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Mathematics · 2023 · 6 Apr · Shift 2

21 questions from this JEE Main paper

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2023 · 6 Apr · Shift 2
Mathematics

Mathematics · 2023 · 6 Apr · Shift 2

21 questions from this JEE Main paper

Binomial Theorem2 questions Area Under the Curves1 questions Permutations and Combinations2 questions Complex Numbers2 questions Matrices and Determinants2 questions Differential Equations1 questions Definite Integration2 questions Ellipse1 questions Probability1 questions Functions1 questions Statistics1 questions Hyperbola1 questions Trigonometric Ratio and Identites1 questions 3D Geometry1 questions Sequences and Series1 questions Application of Derivatives1 questions

Q24.If the coefficient of $x^{7}$ in $(a x^{2} + \frac{1}{2 b x})^{11}$ and $x^{- 7}$ in $(a x - \frac{1}{3 b x ^{2}})^{11}$ are equal, then :
Mathematics · Binomial Theorem · MCQ
Q25.The area bounded by the curves $y = ∣ x - 1∣ + ∣ x - 2∣$ and $y = 3$ is equal to :
Mathematics · Area Under the Curves · MCQ
Q26.All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is :
Mathematics · Permutations and Combinations · MCQ
Q27.Let $a e q b$ be two non-zero real numbers. Then the number of elements in the set $X = {z \in C : Re (a z^{2} + b z) = a$ and $Re (b z^{2} + a z) = b}$ is equal…
Mathematics · Complex Numbers · MCQ
Q28.Let $P$ be a square matrix such that $P^{2} = I - P$ . For $α, β, γ, δ \in N$ , if $P^{α} + P^{β} = γ I - 29 P$ and $P^{α} - P^{β} = δ I - 13 P$ , then $α + β + γ - δ$ is equal to :
Mathematics · Matrices and Determinants · MCQ
Q29.Among the statements : (S1) : $202 3^{2022} - 199 9^{2022}$ is divisible by 8 (S2) : $13 (13)^{n} - 12 n - 13$ is divisible by 144 for infinitely many $n \in N$
Mathematics · Binomial Theorem · MCQ
Q30.If the solution curve $f (x, y) = 0$ of the differential equation $(1 + lo g_{e} x) \frac{d x}{d y} - x lo g_{e} x = e^{y}, x > 0$ , passes through the points $(1, 0)$ and $(α, 2)$ , then $α^{α}$ is equal to :
Mathematics · Differential Equations · MCQ
Q31.Let $f (x)$ be a function satisfying $f (x) + f (π - x) = π^{2}, \forall x \in R$ . Then $\int_{0}^{π} f (x) sin x d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q32. $lim_{n \to \infty} {(2^{\frac{1}{2}} - 2^{\frac{1}{3}}) (2^{\frac{1}{2}} - 2^{\frac{1}{5}}) \dots .. (2^{\frac{1}{2}} - 2^{\frac{1}{2 n + 1}})}$ is equal to :
Mathematics · Definite Integration · MCQ
Q33.In a group of 100 persons 75 speak English and 40 speak Hindi. Each person speaks at least one of the two languages. If the number of persons, who speak only English is $α$ and the number of persons who speak only Hindi is $β$ ,…
Mathematics · Ellipse · MCQ
Q34.Three dice are rolled. If the probability of getting different numbers on the three dice is $\frac{p}{q}$ , where $p$ and $q$ are co-prime, then $q - p$ is equal to :
Mathematics · Probability · MCQ
Q35.For the system of equations $x + y + z = 6 x + 2 y + α z = 10 x + 3 y + 5 z = β$ , which one of the following is NOT true?
Mathematics · Matrices and Determinants · MCQ
Q36.Let the sets A and B denote the domain and range respectively of the function $f (x) = \frac{1}{⌈ x ⌉ - x}$ , where $⌈ x ⌉$ denotes the smallest integer greater than or equal to $x$ . Then among the statements (S1) : $A \cap B = (1, \infty) - N$ …
Mathematics · Functions · MCQ
Q37.If the mean and variance of the frequency distribution are 9 and 15.08 respectively, then the value of $α^{2} + β^{2} - α β$ is . Includes table
Mathematics · Statistics · Numerical
Q38.Let the eccentricity of an ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ is reciprocal to that of the hyperbola $2 x^{2} - 2 y^{2} = 1$ . If the ellipse intersects the hyperbola at right angles, then square of length of the latus-rectum…
Mathematics · Hyperbola · Numerical
Q39.The number of 4-letter words, with or without meaning, each consisting of 2 vowels and 2 consonants, which can be formed from the letters of the word UNIVERSE without repetition is .
Mathematics · Permutations and Combinations · Numerical
Q40.The value of $tan 9^{\circ} - tan 2 7^{\circ} - tan 6 3^{\circ} + tan 8 1^{\circ}$ is .
Mathematics · Trigonometric Ratio and Identites · Numerical
Q41.For $α, β, z \in C$ and $λ > 1$ , if $λ - 1$ is the radius of the circle $∣ z - α ∣^{2} + ∣ z - β ∣^{2} = 2 λ$ , then $∣ α - β ∣$ is equal to .
Mathematics · Complex Numbers · Numerical
Q42.If the lines $\frac{x - 1}{2} = \frac{2 - y}{- 3} = \frac{z - 3}{α}$ and $\frac{x - 4}{5} = \frac{y - 1}{2} = \frac{z}{β}$ intersect, then the magnitude of the minimum value of $8 α β$ is .
Mathematics · 3D Geometry · Numerical
Q43.If $(20)^{19} + 2 (21) (20)^{18} + 3 (21)^{2} (20)^{17} + \dots + 20 (21)^{19} = k (20)^{19}$ , then $k$ is equal to .
Mathematics · Sequences and Series · Numerical
Q44.The number of points, where the curve $y = x^{5} - 20 x^{3} + 50 x + 2$ crosses the $x$ -axis, is .
Mathematics · Application of Derivatives · Numerical