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Mathematics · 2024 · 5 Apr · Shift 1

30 questions from this JEE Main paper

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2024 · 5 Apr · Shift 1
Mathematics

Mathematics · 2024 · 5 Apr · Shift 1

30 questions from this JEE Main paper

Application of Derivatives3 questions Functions2 questions Straight Lines and Pair of Straight Lines1 questions 3D Geometry2 questions Complex Numbers1 questions Matrices and Determinants2 questions Circle1 questions Probability2 questions Definite Integration2 questions Sequences and Series2 questions Limits Continuity and Differentiability2 questions Ellipse1 questions Trigonometric Ratio and Identites1 questions Vector Algebra2 questions Differential Equations1 questions Area Under the Curves1 questions Parabola1 questions Permutations and Combinations1 questions Binomial Theorem1 questions Quadratic Equation and Inequalities1 questions

Q31.Let a rectangle ABCD of sides 2 and 4 be inscribed in another rectangle PQRS such that the vertices of the rectangle ABCD lie on the sides of the rectangle PQRS. Let a and b be the sides of the rectangle PQRS when its area is maximum. Then…
Mathematics · Application of Derivatives · MCQ
Q32.Let $A = {1, 3, 7, 9, 11}$ and $B = {2, 4, 5, 7, 8, 10, 12}$ . Then the total number of one-one maps $f : A \to B$ , such that $f (1) + f (3) = 14$ , is :
Mathematics · Functions · MCQ
Q33.Let two straight lines drawn from the origin $O$ intersect the line $3 x + 4 y = 12$ at the points $P$ and $Q$ such that $△ OPQ$ is an isosceles triangle and $∠ POQ = 9 0^{\circ}$ . If $l = OP^{2} + PQ^{2} + QO^{2}$ …
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q34.If the line $\frac{2 - x}{3} = \frac{3 y - 2}{4 λ + 1} = 4 - z$ makes a right angle with the line $\frac{x + 3}{3 μ} = \frac{1 - 2 y}{6} = \frac{5 - z}{7}$ , then $4 λ + 9 μ$ is equal to :
Mathematics · 3D Geometry · MCQ
Q35.Consider the following two statements : Statement I: For any two non-zero complex numbers $z_{1}, z_{2}, (∣ z_{1} ∣ + ∣ z_{2} ∣) \frac{z _{1}}{∣ z _{1} ∣} + \frac{z _{2}}{∣ z _{2} ∣} \leq 2 (∣ z_{1} ∣ + ∣ z_{2} ∣), and$ …
Mathematics · Complex Numbers · MCQ
Q36.Let A and B be two square matrices of order 3 such that $∣A∣ = 3$ and $∣B∣ = 2$ . Then $∣ A^{T} A (adj (2 A))^{- 1} (adj (4 B)) (adj (AB))^{- 1} AA^{T} ∣$ …
Mathematics · Matrices and Determinants · MCQ
Q37.Let a circle C of radius 1 and closer to the origin be such that the lines passing through the point $(3, 2)$ and parallel to the coordinate axes touch it. Then the shortest distance of the circle C from the point $(5, 5)$ is :
Mathematics · Circle · MCQ
Q38.Let $f (x) = x^{5} + 2 x^{3} + 3 x + 1, x \in R$ , and $g (x)$ be a function such that $g (f (x)) = x$ for all $x \in R$ . Then $\frac{g ( 7 )}{g ^{'} ( 7 )}$ is equal to :
Mathematics · Application of Derivatives · MCQ
Q39.The coefficients $a, b, c$ in the quadratic equation $a x^{2} + b x + c = 0$ are chosen from the set ${1, 2, 3, 4, 5, 6, 7, 8}$ . The probability of this equation having repeated roots is :
Mathematics · Probability · MCQ
Q40.If the system of equations $11 x + y + λ z = - 5 2 x + 3 y + 5 z = 3 8 x - 19 y - 39 z = μ$ has infinitely many solutions, then $λ^{4} - μ$ is equal to :
Mathematics · Matrices and Determinants · MCQ
Q41.The integral $0 \int π /4 \frac{136 s i n x}{3 s i n x + 5 c o s x} d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q42.If $\frac{1}{1 + 2} + \frac{1}{2 + 3} + \dots + \frac{1}{99 + 100} = m$ and $\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \dots + \frac{1}{99 \cdot 100} = n$ , then the point $(m, n)$ lies…
Mathematics · Sequences and Series · MCQ
