JEE Advanced 2026 Paper 1 Online

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 ...

Consider the function $f : (0, \infty) \to (-\infty, \infty)$ given by
$f(x) = \sqrt{x} \log_e(x) - x + 1$.Then which one of the following statements is TRUE?

Let $P$ be the point on the parabola $y = x^2$ such that the slope of the tangent to the parabola at the point $P$ is $4$. Let $Q$ be the point in the first quadrant lying on the circle $x^2 + y^2 = 2$ such that the slope of the tangent to ...

Let$$ \alpha = \left( 1 - 2\cos\left(\frac{\pi}{11}\right) \right) \left( 1 - 2\cos\left(\frac{3\pi}{11}\right) \right) \left( 1 - 2\cos\left(\frac{9\pi}{11}\right) \right) \left( 1 - 2\cos\left(\frac{27\pi}{11}\right) \right) \left( 1 - 2\...

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



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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

...

Considering only the principal values of the inverse trigonometric functions, the value of \(\cot^{-1}(\cot(-11)) + 10 \sin\left(2 \cos^{-1}\left(\frac{1}{\sqrt{2}}\right)\right) + 10\sin(2 \tan^{-1}(2))\)is

Let $\mathbb{R}$ denote the set of all real numbers. Let $f : \mathbb{R} \to \mathbb{R}$ be an arbitrary function and let $g : \mathbb{R} \to \mathbb{R}$ be the function defined by\(g(x) = x f(x), \quad \text{for all } x \in \mathbb{R}.\)Th...

Consider the function $f:\left(-\frac{\pi}{2},\frac{\pi}{2}\right) \to (-\infty, \infty)$ defined by\(f(x) = (|x| + |x-1|) \sin x + \left[ x \sin x \right],\)where $\left[ x \sin x \right]$ is the greatest integer less than or equal to $x \...

Which one of the following matrices can be obtained by performing elementary row transformations on the $3 \times 3$ identity matrix?

Consider the matrix $$ M = \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix}. $$ Let $p, q, r, s, a, b, c$ and $d$ be integers such that $$ M^{26} = \begin{bmatrix} p & q \\ r & s \end{bmatrix} \quad \text{and} \quad \sum\limits_{k=1}^{26} M^k ...

Let $S = \{1, 2, 3, \ldots, 10\}$. Consider the set $X = \{R : R \text{ is an equivalence relation on the set } S \text{ such that } R \text{ has exactly 42 elements}\}$. Then the number of elements in $X$ is ____________.

The number of ways to distribute 10 identical red pens and 14 identical blue pens among four persons such that each person gets 6 pens, is ______________.

Suppose that Box I contains 6 red balls and 9 green balls, and Box II contains 8 red balls and 12 green balls. All the balls of Box I and Box II are mixed together and a ball is chosen at random from them. Let $E_1$ be the event that the ba...

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 ...

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{...