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Mathematics · 2024 · 31 Jan · Shift 1

30 questions from this JEE Main paper

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2024 · 31 Jan · Shift 1
Mathematics

Mathematics · 2024 · 31 Jan · Shift 1

30 questions from this JEE Main paper

Limits Continuity and Differentiability2 questions Inverse Trigonometric Functions1 questions Quadratic Equation and Inequalities1 questions Straight Lines and Pair of Straight Lines1 questions Sequences and Series2 questions Functions1 questions Differential Equations2 questions Probability2 questions Vector Algebra3 questions Matrices and Determinants1 questions Area Under the Curves1 questions Binomial Theorem2 questions Application of Derivatives1 questions Circle1 questions Hyperbola2 questions Complex Numbers1 questions Definite Integration3 questions 3D Geometry1 questions Permutations and Combinations1 questions Sets and Relations1 questions

Q31. $lim_{x \to 0} \frac{e ^{2∣ s i n x ∣} - 2∣ s i n x ∣ - 1}{x ^{2}}$
Mathematics · Limits Continuity and Differentiability · MCQ
Q32.For $α, β, γ e q 0$ , if $sin^{- 1} α + sin^{- 1} β + sin^{- 1} γ = π$ and $(α + β + γ) (α - γ + β) = 3 α β$ , then $γ$ equals
Mathematics · Inverse Trigonometric Functions · MCQ
Q33.Let $S$ be the set of positive integral values of $a$ for which $\frac{a x ^{2} + 2 ( a + 1 ) x + 9 a + 4}{x ^{2} - 8 x + 32} < 0, \forall x \in R$ . Then, the number of elements in $S$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q34.Let $α, β, γ, δ \in Z$ and let $A (α, β), B (1, 0), C (γ, δ)$ and $D (1, 2)$ be the vertices of a parallelogram $ABCD$ . If $A B = 10$ and the points $A$ and $C$ lie…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q35.For $0 < c < b < a$ , let $(a + b - 2 c) x^{2} + (b + c - 2 a) x + (c + a - 2 b) = 0$ and $α \neq = 1$ be one of its root. Then, among the two statements (I) If $α \in (- 1, 0)$ , then $b$ cannot be the geometric mean of $a$ and $c$ (II) If $α \in (0, 1)$ …
Mathematics · Sequences and Series · MCQ
Q36.If $f (x) = \frac{4 x + 3}{6 x - 4}, x e q \frac{2}{3}$ and $(f \circ f) (x) = g (x)$ , where $g : R - {\frac{2}{3}} \to R - {\frac{2}{3}}$ , then $(g o g o g) (4)$ is equal to
Mathematics · Functions · MCQ
Q37.Let $y = y (x)$ be the solution of the differential equation $\frac{d y}{d x} = \frac{( t a n x ) + y}{s i n x ( s e c x - s i n x t a n x )}, x \in (0, \frac{π}{2})$ satisfying the condition $y (\frac{π}{4}) = 2$ . Then, $y (\frac{π}{3})$ …
Mathematics · Differential Equations · MCQ
Q38.Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable $x$ to be the number of rotten apples in a draw of two apples, the variance of $x$ is
Mathematics · Probability · MCQ
Q39.Let $a = 3 \hat{i} + \hat{j} - 2 \hat{k}, b = 4 \hat{i} + \hat{j} + 7 \hat{k}$ and $c = \hat{i} - 3 \hat{j} + 4 \hat{k}$ be three vectors. If a vectors $p$ satisfies $p \times b = c \times b$ and $p \cdot a = 0$ …
Mathematics · Vector Algebra · MCQ
Q40.The sum of the series $\frac{1}{1 - 3 \cdot 1 ^{2} + 1 ^{4}} + \frac{2}{1 - 3 \cdot 2 ^{2} + 2 ^{4}} + \frac{3}{1 - 3 \cdot 3 ^{2} + 3 ^{4}} + \dots$ up to 10 -terms is
Mathematics · Sequences and Series · MCQ
Q41.Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each drawing. Then the probability, that first drawn marble is red and second drawn marble is…
Mathematics · Probability · MCQ
Q42.The distance of the point $Q (0, 2, - 2)$ form the line passing through the point $P (5, - 4, 3)$ and perpendicular to the lines $r = (- 3 \hat{i} + 2 \hat{k}) + λ (2 \hat{i} + 3 \hat{j} + 5 \hat{k}), λ \in R$ and $r = (\hat{i} - 2 \hat{j} + \hat{k}) + μ (- \hat{i} + 3 \hat{j} + 2 \hat{k}), μ \in R$ …
Mathematics · Vector Algebra · MCQ
Q43.If the system of linear equations $x - 2 y + z = - 4 2 x + α y + 3 z = 5 3 x - y + β z = 3$ has infinitely many solutions, then $12 α + 13 β$ is equal to
Mathematics · Matrices and Determinants · MCQ
