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Mathematics · 2024 · Shift 1

17 questions from this JEE Advanced paper

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JEE Advanced
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2024 · Shift 1
Mathematics

Mathematics · 2024 · Shift 1

17 questions from this JEE Advanced paper

Differential Equations1 questions Probability2 questions Trigonometric Functions and Equations1 questions Ellipse1 questions Complex Numbers2 questions Matrices and Determinants3 questions 3D Geometry2 questions Quadratic Equation and Inequalities1 questions Permutations and Combinations1 questions Vector Algebra1 questions Circle1 questions Limits Continuity and Differentiability1 questions

Q18.Let $f (x)$ be a continuously differentiable function on the interval $(0, \infty)$ such that $f (1) = 2$ and $t \to x lim \frac{t ^{10} f ( x ) - x ^{10} f ( t )}{t ^{9} - x ^{9}} = 1$ for each $x > 0$ . Then, for all $x > 0, f (x)$ is equal…
Mathematics · Differential Equations · MCQ
Q19.A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student knows the answers of some questions and guesses the answers for the remaining questions. Whenever the student knows the…
Mathematics · Probability · MCQ
Q20.Let $\frac{π}{2}$ $(sin \frac{11 x}{2}) (sin 6 x - cos 6 x) + (cos \frac{11 x}{2}) (sin 6 x + cos 6 x)$ $ is equal to :
Mathematics · Trigonometric Functions and Equations · MCQ
Q21.Consider the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ . Let $S (p, q)$ be a point in the first quadrant such that $\frac{p ^{2}}{9} + \frac{q ^{2}}{4} > 1$ . Two tangents are drawn from $S$ to the ellipse, of which one meets the ellipse at one end…
Mathematics · Ellipse · MCQ
Q22.Let $S = {a + b 2 : a, b \in Z}, T_{1} = {(- 1 + 2)^{n} : n \in N}$ , and $T_{2} = {(1 + 2)^{n} : n \in N}$ . Then which of the following statements is (are) TRUE?
Mathematics · Complex Numbers · Multiple correct
Q23.Let $R^{2}$ denote $R \times R$ . Let $S = {(a, b, c) : a, b, c \in R and a x^{2} + 2 b x y + c y^{2} > 0 for all (x, y) \in R^{2} - {(0, 0)}} .$ Then which of the following…
Mathematics · Matrices and Determinants · Multiple correct
Q24.Let $R^{3}$ denote the three-dimensional space. Take two points $P = (1, 2, 3)$ and $Q = (4, 2, 7)$ . Let $dist (X, Y)$ denote the distance between two points $X$ and $Y$ in $R^{3}$ . Let $S = {X \in R^{3} : (dist (X, P))^{2} - (dist (X, Q))^{2} = 50} and T = {Y \in R^{3} : (dist (Y, Q))^{2} - (dist (Y, P))^{2} = 50} .$ …
Mathematics · 3D Geometry · Multiple correct
Q25.Let $a = 32$ and $b = \frac{1}{5 ^{1/6} 6}$ . If $x, y \in R$ are such that $3 x + 2 y = lo g_{a} (18)^{\frac{5}{4}} and 2 x - y = lo g_{b} (1080),$ then $4 x + 5 y$ …
Mathematics · Quadratic Equation and Inequalities · Numerical
Q26.Let $f (x) = x^{4} + a x^{3} + b x^{2} + c$ be a polynomial with real coefficients such that $f (1) = - 9$ . Suppose that $i 3$ is a root of the equation $4 x^{3} + 3 a x^{2} + 2 b x = 0$ , where $i = - 1$ . If $α_{1}, α_{2}, α_{3}$ , and $α_{4}$ …
Mathematics · Complex Numbers · Numerical
Q27.Let $S = ⎩ ⎨ ⎧ A = 011 1 a b c d e : a, b, c, d, e \in {0, 1}$ and $∣ A ∣ \in {- 1, 1}}$ , where $∣ A ∣$ denotes the determinant of $A$ . Then…
Mathematics · Matrices and Determinants · Numerical
Q28.A group of 9 students, $s_{1}, s_{2}, \dots, s_{9}$ , is to be divided to form three teams $Z$ , and $Z$ of sizes 2,3 , and 4 , respectively. Suppose that $s_{1}$ cannot be selected for the team $X$ , and $s_{2}$ cannot be selected for the team…
Mathematics · Permutations and Combinations · Numerical
Q29.Let $O P = \frac{α - 1}{α} \hat{i} + \hat{j} + \hat{k}, O Q = \hat{i} + \frac{β - 1}{β} \hat{j} + \hat{k}$ and $O R = \hat{i} + \hat{j} + \frac{1}{2} \hat{k}$ be three vectors, where $α, β \in R - {0}$ …
Mathematics · Vector Algebra · Numerical
Q30.Let $X$ be a random variable, and let $P (X = x)$ denote the probability that $X$ takes the value $x$ . Suppose that the points $(x, P (X = x)), x = 0, 1, 2, 3, 4$ , lie on a fixed straight line in the $x y$ -plane, and $P (X = x) = 0$ for all $x \in R - {0, 1, 2, 3, 4}$ …
Mathematics · Probability · Numerical
Q31.Let $α$ and $β$ be the distinct roots of the equation $x^{2} + x - 1 = 0$ . Consider the set $T = {1, α, β}$ . For a $3 \times 3$ matrix $M = (a_{ij})_{3 \times 3}$ , define $R_{i} = a_{i 1} + a_{i 2} + a_{i 3}$ and $C_{j} = a_{1 j} + a_{2 j} + a_{3 j}$ … Includes table
Mathematics · Matrices and Determinants · MCQ
Q32.Let the straight line $y = 2 x$ touch a circle with center $(0, α), α > 0$ , and radius $r$ at a point $A_{1}$ . Let $B_{1}$ be the point on the circle such that the line segment $A_{1} B_{1}$ is a diameter of the circle. Let $α + r = 5 + 5$ … Includes table
Mathematics · Circle · MCQ
Q33.Let $γ \in R$ be such that the lines $L_{1} : \frac{x + 11}{1} = \frac{y + 21}{2} = \frac{z + 29}{3}$ and $L_{2} : \frac{x + 16}{3} = \frac{y + 11}{2} = \frac{z + 4}{γ}$ intersect. Let $R_{1}$ be the point of intersection of $L_{1}$ and $L_{2}$ . Let $O = (0, 0, 0)$ … Includes table
Mathematics · 3D Geometry · MCQ
Q34.Let $f : R \to R$ and $g : R \to R$ be functions defined by $f (x) = {x ∣ x ∣ sin (\frac{1}{x}), 0, x e q 0, x = 0, and g (x) = {1 - 2 x, 0, 0 \leq x \leq \frac{1}{2}, otherwise .$ … Includes table
Mathematics · Limits Continuity and Differentiability · MCQ