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Mathematics · 2023 · 11 Apr · Shift 1

24 questions from this JEE Main paper

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2023 · 11 Apr · Shift 1
Mathematics

Mathematics · 2023 · 11 Apr · Shift 1

24 questions from this JEE Main paper

Hyperbola2 questions Probability1 questions Sequences and Series1 questions Complex Numbers1 questions Differential Equations1 questions Definite Integration2 questions Statistics1 questions Vector Algebra2 questions Matrices and Determinants2 questions Limits Continuity and Differentiability1 questions Ellipse1 questions Area Under the Curves1 questions Permutations and Combinations2 questions Logarithm1 questions Sets and Relations1 questions 3D Geometry1 questions Binomial Theorem2 questions Quadratic Equation and Inequalities1 questions

Q25.Let R be a rectangle given by the lines $x = 0, x = 2, y = 0$ and $y = 5$ . Let A $(α, 0)$ and B $(0, β), α \in [0, 2]$ and $β \in [0, 5]$ , be such that the line segment AB divides the area of the rectangle R in the ratio 4 : 1. Then, the…
Mathematics · Hyperbola · MCQ
Q26.Let $S = {M = [a_{ij}], a_{ij} \in {0, 1, 2}, 1 \leq i, j \leq 2}$ be a sample space and $A = {M \in S : M$ is invertible $}$ be an event. Then $P (A)$ is equal to :
Mathematics · Probability · MCQ
Q27.Let $x_{1}, x_{2}, \dots, x_{100}$ be in an arithmetic progression, with $x_{1} = 2$ and their mean equal to 200 . If $y_{i} = i (x_{i} - i), 1 \leq i \leq 100$ , then the mean of $y_{1}, y_{2}, \dots, y_{100}$ is :
Mathematics · Sequences and Series · MCQ
Q28.Let $w_{1}$ be the point obtained by the rotation of $z_{1} = 5 + 4 i$ about the origin through a right angle in the anticlockwise direction, and $w_{2}$ be the point obtained by the rotation of $z_{2} = 3 + 5 i$ about the origin through a right…
Mathematics · Complex Numbers · MCQ
Q29.Let $y = y (x)$ be a solution curve of the differential equation. $(1 - x^{2} y^{2}) d x = y d x + x d y$ . If the line $x = 1$ intersects the curve $y = y (x)$ at $y = 2$ and the line $x = 2$ intersects the curve $y = y (x)$ at $y = α$ , then a…
Mathematics · Differential Equations · MCQ
Q30.The value of the integral $\int_{- l o g_{e} 2}^{l o g_{e} 2} e^{x} (lo g_{e} (e^{x} + 1 + e^{2 x})) d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q31.Let sets A and B have 5 elements each. Let the mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A and B be 12 and 20 respectively. A new set C of 10 elements is formed by subtracting 3…
Mathematics · Statistics · MCQ
Q32.For any vector $a = a_{1} \hat{i} + a_{2} \hat{j} + a_{3} \hat{k}$ , with $10 ∣ a_{i} ∣ (A) :$ \max \left\{\left|a_{1}\right|,\left|a_{2}\right|,\left|a_{3}\right|\right\} \leq|\vec{a}| $(B) :$ |\vec{a}| \leq 3 \max…
Mathematics · Vector Algebra · MCQ
Q33.Let $A$ be a $2 \times 2$ matrix with real entries such that $A^{'} = α A + I$ , where $α \in R - {- 1, 1}$ . If $det (A^{2} - A) = 4$ , then the sum of all possible values…
Mathematics · Matrices and Determinants · MCQ
Q34.Let $f (x) = [x^{2} - x] + ∣ - x + [x] ∣$ , where $x \in R$ and $[t]$ denotes the greatest integer less than or equal to $t$ . Then, $f$ is :
Mathematics · Limits Continuity and Differentiability · MCQ
Q35.Consider ellipses $E_{k} : k x^{2} + k^{2} y^{2} = 1, k = 1, 2, \dots, 20$ . Let $C_{k}$ be the circle which touches the four chords joining the end points (one on minor axis and another on major axis) of the ellipse $E_{k}$ …
Mathematics · Ellipse · MCQ
Q36.Area of the region ${(x, y) : x^{2} + (y - 2)^{2} \leq 4, x^{2} \geq 2 y}$ is
Mathematics · Area Under the Curves · MCQ
Q37.Let $a$ be a non-zero vector parallel to the line of intersection of the two planes described by $\hat{i} + \hat{j}, \hat{i} + \hat{k}$ and $\hat{i} - \hat{j}, \hat{j} - \hat{k}$ . If $θ$ is the angle between the vector $a$ and the…
Mathematics · Vector Algebra · MCQ
Q38.The number of triplets $(x, y, z)$ , where $x, y, z$ are distinct non negative integers satisfying $x + y + z = 15$ , is :
Mathematics · Permutations and Combinations · MCQ
Q39.The number of integral solutions $x$ of $lo g_{(x + \frac{7}{2})} (\frac{x - 7}{2 x - 3})^{2} \geq 0$ is :
Mathematics · Logarithm · MCQ
Q40.An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?
Mathematics · Sets and Relations · MCQ
Q41.Let $A = 0 a 1 10 c 230$ , where $a, c \in R$ . If $A^{3} = A$ and the positive value of $a$ belongs to the interval $(n - 1, n]$ , where $n \in N$ …
Mathematics · Matrices and Determinants · Numerical
Q42.Let $H_{n} : \frac{x ^{2}}{1 + n} - \frac{y ^{2}}{3 + n} = 1, n \in N$ . Let $k$ be the smallest even value of $n$ such that the eccentricity of $H_{k}$ is a rational number. If $l$ is the length…
Mathematics · Hyperbola · Numerical
Q43.For $m, n > 0$ , let $α (m, n) = \int_{0}^{2} t^{m} (1 + 3 t)^{n} d t$ . If $11 α (10, 6) + 18 α (11, 5) = p (14)^{6}$ , then $p$ is equal to .
Mathematics · Definite Integration · Numerical
Q44.In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sits on the allotted seat, is .
Mathematics · Permutations and Combinations · Numerical
Q45.Let a line $l$ pass through the origin and be perpendicular to the lines $l_{1} : r = (\overset{}{^} - 11 \overset{}{^} - 7 \hat{k}) + λ (\hat{i} + 2 \overset{}{^} + 3 \hat{k}), λ \in R$ and $l_{2} : r = (- \overset{}{^} + \hat{k}) + μ (2 \overset{}{^} + 2 \overset{}{^} + \hat{k}), μ \in R$ …
Mathematics · 3D Geometry · Numerical
Q46.The mean of the coefficients of $x, x^{2}, \dots, x^{7}$ in the binomial expansion of $(2 + x)^{9}$ is .
Mathematics · Binomial Theorem · Numerical
Q47.If $a$ and $b$ are the roots of the equation $x^{2} - 7 x - 1 = 0$ , then the value of $\frac{a ^{21} + b ^{21} + a ^{17} + b ^{17}}{a ^{19} + b ^{19}}$ is equal to .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q48.The number of integral terms in the expansion of $(3^{\frac{1}{2}} + 5^{\frac{1}{4}})^{680}$ is equal to .
Mathematics · Binomial Theorem · Numerical