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 · 2024 · Shift 2

17 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
2024 · Shift 2
Mathematics

Mathematics · 2024 · Shift 2

17 questions from this JEE Advanced paper

Inverse Trigonometric Functions1 questions Application of Integration2 questions Limits Continuity and Differentiability3 questions 3D Geometry1 questions Parabola2 questions Functions2 questions Probability1 questions Vector Algebra1 questions Permutations and Combinations2 questions Definite Integration2 questions

Q18.Considering only the principal values of the inverse trigonometric functions, the value of $tan (sin^{- 1} (\frac{3}{5}) - 2 cos^{- 1} (\frac{2}{5}))$ is
Mathematics · Inverse Trigonometric Functions · MCQ
Q19.Let $S = {(x, y) \in R \times R : x \geq 0, y \geq 0, y^{2} \leq 4 x, y^{2} \leq 12 - 2 x$ and $3 y + 8 x \leq 58}$ . If the area of the region $S$ is $α 2$ , then $α$ is equal…
Mathematics · Application of Integration · MCQ
Q20.Let $k \in R$ . If $x \to 0 + lim (sin (sin k x) + cos x + x)^{\frac{2}{x}} = e^{6}$ , then the value of $k$ is
Mathematics · Limits Continuity and Differentiability · MCQ
Q21.Let $f : R \to R$ be a function defined by $f (x) = {x^{2} sin (\frac{π}{x ^{2}}), 0, if x e q 0, if x = 0.$ Then which of the…
Mathematics · Limits Continuity and Differentiability · MCQ
Q22.Let $S$ be the set of all $(α, β) \in R \times R$ such that $x \to \infty lim \frac{s i n ( x ^{2} ) ( l o g _{e} x ) ^{α} s i n ( \frac{1}{x ^{2}} )}{x ^{α β} ( l o g _{e} ( 1 + x ) ) ^{β}} = 0.$ …
Mathematics · Limits Continuity and Differentiability · Multiple correct
Q23.A straight line drawn from the point $P (1, 3, 2)$ , parallel to the line $\frac{x - 2}{1} = \frac{y - 4}{2} = \frac{z - 6}{1}$ , intersects the plane $L_{1} : x - y + 3 z = 6$ at the point $Q$ . Another straight line which passes through $Q$ and is perpendicular…
Mathematics · 3D Geometry · Multiple correct
Q24.Let $A_{1}, B_{1}, C_{1}$ be three points in the $x y$ -plane. Suppose that the lines $A_{1} C_{1}$ and $B_{1} C_{1}$ are tangents to the curve $y^{2} = 8 x$ at $A_{1}$ and $B_{1}$ , respectively. If $O = (0, 0)$ and $C_{1} = (- 4, 0)$ , then which of the following…
Mathematics · Parabola · Multiple correct
Q25.Let $f : R \to R$ be a function such that $f (x + y) = f (x) + f (y)$ for all $x, y \in R$ , and $g : R \to (0, \infty)$ be a function such that $g (x + y) = g (x) g (y)$ for all $x, y \in R$ . If $f (\frac{- 3}{5}) = 12$ …
Mathematics · Functions · Numerical
Q26.A bag contains $N$ balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue. Assume that the balls are identical otherwise. Three balls are drawn randomly one after the other without replacement. For $i = 1, 2, 3$ …
Mathematics · Probability · Numerical
Q27.Let the function $f : R \to R$ be defined by $f (x) = \frac{s i n x}{e ^{π x}} \frac{( x ^{2023} + 2024 x + 2025 )}{( x ^{2} - x + 3 )} + \frac{2}{e ^{π x}} \frac{( x ^{2023} + 2024 x + 2025 )}{( x ^{2} - x + 3 )} .$ …
Mathematics · Functions · Numerical
Q28.Let $p = 2 \hat{i} + \hat{j} + 3 \hat{k}$ and $q = \hat{i} - \hat{j} + \hat{k}$ . If for some real numbers $γ$ , and $γ$ , we have $15 \hat{i} + 10 \hat{j} + 6 \hat{k} = α (2 p + q) + β (p - 2 q) + γ (p \times q),$ …
Mathematics · Vector Algebra · Numerical
Q29.A normal with slope $\frac{1}{6}$ is drawn from the point $(0, - α)$ to the parabola $x^{2} = - 4 a y$ , where $a > 0$ . Let $L$ be the line passing through $(0, - α)$ and parallel to the directrix of the parabola. Suppose that $L$ …
Mathematics · Parabola · Numerical
Q30.Let the function $f : [1, \infty) \to R$ be defined by $f (t) = {(- 1)^{n + 1} \cdot 2 \frac{( 2 n + 1 - t )}{2} f (2 n - 1) + \frac{( t - ( 2 n - 1 ))}{2} f (2 n + 1) if t = 2 n - 1, n \in N if 2 n - 1 < t < 2 n + 1, n \in N$ …
Mathematics · Application of Integration · Numerical
Q31.Let $S = {1, 2, 3, 4, 5, 6}$ and $X$ be the set of all relations $R$ from $S$ to $S$ that satisfy both the following properties: i. $R$ has exactly 6 elements. ii. For each $(a, b) \in R$ , we have $∣ a - b ∣ \geq 2$ . Let $Y = {R \in X$ : The range of…
Mathematics · Permutations and Combinations · Numerical
Q32.Let $S = {1, 2, 3, 4, 5, 6}$ and $X$ be the set of all relations $R$ from $S$ to $S$ that satisfy both the following properties: i. $R$ has exactly 6 elements. ii. For each $(a, b) \in R$ , we have $∣ a - b ∣ \geq 2$ . Let $Y = {R \in X$ : The range of…
Mathematics · Permutations and Combinations · Numerical
Q33.Let $f : [0, \frac{π}{2}] \to [0, 1]$ be the function defined by $f (x) = sin^{2} x$ and let $g : [0, \frac{π}{2}] \to [0, \infty)$ be the function defined by $g (x) = \frac{π x}{2} - x^{2}$ .The value of $2 0 \int \frac{π}{2} f (x) g (x) d x - 0 \int \frac{π}{2} g (x) d x$ …
Mathematics · Definite Integration · Numerical
Q34.Let $f : [0, \frac{π}{2}] \to [0, 1]$ be the function defined by $f (x) = sin^{2} x$ and let $g : [0, \frac{π}{2}] \to [0, \infty)$ be the function defined by $g (x) = \frac{π x}{2} - x^{2}$ .The value of $\frac{16}{π ^{3}} 0 \int \frac{π}{2} f (x) g (x) d x$ …
Mathematics · Definite Integration · Numerical