List of top Questions asked in JEE Advanced- 2026

Let \[ S=\{1,2,3,\ldots,10\}. \] Consider the set \[ X=\{R : R \text{ is an equivalence relation on } S \text{ such that } R \text{ has exactly } 42 \text{ elements}\}. \] Then the number of elements in \(X\) 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 \[ g(x)=xf(x),\qquad \forall x\in\mathbb R \] Then which of the following statements is (are) TRUE?