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Mathematics · 2023 · 10 Apr · Shift 2

18 questions from this JEE Main paper

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2023 · 10 Apr · Shift 2
Mathematics

Mathematics · 2023 · 10 Apr · Shift 2

18 questions from this JEE Main paper

Complex Numbers1 questions Permutations and Combinations2 questions Binomial Theorem2 questions Application of Derivatives1 questions Definite Integration1 questions Indefinite Integrals1 questions Statistics1 questions Vector Algebra2 questions Circle1 questions Sets and Relations1 questions Differential Equations1 questions Area Under the Curves1 questions Matrices and Determinants1 questions Inverse Trigonometric Functions1 questions Straight Lines and Pair of Straight Lines1 questions

Q21.Let $S = {z = x + i y : \frac{2 z - 3 i}{4 z + 2 i} is a real number}$ . Then which of the following is NOT correct?
Mathematics · Complex Numbers · MCQ
Q22.Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways, in which they can be transported, is :
Mathematics · Permutations and Combinations · MCQ
Q23.Let the number $(22)^{2022} + (2022)^{22}$ leave the remainder $α$ when divided by 3 and $β$ when divided by 7. Then $(α^{2} + β^{2})$ is equal to :
Mathematics · Binomial Theorem · MCQ
Q24.Let $g (x) = f (x) + f (1 - x)$ and $f^{''} (x) > 0, x \in (0, 1)$ . If $g$ is decreasing in the interval $(0, a)$ and increasing in the interval $(α, 1)$ , then $tan^{- 1} (2 α) + tan^{- 1} (\frac{1}{α}) + tan^{- 1} (\frac{α + 1}{α})$ …
Mathematics · Application of Derivatives · MCQ
Q25.If the coefficients of $x$ and $x^{2}$ in $(1 + x)^{p} (1 - x)^{q}$ are 4 and $-$ 5 respectively, then $2 p + 3 q$ is equal to :
Mathematics · Binomial Theorem · MCQ
Q26.Let $f$ be a continuous function satisfying $\int_{0}^{t^{2}} (f (x) + x^{2}) d x = \frac{4}{3} t^{3}, \forall t > 0$ . Then $f (\frac{π ^{2}}{4})$ is equal to :
Mathematics · Definite Integration · MCQ
Q27.For $α, β, γ, δ \in N$ , if $\int ((\frac{x}{e})^{2 x} + (\frac{e}{x})^{2 x}) lo g_{e} x d x = \frac{1}{α} (\frac{x}{e})^{β x} - \frac{1}{γ} (\frac{e}{x})^{δ x} + C$ …
Mathematics · Indefinite Integrals · MCQ
Q28.Let $μ$ be the mean and $σ$ be the standard deviation of the distribution where $\sum f_{i} = 62$ . If $[x]$ denotes the greatest integer $\leq x$ , then $[μ^{2} + σ^{2}]$ is equal to : Includes table
Mathematics · Statistics · MCQ
Q29.Let $a = 2 \hat{i} + 7 \hat{j} - \hat{k}, b = 3 \hat{i} + 5 \hat{k}$ and $c = \hat{i} - \hat{j} + 2 \hat{k}$ . Let $d$ be a vector which is perpendicular to both $a$ and $b$ , and $c \cdot d = 12$ . Then $(- \hat{i} + \hat{j} - \hat{k}) \cdot (c \times d)$ …
Mathematics · Vector Algebra · MCQ
Q30.If the points $P$ and $Q$ are respectively the circumcenter and the orthocentre of a $△ ABC$ , then $PA + PB + PC$ is equal to :
Mathematics · Vector Algebra · MCQ
Q31.Let A be the point $(1, 2)$ and B be any point on the curve $x^{2} + y^{2} = 16$ . If the centre of the locus of the point P, which divides the line segment $AB$ in the ratio $3 : 2$ is the point C $(α, β)$ , then the length of…
Mathematics · Circle · MCQ
Q32.Let $A = {2, 3, 4}$ and $B = {8, 9, 12}$ . Then the number of elements in the relation $R = {((a_{1}, b_{1}), (a_{2}, b_{2})) \in (A \times B, A \times B) : a_{1}$ …
Mathematics · Sets and Relations · MCQ
Q33.Let the tangent at any point P on a curve passing through the points (1, 1) and $(\frac{1}{10}, 100)$ , intersect positive $x$ -axis and $y$ -axis at the points A and B respectively. If $PA : PB = 1 : k$ and…
Mathematics · Differential Equations · Numerical
Q34.If the area of the region ${(x, y) : x^{2} - 2 \leq y \leq x}$ is $A$ , then $6 A + 162$ is equal to .
Mathematics · Area Under the Curves · Numerical
Q35.The sum of all the four-digit numbers that can be formed using all the digits 2, 1, 2, 3 is equal to .
Mathematics · Permutations and Combinations · Numerical
Q36.Let $S$ be the set of values of $λ$ , for which the system of equations $6 λ x - 3 y + 3 z = 4 λ^{2}$ , $2 x + 6 λ y + 4 z = 1$ , $3 x + 2 y + 3 λ z = λ$ has no solution. Then $12 \sum_{i \in S} ∣ λ ∣$ is equal…
Mathematics · Matrices and Determinants · Numerical
Q37.If the domain of the function $f (x) = sec^{- 1} (\frac{2 x}{5 x + 3})$ is $[α, β) U (γ, δ]$ , then $∣3 α + 10 (β + γ) + 21 δ ∣$ is equal to .
Mathematics · Inverse Trigonometric Functions · Numerical
Q38.Let the equations of two adjacent sides of a parallelogram $ABCD$ be $2 x - 3 y = - 23$ and $5 x + 4 y = 23$ . If the equation of its one diagonal $AC$ is $3 x + 7 y = 23$ and the distance of A from the other diagonal is $d$ ,…
Mathematics · Straight Lines and Pair of Straight Lines · Numerical