument View
17. $f ( x )$ is a differentiable function and $g ( x )$ is a double differentiable function such that $| f ( x ) | < 1$ and $f ^ { \prime } ( x ) = g ( x )$. If $f ^ { 2 } ( 0 ) + g ^ { 2 } ( 0 ) = 0$. Prove that there exists some $c \hat { I } ( - 3,3 )$ such that $\mathrm { g } ( \mathrm { c } ) . \mathrm { gn } ( \mathrm { c } ) < 0$.
Q18 Solving quadratics and applications Determining quadratic function from given conditions View
18. If
$$\left[ \begin{array} { l l l } 4 a ^ { 2 } & 4 a & 1 \\ 4 b ^ { 2 } & 4 b & 1 \\ 4 c ^ { 2 } & 4 c & 1 \end{array} \right] \left[ \begin{array} { c } f ( - 1 ) \\ f ( 1 ) \\ f ( 2 ) \end{array} \right] = \left[ \begin{array} { l l l } 3 a ^ { 2 } & + & 3 a \\ 3 b ^ { 2 } & + & 3 b \\ 3 c ^ { 2 } & + & 3 c \end{array} \right] ,$$
$f ( x )$ is a quadratic function and its maximum value occurs at a point $V$. $A$ is a point of intersection of $y = f ( x )$ with $x$-axis and point $B$ is such that chord $A B$ subtends a right angle at V . Find the area enclosed by $\mathrm { f } ( \mathrm { x } )$ and chord AB .