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Mathematics · 2023 · 1 Feb · Shift 1

22 questions from this JEE Main paper

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2023 · 1 Feb · Shift 1
Mathematics

Mathematics · 2023 · 1 Feb · Shift 1

22 questions from this JEE Main paper

Permutations and Combinations3 questions Inverse Trigonometric Functions1 questions Sets and Relations1 questions 3D Geometry1 questions Matrices and Determinants1 questions Quadratic Equation and Inequalities1 questions Complex Numbers1 questions Statistics1 questions Differentiation2 questions Functions1 questions Differential Equations2 questions Straight Lines and Pair of Straight Lines1 questions Definite Integration2 questions Sequences and Series1 questions Binomial Theorem1 questions Area Under the Curves1 questions Vector Algebra1 questions

Q22.The value of $\frac{1}{1 ! 50 !} + \frac{1}{3 ! 48 !} + \frac{1}{5 ! 46 !} + \dots . + \frac{1}{49 ! 2 !} + \frac{1}{51 ! 1 !}$ is :
Mathematics · Permutations and Combinations · MCQ
Q23.Let $S$ be the set of all solutions of the equation $cos^{- 1} (2 x) - 2 cos^{- 1} (1 - x^{2}) = π, x \in [- \frac{1}{2}, \frac{1}{2}]$ . Then $\sum_{x \in S} 2 sin^{- 1} (x^{2} - 1)$ is equal to :
Mathematics · Inverse Trigonometric Functions · MCQ
Q24.Let $R$ be a relation on $R$ , given by $R = {(a, b) : 3 a - 3 b + 7$ is an irrational number $}$ . Then $R$ is
Mathematics · Sets and Relations · MCQ
Q25.The shortest distance between the lines $\frac{x - 5}{1} = \frac{y - 2}{2} = \frac{z - 4}{- 3}$ and $\frac{x + 3}{1} = \frac{y + 5}{4} = \frac{z - 1}{- 5}$ is :
Mathematics · 3D Geometry · MCQ
Q26.Let $S$ denote the set of all real values of $λ$ such that the system of equations $λ x + y + z = 1 x + λ y + z = 1 x + y + λ z = 1$ is inconsistent, then $\sum_{λ \in S} (∣ λ ∣^{2} + ∣ λ ∣)$ is equal to
Mathematics · Matrices and Determinants · MCQ
Q27.Let $S = {x : x \in R and (3 + 2)^{x^{2} - 4} + (3 - 2)^{x^{2} - 4} = 10}$ . Then $n (S)$ is equal to
Mathematics · Quadratic Equation and Inequalities · MCQ
Q28.If the center and radius of the circle $\frac{z - 2}{z - 3} = 2$ are respectively $(α, β)$ and $γ$ , then $3 (α + β + γ)$ is equal to :
Mathematics · Complex Numbers · MCQ
Q29.The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1, 3, 5, then the sum of cubes of the remaining two observations is :
Mathematics · Statistics · MCQ
Q30.Let $f (x) = 2 x + tan^{- 1} x$ and $g (x) = lo g_{e} (1 + x^{2} + x), x \in [0, 3]$ . Then
Mathematics · Differentiation · MCQ
Q31.Let $f (x) = 1 + sin^{2} x sin^{2} x sin^{2} x cos^{2} x 1 + cos^{2} x cos^{2} x sin 2 x sin 2 x 1 + sin 2 x, x \in [\frac{π}{6}, \frac{π}{3}]$ …
Mathematics · Functions · MCQ
Q32.The area enclosed by the closed curve $C$ given by the differential equation $\frac{d y}{d x} + \frac{x + a}{y - 2} = 0, y (1) = 0$ is $4 π$ . Let $P$ and $Q$ be the points of intersection of the curve $C$ and the $y$ -axis. If…
Mathematics · Differential Equations · MCQ
Q33.If the orthocentre of the triangle, whose vertices are (1, 2), (2, 3) and (3, 1) is $(α, β)$ , then the quadratic equation whose roots are $α + 4 β$ and $4 α + β$ , is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q34.If $y = y (x)$ is the solution curve of the differential equation $\frac{d y}{d x} + y tan x = x sec x, 0 \leq x \leq \frac{π}{3}, y (0) = 1$ , then $y (\frac{π}{6})$ is equal to
Mathematics · Differential Equations · MCQ
Q35.If $\int_{0}^{1} (x^{21} + x^{14} + x^{7}) (2 x^{14} + 3 x^{7} + 6)^{1/7} d x = \frac{1}{l} (11)^{m / n}$ where $l, m, n \in N, m$ and $n$ are coprime then $l + m + n$ is equal to .
Mathematics · Definite Integration · Numerical
Q36.Let $a_{1} = 8, a_{2}, a_{3}, \dots, a_{n}$ be an A.P. If the sum of its first four terms is 50 and the sum of its last four terms is 170 , then the product of its middle two terms is .
Mathematics · Sequences and Series · Numerical
Q37.Let $f : R \to R$ be a differentiable function such that $f^{'} (x) + f (x) = \int_{0}^{2} f (t) d t$ . If $f (0) = e^{- 2}$ , then $2 f (0) - f (2)$ is equal to .
Mathematics · Definite Integration · Numerical
Q38.The remainder, when $1 9^{200} + 2 3^{200}$ is divided by 49 , is .
Mathematics · Binomial Theorem · Numerical
Q39.The number of 3-digit numbers, that are divisible by either 2 or 3 but not divisible by 7, is .
Mathematics · Permutations and Combinations · Numerical
Q40.The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is .
Mathematics · Permutations and Combinations · Numerical
Q41.Let $A$ be the area bounded by the curve $y = x ∣ x - 3∣$ , the $x$ -axis and the ordinates $x = - 1$ and $x = 2$ . Then $12 A$ is equal to .
Mathematics · Area Under the Curves · Numerical
Q42. $A (2, 6, 2), B (- 4, 0, λ), C (2, 3, - 1)$ and $D (4, 5, 0), ∣ λ ∣ \leq 5$ are the vertices of a quadrilateral $A B C D$ . If its area is 18 square units, then $5 - 6 λ$ is equal to .
Mathematics · Vector Algebra · Numerical
Q43.If $f (x) = x^{2} + g^{'} (1) x + g^{''} (2)$ and $g (x) = f (1) x^{2} + x f^{'} (x) + f^{''} (x)$ , then the value of $f (4) - g (4)$ is equal to .
Mathematics · Differentiation · Numerical