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Mathematics · 2024 · 8 Apr · Shift 2

30 questions from this JEE Main paper

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2024 · 8 Apr · Shift 2
Mathematics

Mathematics · 2024 · 8 Apr · Shift 2

30 questions from this JEE Main paper

Differential Equations2 questions 3D Geometry2 questions Probability1 questions Area Under the Curves1 questions Vector Algebra2 questions Straight Lines and Pair of Straight Lines2 questions Matrices and Determinants2 questions Definite Integration1 questions Functions1 questions Sequences and Series2 questions Limits Continuity and Differentiability2 questions Sets and Relations1 questions Complex Numbers1 questions Permutations and Combinations1 questions Application of Derivatives2 questions Trigonometric Ratio and Identites1 questions Circle1 questions Binomial Theorem1 questions Statistics1 questions Quadratic Equation and Inequalities1 questions Indefinite Integrals1 questions Hyperbola1 questions

Q31.Let $y = y (x)$ be the solution curve of the differential equation $sec y \frac{d y}{d x} + 2 x sin y = x^{3} cos y, y (1) = 0$ . Then $y (3)$ is equal to:
Mathematics · Differential Equations · MCQ
Q32.If the shortest distance between the lines $\frac{x - λ}{2} = \frac{y - 4}{3} = \frac{z - 3}{4}$ and $\frac{x - 2}{4} = \frac{y - 4}{6} = \frac{z - 7}{8}$ is $\frac{13}{29}$ , then a value of $λ$ is :
Mathematics · 3D Geometry · MCQ
Q33.There are three bags $Z$ and $Z$ . Bag $X$ contains 5 one-rupee coins and 4 five-rupee coins; Bag $Y$ contains 4 one-rupee coins and 5 five-rupee coins and Bag $Z$ contains 3 one-rupee coins and 6 five-rupee coins. A bag is selected at…
Mathematics · Probability · MCQ
Q34.The area of the region in the first quadrant inside the circle $x^{2} + y^{2} = 8$ and outside the parabola $y^{2} = 2 x$ is equal to :
Mathematics · Area Under the Curves · MCQ
Q35.Let $a = 4 \hat{i} - \hat{j} + \hat{k}, b = 11 \hat{i} - \hat{j} + \hat{k}$ and $c$ be a vector such that $(a + b) \times c = c \times (- 2 a + 3 b)$ …
Mathematics · Vector Algebra · MCQ
Q36.If the line segment joining the points $(5, 2)$ and $(2, a)$ subtends an angle $\frac{π}{4}$ at the origin, then the absolute value of the product of all possible values of $a$ is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q37.If $α e q a, β e q b, γ e q c$ and $α a a b β b c c γ = 0$ …
Mathematics · Matrices and Determinants · MCQ
Q38.Let $α \int l o g_{e} 4 \frac{d x}{e ^{x} - 1} = \frac{π}{6}$ . Then $e^{α}$ and $e^{- α}$ are the roots of the equation :
Mathematics · Definite Integration · MCQ
Q39.If the system of equations $x + 4 y - z = λ, 7 x + 9 y + μ z = - 3, 5 x + y + 2 z = - 1$ has infinitely many solutions, then $(2 μ + 3 λ)$ is equal to :
Mathematics · Matrices and Determinants · MCQ
Q40.Let $f (x) = {- a x + a if if - a \leq x \leq 0 0 < x \leq a$ where $a > 0$ and $g (x) = (f (∣ x ∣) - ∣ f (x) ∣) /2$ …
Mathematics · Functions · MCQ
Q41.In an increasing geometric progression of positive terms, the sum of the second and sixth terms is $\frac{70}{3}$ and the product of the third and fifth terms is 49. Then the sum of the $4^{th}, 6^{th}$ and $8^{th}$ …
Mathematics · Sequences and Series · MCQ
Q42.For $a, b > 0$ , let $f (x) = {\frac{t a n (( a + 1 ) x ) + b t a n x}{x}, x 0$ be a continuous function at $x = 0$ . Then $\frac{b}{a}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q43.Let $A = {2, 3, 6, 8, 9, 11}$ and $B = {1, 4, 5, 10, 15}$ . Let $R$ be a relation on $A \times B$ defined by $(a, b) R (c, d)$ if and only if $3 a d - 7 b c$ is an even integer. Then the relation $R$ is
