JEE Advanced 2026 Paper 2 Online

Let L be the straight line joining the points P(1, 2, –1) and Q(2, 3, 1). Let S be the foot of the perpendicular drawn from the point R(4, –1, 5) to the line L. Another line passing through R intersects L at a point T such that the point S ...

Consider the curve $C_1$ given by
\(y=e^{-x} \quad \text { for } x \in[0,10 \pi],\)
and the curve $C_2$ given by
\(y=e^{-x}(\sin x+\cos x) \quad \text { for } x \in[0,10 \pi] .\)
Let $n$ be the total number of points of intersection of ...

Consider the ellipses given by
\(x^2+4 y^2=1 \quad \text { and } \quad 4 x^2+y^2=1 .\)
If $\alpha$ is the area of the common region that lies inside both the given ellipses, then the value of $\cot \alpha$ is $\_\_\_\_$ .

Let $\mathbb{R}$ denote the set of all real numbers and let $i=\sqrt{-1}$. Consider the matrices
$$ S=\left[\begin{array}{rr} 0 & -1 \\ 1 & 0 \end{array}\right] \quad \text { and } \quad T=\left[\begin{array}{ll} 1 & 1 \\ 0 & 1 \end{array}\...

The value of the definite integral\(\int\limits_{0}^{2} \frac{1}{3^x + 3} dx\)is

Let $y : (-\infty, \infty) \to (0, \infty)$ be the solution of the differential equation
\(\frac{dy}{dx} = \frac{e^{5x} y^3 + y^3}{e^x + e^x y^4},\)
satisfying $y(0) = \frac{1}{\sqrt{2}}$. Then the value of $y(\log_e 2)$ is

Let $y = f(x)$ be the real valued function defined on the interval $(0, \infty)$, satisfying $y(1) = 0$ and the differential equation\(x \frac{dy}{dx} = y - x^3.\)Then which of the following statements is (are) TRUE?

Let $\mathbb{R}$ denote the set of all real numbers. Consider the polynomial function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined by
$$ f(x)=\frac{d^{10}}{d x^{10}}\left(\left(x^2-1\right)^{10}\right), \quad \text { for all } x \in \math...

Consider the ellipses given by
\(x^2+4 y^2=1 \quad \text { and } \quad 4 x^2+y^2=1\)
Let $P$ be the point in the first quadrant where the given ellipses intersect. If $\theta$ is the acute angle between the tangents to the given ellipses ...

Let $\mathbb{N}$ denote the set of all positive integers. Consider the sets
\(A=\{1,2,3,4,5\} \text { and } B=\{1,2,3,4,5,6,7\} .\)
Let $S$ be the set of all functions $f: A \rightarrow B$ such that $f(2) \neq 2$ and $f(4) \neq 4$. Consid...

Consider the ellipse $E$ given by $\frac{x^2}{18}+\frac{y^2}{12}=1$. Let $H$ be the hyperbola whose eccentricity is the reciprocal of the eccentricity of $E$ and whose foci are the same as that of $E$. Let $P$ and $Q$ be the points of inter...

For a real number $\alpha$, let $[\alpha]$ denote the greatest integer less than or equal to $\alpha$. For a finite set $S$, let $|S|$ denote the number of elements in the set $S$.
Consider the functions $f:(-3,3) \rightarrow(-\infty, \inft...

Let T be the tangent to the parabola $y^2 = 16x$ at the point $(64, 32)$. Let L be the tangent to the same parabola at another point $(x_1, y_1)$ on the parabola. If L and T are perpendicular to each other, then the distance between the poi...

A bookshelf contains 6 distinct books of Mathematics and 5 distinct books of Physics. From these 11 books, 6 books are chosen at random. Let $X$ be the absolute value of the difference between the number of Mathematics books chosen and the ...

Let a, b, c be positive integers in arithmetic progression such that the equation\(ax^2 + bx + c = 0\)has only integer solutions.Then which of the following statements is (are) TRUE?

Consider a data consisting of 10 observations $x_1, x_2, \ldots, x_{10}$, whose mean is 5 and variance is 7 . If the mean and the variance of the first 8 observations $x_1, x_2, \ldots, x_8$ are 4 and 3.5 , respectively, and $x_9 < x_{10}$,...

Consider the curve $C_1$ given by
\(y=e^{-x} \quad \text { for } x \in[0,10 \pi],\)
and the curve $C_2$ given by
\(y=e^{-x}(\sin x+\cos x) \quad \text { for } x \in[0,10 \pi] .\)
Let $n$ be the total number of points of intersection of ...

Let $ \vec{a}, \vec{b} $ be two vectors, and let P, Q and R be the points with position vectors $ \vec{a}, \vec{b} $ and $ \vec{a} + \vec{b} $, respectively, with respect to the origin O. If $ |\vec{a} + \vec{b}| = \sqrt{21} $, $ |\vec{a} -...