New chat PYQ Library Doubts Rank report

Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →

Mathematics · 2025 · Shift 2

16 questions from this JEE Advanced paper

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Advanced
Papers
2025 · Shift 2
Mathematics

Mathematics · 2025 · Shift 2

16 questions from this JEE Advanced paper

Limits Continuity and Differentiability1 questions Application of Integration1 questions Inverse Trigonometric Functions1 questions Straight Lines and Pair of Straight Lines1 questions Matrices and Determinants1 questions Parabola1 questions Ellipse1 questions Application of Derivatives1 questions Differential Equations1 questions Mathematical Induction and Binomial Theorem1 questions Probability1 questions Vector Algebra1 questions Complex Numbers1 questions Functions1 questions Trigonometric Functions and Equations1 questions Definite Integration1 questions

Q17.Let $x_{0}$ be the real number such that $e^{x_{0}} + x_{0} = 0$ . For a given real number $α$ , define $g (x) = \frac{3 x e ^{x} + 3 x - α e ^{x} - α x}{3 ( e ^{x} + 1 )}$ for all real numbers $x$ . Then which one of the following statements is…
Mathematics · Limits Continuity and Differentiability · MCQ
Q18.Let ℝ denote the set of all real numbers. Then the area of the region $ \left\{ (x, y) \in \mathbb{R} \times \mathbb{R} : x > 0, y > \frac{1}{x}, 5x - 4y - 1 > 0, 4x + 4y - 17 is
Mathematics · Application of Integration · MCQ
Q19.The total number of real solutions of the equation $θ = tan^{- 1} (2 tan θ) - \frac{1}{2} sin^{- 1} (\frac{6 t a n θ}{9 + t a n ^{2} θ})$ is (Here, the inverse trigonometric functions $sin^{- 1} x$ and $\tan^{-1}…
Mathematics · Inverse Trigonometric Functions · MCQ
Q20.Let S denote the locus of the point of intersection of the pair of lines $4 x - 3 y = 12 α$ , $4 α x + 3 α y = 12$ , where $α$ varies over the set of non-zero real numbers. Let T be the tangent to S passing through the points $(p, 0)$ …
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q21.Let $I = (1001)$ and $P = (2003)$ . Let $Q = (x z y 4)$ for some non-zero real…
Mathematics · Matrices and Determinants · Multiple correct
Q22.Let $S$ denote the locus of the mid-points of those chords of the parabola $y^{2} = x$ , such that the area of the region enclosed between the parabola and the chord is $\frac{4}{3}$ . Let $R$ denote the region lying in the first…
Mathematics · Parabola · Multiple correct
Q23.Let $P (x_{1}, y_{1})$ and $Q (x_{2}, y_{2})$ be two distinct points on the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ such that $y_{1} > 0$ , and $y_{2} > 0$ . Let $C$ denote the circle $x^{2} + y^{2} = 9$ , and $M$ be the point $(3, 0)$ .…
Mathematics · Ellipse · Multiple correct
Q24.Let ℝ denote the set of all real numbers. Let f: ℝ → ℝ be defined by $f (x) = ⎩ ⎨ ⎧ \frac{6 x + sin x}{2 x + sin x}, \frac{7}{3}, if x e q 0, if x = 0.$ Then which of the following…
Mathematics · Application of Derivatives · Multiple correct
Q25.Let $y (x)$ be the solution of the differential equation $x^{2} \frac{d y}{d x} + x y = x^{2} + y^{2}, x > \frac{1}{e}$ satisfying $y (1) = 0$ . Then the value of $2 \frac{( y ( e ) ) ^{2}}{y ( e ^{2} )}$ is .
Mathematics · Differential Equations · Numerical
Q26.Let $a_{0}, a_{1}, \dots, a_{23}$ be real numbers such that $(1 + \frac{2}{5} x)^{23} = i = 0 \sum 23 a_{i} x^{i}$ for every real number $x$ . Let $a_{r}$ be the largest among the numbers $a_{j}$ for $0 \leq j \leq 23$ . Then the…
Mathematics · Mathematical Induction and Binomial Theorem · Numerical
Q27.A factory has a total of three manufacturing units, $M_{1}, M_{2}$ , and $M_{3}$ , which produce bulbs independent of each other. The units $M_{1}, M_{2}$ , and $M_{3}$ produce bulbs in the proportions of $2 : 2 : 1$ , respectively. It is known that $20%$ …
Mathematics · Probability · Numerical
Q28.Consider the vectors $x = \overset{}{^} + 2 \overset{}{^} + 3 \hat{k}, y = 2 \overset{}{^} + 3 \overset{}{^} + \hat{k}, and z = 3 \overset{}{^} + \overset{}{^} + 2 \hat{k}$ For two distinct positive real numbers $α$ …
Mathematics · Vector Algebra · Numerical
Q29.For a non-zero complex number $z$ , let $ar g (z)$ denote the principal argument of $z$ , with $- π$ $α = ar g (n = 1 \sum 2025 (- ω)^{n})$ $T h e n t h e v a l u eo f$ \frac{3 \alpha}{\pi} $i s$ \underline{\hspace{2cm}}$.
Mathematics · Complex Numbers · Numerical
Q30.Let $R$ denote the set of all real numbers. Let $f : R \to R$ and $g : R \to (0, 4)$ be functions defined by $f (x) = lo g_{e} (x^{2} + 2 x + 4), and g (x) = \frac{4}{1 + e ^{- 2 x}}$ …
Mathematics · Functions · Numerical
Q31.Let $α = \frac{1}{s i n 6 0 ^{\circ} s i n 6 1 ^{\circ}} + \frac{1}{s i n 6 2 ^{\circ} s i n 6 3 ^{\circ}} + \dots + \frac{1}{s i n 11 8 ^{\circ} s i n 11 9 ^{\circ}}$ Then the value of $(\frac{cosec 1 ^{\circ}}{α})^{2}$ is …
Mathematics · Trigonometric Functions and Equations · Numerical
Q32.If $α = \frac{1}{2} \int 2 \frac{t a n ^{- 1} x}{2 x ^{2} - 3 x + 2} d x$ then the value of $7 tan (\frac{2 α 7}{π})$ is . (Here, the inverse trigonometric function $tan^{- 1} x$ …
Mathematics · Definite Integration · Numerical