Mathematics · Sets and Relations · MCQ
Q44.Let $a = \hat{i} + 2 \hat{j} + 3 \hat{k}, b = 2 \hat{i} + 3 \hat{j} - 5 \hat{k}$ and $c = 3 \hat{i} - \hat{j} + λ \hat{k}$ be three vectors. Let $r$ …
Mathematics · Vector Algebra · MCQ
Q45.The sum of all possible values of $θ \in [- π, 2 π]$ , for which $\frac{1 + i c o s θ}{1 - 2 i c o s θ}$ is purely imaginary, is equal to :
Mathematics · Complex Numbers · MCQ
Q46.The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets are not necessarily distinct, is equal to:
Mathematics · Permutations and Combinations · MCQ
Q47.If the function $f (x) = 2 x^{3} - 9 ax^{2} + 12 a^{2} x + 1, a > 0$ has a local maximum at $x = α$ and a local minimum at $x = α^{2}$ , then $α$ and $α^{2}$ are the roots of the equation :
Mathematics · Application of Derivatives · MCQ
Q48.If the value of $\frac{3 c o s 3 6 ^{\circ} + 5 s i n 1 8 ^{\circ}}{5 c o s 3 6 ^{\circ} - 3 s i n 1 8 ^{\circ}}$ is $\frac{a 5 - b}{c}$ , where $a, b, c$ are natural numbers and $gcd (a, c) = 1$ , then $a + b + c$ is equal to :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q49.If the image of the point $(- 4, 5)$ in the line $x + 2 y = 2$ lies on the circle $(x + 4)^{2} + (y - 3)^{2} = r^{2}$ , then $r$ is equal to:
Mathematics · Circle · MCQ
Q50.If the term independent of $x$ in the expansion of $(a x^{2} + \frac{1}{2 x ^{3}})^{10}$ is 105 , then $a^{2}$ is equal to :
Mathematics · Binomial Theorem · MCQ
Q51.Let $a, b, c \in N$ and $a < b < c$ . Let the mean, the mean deviation about the mean and the variance of the 5 observations $9, 25, a, b, c$ be 18, 4 and $\frac{136}{5}$ ,…
Mathematics · Statistics · Numerical
Q52.The number of distinct real roots of the equation $∣ x + 1∣∣ x + 3∣ - 4∣ x + 2∣ + 5 = 0$ , is
Mathematics · Quadratic Equation and Inequalities · Numerical
Q53.If $\int \frac{1}{5 ( x - 1 ) ^{4} ( x + 3 ) ^{6}} d x = A (\frac{α x - 1}{β x + 3})^{B} + C$ , where $C$ is the constant of integration, then the value of $α + β + 20 AB$ is …
Mathematics · Indefinite Integrals · Numerical
Q54.Let $S$ be the focus of the hyperbola $\frac{x ^{2}}{3} - \frac{y ^{2}}{5} = 1$ , on the positive $x$ -axis. Let $C$ be the circle with its centre at $A (6, 5)$ and passing through the point $S$ . If $O$ …
Mathematics · Hyperbola · Numerical
Q55.Let $P (α, β, γ)$ be the image of the point $Q (1, 6, 4)$ in the line $\frac{x}{1} = \frac{y - 1}{2} = \frac{z - 2}{3}$ . Then $2 α + β + γ$ is equal to
Mathematics · 3D Geometry · Numerical
Q56.Let $A$ be the region enclosed by the parabola $y^{2} = 2 x$ and the line $x = 24$ . Then the maximum area of the rectangle inscribed in the region $A$ is .
Mathematics · Application of Derivatives · Numerical
Q57.Let $α ∣ x ∣ = ∣ y ∣ e^{x y - β}, α, β \in N$ be the solution of the differential equation $x d y - y d x + x y (x d y + y d x) = 0, y (1) = 2$ . Then $α + β$ is equal to …
Mathematics · Differential Equations · Numerical
Q58.If $α = lim_{x \to 0^{+}} (\frac{e ^{t a n x} - e ^{x}}{t a n x - x})$ and $β = lim_{x \to 0} (1 + sin x)^{\frac{1}{2} c o t x}$ are the roots of the quadratic…
Mathematics · Limits Continuity and Differentiability · Numerical
Q59.An arithmetic progression is written in the following way The sum of all the terms of the 10th row is . Includes diagram
Mathematics · Sequences and Series · Numerical
Q60.Let a ray of light passing through the point $(3, 10)$ reflects on the line $2 x + y = 6$ and the reflected ray passes through the point $(7, 2)$ . If the equation of the incident ray is $a x + b y + 1 = 0$ , then $a^{2} + b^{2} + 3 ab$ is equal to …
Mathematics · Straight Lines and Pair of Straight Lines · Numerical