JEE Advanced 2026 Paper 1 Online | JEE Advanced Year Wise Previous Years Questions

JEE Advanced 2026 Paper 1 Online

MCQ (Single Correct Answer)

-1

Match each entry in List-I to the correct entry in List-II and choose the correct option.

List-I	List-II
(P) If $\alpha$ and $\beta$ are the distinct roots of the equation $x^2 + x + 1 = 0$, then the quadratic equation with roots $\frac{1}{(\alpha+1)^{2026}}$ and $\frac{1}{(\beta+1)^{2026}}$ is	(1) $x^2 + x + 1 = 0$
(Q) If $\alpha$ and $\beta$ are the distinct roots of the equation $x^2 + x + 1 = 0$, then the quadratic equation with roots $\frac{1}{(\alpha+1)^{2027}}$ and $\frac{1}{(\beta+1)^{2027}}$ is	(2) $x^2 - x + 1 = 0$
(R) If $\gamma$ and $\delta$ are the distinct roots of the equation $x^2 - x + 1 = 0$, then the value of $\frac{1}{(\gamma-1)^{2026}} + \frac{1}{(\delta-1)^{2026}}$ is	(3) $x^2 + x - 1 = 0$
(S) If $p$ and $r$ are the distinct roots of the equation $x^2 + x - 1 = 0$, then the value of $\frac{1}{(p+1)^3} + \frac{1}{(r+1)^3}$ is	(4) $-1$
	(5) $-4$

(P) $\rightarrow$ (1), (Q) $\rightarrow$ (2), (R) $\rightarrow$ (5), (S) $\rightarrow$ (4)

(P) $\rightarrow$ (3), (Q) $\rightarrow$ (1), (R) $\rightarrow$ (4), (S) $\rightarrow$ (5)

(P) $\rightarrow$ (1), (Q) $\rightarrow$ (2), (R) $\rightarrow$ (4), (S) $\rightarrow$ (5)

(P) $\rightarrow$ (2), (Q) $\rightarrow$ (3), (R) $\rightarrow$ (5), (S) $\rightarrow$ (4)

JEE Advanced 2026 Paper 1 Online

MCQ (Single Correct Answer)

-1

Match each entry in List-I to the correct entry in List-II and choose the correct option.

List-I	List-II
(P) The number of elements in the set $$\left\{x \in [-\pi,\pi] : \sin^6 x + \cos^4 x = 1 \right\}$$	(1) is 1
(Q) The number of elements in the set $$\left\{x \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] : \sin^2 x + \cos^6 x = 1 \right\}$$	(2) is 2
(R) The number of elements in the set $$\left\{x \in [-\pi,\pi] : \cos^2\left(\frac{x}{2}\right) - \sin^2 x = \frac{1}{2} \right\}$$	(3) is 3
(S) The number of elements in the set $$\left\{x \in [-2\pi,2\pi] : 6\sin^2\left(\frac{x}{2}\right) - \cos 3x = 3 \right\}$$	(4) is 4 (5) is 5

(P) $\to$ (2), (Q) $\to$ (5), (R) $\to$ (3), (S) $\to$ (4)

(P) $\to$ (5), (Q) $\to$ (3), (R) $\to$ (2), (S) $\to$ (4)

(P) $\to$ (5), (Q) $\to$ (4), (R) $\to$ (1), (S) $\to$ (3)

(P) $\to$ (4), (Q) $\to$ (3), (R) $\to$ (2), (S) $\to$ (5)

JEE Advanced 2026 Paper 1 Online

MCQ (Single Correct Answer)

-1

For real numbers $\alpha$, $\beta$, $\gamma$, $\delta$ and $\mu$, consider the matrix

$$ M = \begin{bmatrix} \alpha & \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \beta & \frac{1}{\sqrt{3}} \\ \gamma & \delta & \mu \end{bmatrix}. $$

Suppose that $MM^{T} = I$, where $M^{T}$ is the transpose of the matrix $M$, and $I$ is the $3 \times 3$ identity matrix. Let

$$ \vec{u} = \alpha\,\hat{i} + \frac{1}{\sqrt{3}}\hat{j} + \gamma\,\hat{k}, \qquad \vec{v} = \frac{1}{\sqrt{2}}\hat{i} + \beta\hat{j} + \delta\hat{k} \qquad \text{and} \qquad \vec{w} = -\frac{1}{\sqrt{2}}\hat{i} + \frac{1}{\sqrt{3}}\hat{j} + \mu\hat{k}. $$

Match each entry in List-I to the correct entry in List-II and choose the correct option.

List-I	List-II
(P) The value of $$\gamma^2 + \delta^2$$ is	(1) 0
(Q) If $$x\vec{u} + y\vec{v} + z\vec{w} = \hat{j}$$ for some real numbers $x$, $y$ and $z$, then the value of $x$ is	(2) 1
(R) The value of $$\left\|\vec{u} \cdot (\vec{v} \times \vec{w})\right\|$$ is	(3) $$\frac{1}{\sqrt{2}}$$
(S) The value of $$\left\|\vec{u} \times (\vec{v} \times \vec{w})\right\|$$ is	(4) $$\frac{1}{\sqrt{3}}$$
	(5) $$\frac{5}{6}$$

(P) → (5), (Q) → (4), (R) → (2), (S) → (1)

(P) → (4), (Q) → (5), (R) → (1), (S) → (2)

(P) → (5), (Q) → (3), (R) → (2), (S) → (1)

(P) → (5), (Q) → (4), (R) → (1), (S) → (2)

JEE Advanced 2026 Paper 1 Online

MCQ (Single Correct Answer)

-1

Match each entry in List-I to the correct entry in List-II and choose the correct option.

List-I	List-II
(P) The circle with centre $(1,2)$ and touching the straight line $$3x + 4y = 1$$ passes through	(1) the point $(1,1)$
(Q) The common tangent to the circle $$x^2 + y^2 = 2$$ and the parabola $$y^2 = 8x$$ with positive slope, passes through	(2) the point $(7,9)$
(R) Let $M$ be the end point of the latus rectum of the ellipse $$3x^2 + 4y^2 = 48$$ such that $M$ lies in the first quadrant. Then the normal to the ellipse drawn at $M$ passes through	(3) the point $(3,2)$
(S) Let $H$ be the hyperbola whose centre is at the origin, one of the foci is at $(5,0)$, and one directrix is $$5x + 16 = 0$$ Then $H$ passes through	(4) the point $(2,5)$
	(5) the point $(8, 3\sqrt{3})$

(P) → (3), (Q) → (4), (R) → (1), (S) → (2)

(P) → (3), (Q) → (2), (R) → (1), (S) → (5)

(P) → (3), (Q) → (2), (R) → (4), (S) → (5)

(P) → (4), (Q) → (1), (R) → (2), (S) → (3)

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