Q44.Let $g (x)$ be a linear function and $f (x) = {g (x) (\frac{1 + x}{2 + x})^{\frac{1}{x}}, x \leq 0, x > 0$ , is continuous at $x = 0$ . If $f^{'} (1) = f (- 1)$ , then the value $g (3)$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q45.The area of the region ${(x, y) : y^{2} \leq 4 x, x 0, x e q 3}$ is
Mathematics · Area Under the Curves · MCQ
Q46.The solution curve of the differential equation $y \frac{d x}{d y} = x (lo g_{e} x - lo g_{e} y + 1), x > 0, y > 0$ passing through the point $(e, 1)$ is
Mathematics · Differential Equations · MCQ
Q47.Let $a$ be the sum of all coefficients in the expansion of $(1 - 2 x + 2 x^{2})^{2023} (3 - 4 x^{2} + 2 x^{3})^{2024}$ and $b = lim_{x \to 0} (\frac{\int _{0}^{x} \frac{l o g ( 1 + t )}{t ^{2024} + 1} d t}{x ^{2}})$ . If the…
Mathematics · Binomial Theorem · MCQ
Q48. $If f (x) = x^{3} 3 x^{2} + 2 x^{3} - x 2 x^{2} + 1 2 x 4 1 + 3 x x^{3} + 6 x^{2} - 2 for all x \in R, then 2 f (0) + f^{'} (0) is equal to$ …
Mathematics · Application of Derivatives · MCQ
Q49.If one of the diameters of the circle $x^{2} + y^{2} - 10 x + 4 y + 13 = 0$ is a chord of another circle $C$ , whose center is the point of intersection of the lines $2 x + 3 y = 12$ and $3 x - 2 y = 5$ , then the radius of the circle $C$ is :
Mathematics · Circle · MCQ
Q50.If the foci of a hyperbola are same as that of the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{25} = 1$ and the eccentricity of the hyperbola is $\frac{15}{8}$ times the eccentricity of the ellipse, then the smaller focal distance of the point $(2, \frac{14}{3} \frac{2}{5})$ …
Mathematics · Hyperbola · MCQ
Q51.If $α$ denotes the number of solutions of $∣1 - i ∣^{x} = 2^{x}$ and $β = (\frac{∣ z ∣}{a r g ( z )})$ , where $$z=\frac{\pi}{4}(1+i)^4\left[\frac{1-\sqrt{\pi} i}{\sqrt{\pi}+i}+\frac{\sqrt{\pi}-i}{1+\sqrt{\pi} i}\right],…
Mathematics · Complex Numbers · Numerical
Q52.In the expansion of $(1 + x) (1 - x^{2}) (1 + \frac{3}{x} + \frac{3}{x ^{2}} + \frac{1}{x ^{3}})^{5}, x e q 0$ , the sum of the coefficients of $x^{3}$ and $x^{- 13}$ is equal to .
Mathematics · Binomial Theorem · Numerical
Q53.Let $a$ and $b$ be two vectors such that $∣ a ∣ = 1, ∣ b ∣ = 4$ , and $a \cdot b = 2$ . If $c = (2 a \times b) - 3 b$ and the angle between $b$ and $c$ is $α$ , then $192 sin^{2} α$ …
Mathematics · Vector Algebra · Numerical
Q54.If the integral $525 0 \int \frac{π}{2} sin 2 x cos^{\frac{11}{2}} x (1 + cos^{\frac{5}{2}} x)^{\frac{1}{2}} d x$ is equal to $(n 2 - 64)$ , then $n$ is equal to .
Mathematics · Definite Integration · Numerical
Q55.Let $S = (- 1, \infty)$ and $f : S \to R$ be defined as $f (x) = \int_{- 1}^{x} (e^{t} - 1)^{11} (2 t - 1)^{5} (t - 2)^{7} (t - 3)^{12} (2 t - 10)^{61} d t,$ Let $p =$ Sum of squares of the values of $x$ , where $f (x)$ …
Mathematics · Definite Integration · Numerical
Q56.Let $Q$ and $R$ be the feet of perpendiculars from the point $P (a, a, a)$ on the lines $x = y, z = 1$ and $x = - y, z = - 1$ respectively. If $∠ QPR$ is a right angle, then $12 a^{2}$ is equal to …
Mathematics · 3D Geometry · Numerical
Q57.Let the foci and length of the latus rectum of an ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1, a > bb e (\pm 5, 0)$ and $50$ , respectively. Then, the square of the eccentricity of the hyperbola $\frac{x ^{2}}{b ^{2}} - \frac{y ^{2}}{a ^{2} b ^{2}} = 1$ …
Mathematics · Hyperbola · Numerical
Q58.The total number of words (with or without meaning) that can be formed out of the letters of the word 'DISTRIBUTION' taken four at a time, is equal to .
Mathematics · Permutations and Combinations · Numerical
Q59.Let $A = {1, 2, 3, 4}$ and $R = {(1, 2), (2, 3), (1, 4)}$ be a relation on $A$ . Let $S$ be the equivalence relation on $A$ such that $R \subset S$ and the number of elements in $S$ is $n$ . Then, the…
Mathematics · Sets and Relations · Numerical
Q60.Let $f : R \to R$ be a function defined by $f (x) = \frac{4 ^{x}}{4 ^{x} + 2}$ and $M = \int_{f (a)}^{f (1 - a)} x sin^{4} (x (1 - x)) d x, N = \int_{f (a)}^{f (1 - a)} sin^{4} (x (1 - x)) d x; a e q \frac{1}{2}$ . If $α M = β N, α, β \in N$ …
Mathematics · Definite Integration · Numerical