Q43.Let $d$ be the distance of the point of intersection of the lines $\frac{x + 6}{3} = \frac{y}{2} = \frac{z + 1}{1}$ and $\frac{x - 7}{4} = \frac{y - 9}{3} = \frac{z - 4}{2}$ from the point $(7, 8, 9)$ . Then $d^{2} + 6$ is equal to :
Mathematics · 3D Geometry · MCQ
Q44.If the function $f (x) = \frac{s i n 3 x + α s i n x - β c o s 3 x}{x ^{3}}, x \in R$ , is continuous at $x = 0$ , then $f (0)$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q45.Let the line $2 x + 3 y - k = 0, k > 0$ , intersect the $x$ -axis and $y$ -axis at the points $A$ and $B$ , respectively. If the equation of the circle having the line segment $A B$ as a diameter is $x^{2} + y^{2} - 3 x - 2 y = 0$ …
Mathematics · Ellipse · MCQ
Q46.The value of $\int_{- π}^{π} \frac{2 y ( 1 + s i n y )}{1 + c o s ^{2} y} d y$ is :
Mathematics · Definite Integration · MCQ
Q47.Suppose $θ \in [0, \frac{π}{4}]$ is a solution of $4 cos θ - 3 sin θ = 1$ . Then $cos θ$ is equal to :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q48.For the function $f (x) = sin x + 3 x - \frac{2}{π} (x^{2} + x), where x \in [0, \frac{π}{2}],$ consider the following two statements : (I) $f$ is increasing in $(0, \frac{π}{2})$ . (II) $f^{'}$ …
Mathematics · Application of Derivatives · MCQ
Q49.If $A (1, - 1, 2), B (5, 7, - 6), C (3, 4, - 10)$ and $D (- 1, - 4, - 2)$ are the vertices of a quadrilateral ABCD, then its area is :
Mathematics · Vector Algebra · MCQ
Q50.If $y = y (x)$ is the solution of the differential equation $\frac{d y}{d x} + 2 y = sin (2 x), y (0) = \frac{3}{4}$ , then $y (\frac{π}{8})$ is equal to :
Mathematics · Differential Equations · MCQ
Q51.The area of the region enclosed by the parabolas $y = x^{2} - 5 x$ and $y = 7 x - x^{2}$ is .
Mathematics · Area Under the Curves · Numerical
Q52.From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at random. Let the random variable $X$ denote the number of defective items in the sample. If the variance of $X$ is $σ^{2}$ , then $96 σ^{2}$ is…
Mathematics · Probability · Numerical
Q53.Suppose $AB$ is a focal chord of the parabola $y^{2} = 12 x$ of length $l$ and slope $m < 3$ . If the distance of the chord $AB$ from the origin is $d$ , then $l d^{2}$ is equal to …
Mathematics · Parabola · Numerical
Q54.The number of ways of getting a sum 16 on throwing a dice four times is .
Mathematics · Permutations and Combinations · Numerical
Q55.Let $f$ be a differentiable function in the interval $(0, \infty)$ such that $f (1) = 1$ and $lim_{t \to x} \frac{t ^{2} f ( x ) - x ^{2} f ( t )}{t - x} = 1$ for each $x > 0$ . Then $2 f (2) + 3 f (3)$ is equal to .
Mathematics · Limits Continuity and Differentiability · Numerical
Q56.If $S = {a \in R : ∣2 a - 1∣ = 3 [a] + 2 {a}}$ , where $[t]$ denotes the greatest integer less than or equal to $t$ and ${t}$ represents the fractional part of $t$ , then $72 \sum_{a \in S} a$ is equal to .
Mathematics · Functions · Numerical
Q57.Let $a_{1}, a_{2}, a_{3}, \dots$ be in an arithmetic progression of positive terms. Let $A_{k} = a_{1}^{2} - a_{2}^{2} + a_{3}^{2} - a_{4}^{2} + \dots + a_{2 k - 1}^{2} - a_{2 k}^{2}$ . If $A_{3} = - 153, A_{5} = - 435$ and $a_{1}^{2} + a_{2}^{2} + a_{3}^{2} = 66$ …
Mathematics · Sequences and Series · Numerical
Q58.Let $a = \hat{i} - 3 \hat{j} + 7 \hat{k}, b = 2 \hat{i} - \hat{j} + \hat{k}$ and $c$ be a vector such that $(a + 2 b) \times c = 3 (c \times a)$ …
Mathematics · Vector Algebra · Numerical
Q59.If the constant term in the expansion of $(1 + 2 x - 3 x^{3}) (\frac{3}{2} x^{2} - \frac{1}{3 x})^{9}$ is $p$ , then $108 p$ is equal to .
Mathematics · Binomial Theorem · Numerical
Q60.The number of distinct real roots of the equation $∣ x ∣∣ x + 2∣ - 5∣ x + 1∣ - 1 = 0$ is .
Mathematics · Quadratic Equation and Inequalities · Numerical