JEE Advanced 2026 Question Paper (Available)- Download Paper 1 and Paper 2 Question Paper with Answer Key

JEE Advanced 2026 Questions

• 1.

  Let \(\mathbb{R}\) denote the set of all real numbers and let \(i = \sqrt{-1}\). Consider the matrices \[ S = \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix} \quad \text{and} \quad T = \begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix}. \] Let \(a, b, c, d\) be real numbers such that \[ ST = \begin{pmatrix} a & b \\ c & d \end{pmatrix}. \] Let \[ H = \{x + iy : x, y \in \mathbb{R} \text{ and } y>0\}. \] Then which of the following statements is (are) TRUE?
  

  • $\frac{b + ia}{d + ic} = i$
    
  • If $\omega = \frac{-1 + i\sqrt{3}}{2}$, then $\frac{a\omega + b}{c\omega + d} = \omega$
    
  • If $m$ is an integer greater than 2 such that $(ST)^2 = (ST)^m$, then $m$ is an integer multiple of 8
    
  • If $z \in H$, then $\frac{az + b}{cz + d} \in H$
    
  View Solution

  ---

• 2.

  Consider the matrix \[ M= \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix} \] Let \(p,q,r,s,a,b,c,d\) be integers such that \[ M^{26}= \begin{bmatrix} p & q \\ r & s \end{bmatrix} \] and \[ \sum_{k=1}^{26} M^k= \begin{bmatrix} a & b \\ c & d \end{bmatrix}. \] Then which of the following statements is (are) TRUE?

  • There exists a \(2\times2\) invertible matrix \(N\) with real entries such that \[ MN= N \begin{bmatrix} 1 & 1 0 & 1 \end{bmatrix} \]
  • The value of \(a\) is \(378\)
  • For any two given integers \(m\) and \(n\), there exist unique integers \(x\) and \(y\) such that \[ px+qy=m \] and \[ rx+sy=n \]
  • For each positive real number \(t\), the system of linear equations \[ (a+t)x+by=1 \] \[ cx+(d+t)y=-1 \] has a unique solution
  View Solution

  ---

• 3.

  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?

  • 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 \[\cos^{-1}\left(\frac1{3\sqrt3}\right)\]
  View Solution

  ---

• 4.

  Consider the following reaction sequence in which \(J, K, L\) and \(M\) are the major products.
  
  

  

  
  
  Given:
  Atomic mass (in amu): H : \(1\), C : \(12\), N : \(14\), O : \(16\), S : \(32\), Br : \(80\), Ba : \(137\)
  
  In sulphur estimation by Carius method, the amount of \(\text{BaSO}_4\) formed from \(3.79\,\text{g}\) of \(M\) is _____ g.
  

  View Solution

  ---

• 5.

  Consider the following reaction sequence in which \(J, K, L\) and \(M\) are the major products.
  
  

  

  
  
  Given:
  Atomic mass (in amu): H : \(1\), C : \(12\), N : \(14\), O : \(16\), S : \(32\), Br : \(80\), Ba : \(137\)
  
  The volume of \(1\,\text{M}\) aqueous \(\text{H}_2\text{SO}_4\) required to completely neutralize the ammonia evolved from \(5.72\,\text{g}\) of \(L\) in Kjeldahl’s method of nitrogen estimation is _____ mL.
  

  View Solution