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Mathematics · 2025 · Shift 1

16 questions from this JEE Advanced paper

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JEE Advanced
Papers
2025 · Shift 1
Mathematics

Mathematics · 2025 · Shift 1

16 questions from this JEE Advanced paper

Quadratic Equation and Inequalities1 questions Probability1 questions Limits Continuity and Differentiability3 questions Matrices and Determinants1 questions 3D Geometry1 questions Functions2 questions Complex Numbers1 questions Permutations and Combinations2 questions Vector Algebra2 questions Differential Equations1 questions Statistics1 questions

Q17.Let $R$ denote the set of all real numbers. Let $a_{i}, b_{i} \in R$ for $i \in {1, 2, 3}$ . Define the functions $f : R \to R$ , $g : R \to R$ , and $h : R \to R$ by $f (x) = a_{1} + 10 x + a_{2} x^{2} + a_{3} x^{3} + x^{4} g (x) = b_{1} + 3 x + b_{2} x^{2} + b_{3} x^{3} + x^{4} h (x) = f (x + 1) - g (x + 2)$ …
Mathematics · Quadratic Equation and Inequalities · MCQ
Q18.Three students $S_{1}, S_{2},$ and $S_{3}$ are given a problem to solve. Consider the following events: U: At least one of $S_{1}, S_{2},$ and $S_{3}$ can solve the problem, V: $S_{1}$ can solve the problem, given that neither $S_{2}$ nor $S_{3}$ can solve…
Mathematics · Probability · MCQ
Q19.Let $R$ denote the set of all real numbers. Define the function $f : R \to R$ by $f (x) = {2 - 2 x^{2} - x^{2} sin \frac{1}{x} 2 if x e q 0, if x = 0.$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q20.Consider the matrix $P = 200020003 .$ Let the transpose of a matrix $X$ be denoted by $X^{T}$ . Then the number of $3 \times 3$ invertible matrices $Q$ with…
Mathematics · Matrices and Determinants · MCQ
Q21.Let $L_{1}$ be the line of intersection of the planes given by the equations $2 x + 3 y + z = 4$ and $x + 2 y + z = 5$ . Let $L_{2}$ be the line passing through the point $P (2, - 1, 3)$ and parallel to $L_{1}$ . Let $M$ denote the plane given by the…
Mathematics · 3D Geometry · Multiple correct
Q22.Let ℕ denote the set of all natural numbers, and ℤ denote the set of all integers. Consider the functions f: ℕ → ℤ and g: ℤ → ℕ defined by $f (n) = {\frac{( n + 1 )}{2} \frac{( 4 - n )}{2} if n is odd, if n is even,$ …
Mathematics · Functions · Multiple correct
Q23.Let ℝ denote the set of all real numbers. Let $z_{1} = 1 + 2 i$ and $z_{2} = 3 i$ be two complex numbers, where $i = - 1$ . Let $S = {(x, y) \in R \times R : ∣ x + i y - z_{1} ∣ = 2∣ x + i y - z_{2} ∣} .$ Then which of the…
Mathematics · Complex Numbers · Multiple correct
Q24.Let the set of all relations $R$ on the set ${a, b, c, d, e, f}$ , such that $R$ is reflexive and symmetric, and $R$ contains exactly $10$ elements, be denoted by $S$ . Then the number of elements in $S$ is …
Mathematics · Permutations and Combinations · Numerical
Q25.For any two points $M$ and $N$ in the $X Y$ -plane, let $M N$ denote the vector from $M$ to $N$ , and $0$ denote the zero vector. Let $R$ and $R$ be three distinct points in the $X Y$ -plane. Let $S$ be a point inside…
Mathematics · Vector Algebra · Numerical
Q26.Let $S$ be the set of all seven-digit numbers that can be formed using the digits $2$ and $2$ . For example, $2210222$ is in $S$ , but $0210222$ is NOT in $S$ . Then the number of elements $x$ in $S$ such that at least one of the digits…
Mathematics · Permutations and Combinations · Numerical
Q27.Let α and β be the real numbers such that $x \to 0 lim \frac{1}{x ^{3}} (\frac{α}{2} 0 \int x \frac{1}{1 - t ^{2}} d t + β x cos x) = 2.$ Then the value of α + β is .
Mathematics · Limits Continuity and Differentiability · Numerical
Q28.Let ℝ denote the set of all real numbers. Let f: ℝ → ℝ be a function such that f(x) > 0 for all x ∈ ℝ, and f(x+y) = f(x)f(y) for all x, y ∈ ℝ. Let the real numbers a₁, a₂, ..., a₅₀ be in an arithmetic progression. If f(a₃₁) = 64f(a₂₅),…
Mathematics · Functions · Numerical
Q29.For all x > 0, let y₁(x), y₂(x), and y₃(x) be the functions satisfying $\frac{d y _{1}}{d x} - (sin x)^{2} y_{1} = 0, y_{1} (1) = 5, \frac{d y _{2}}{d x} - (cos x)^{2} y_{2} = 0, y_{2} (1) = \frac{1}{3}, \frac{d y _{3}}{d x} - \frac{( 2 - x ^{3} )}{x ^{3}} y_{3} = 0, y_{3} (1) = \frac{3}{5 e},$ …
Mathematics · Differential Equations · Numerical
Q30.Consider the following frequency distribution: Suppose that the sum of the frequencies is 19 and the median of this frequency distribution is 6. For the given frequency distribution, let $α$ denote the mean deviation about the mean, $β$ … Includes table
Mathematics · Statistics · MCQ
Q31.Let $R$ denote the set of all real numbers. For a real number $x$ , let [ x ] denote the greatest integer less than or equal to $x$ . Let $n$ denote a natural number. Match each entry in List-I to the correct entry in List-II and… Includes table
Mathematics · Limits Continuity and Differentiability · MCQ
Q32.Let $w = \hat{i} + \hat{j} - 2 \hat{k}$ , and $u$ and $v$ be two vectors, such that $u \times v = w$ and $v \times w = u$ . Let $α, β, γ$ , and $t$ be real numbers such that $u = α \hat{i} + β \hat{j} + γ \hat{k}, - t α + β + γ = 0, α - tβ + γ = 0, α + β - t γ = 0.$ … Includes table
Mathematics · Vector Algebra · MCQ