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Mathematics · 2023 · 13 Apr · Shift 2

23 questions from this JEE Main paper

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2023 · 13 Apr · Shift 2
Mathematics

Mathematics · 2023 · 13 Apr · Shift 2

23 questions from this JEE Main paper

Sequences and Series1 questions Vector Algebra2 questions Permutations and Combinations2 questions Complex Numbers1 questions Limits Continuity and Differentiability1 questions 3D Geometry1 questions Binomial Theorem2 questions Quadratic Equation and Inequalities2 questions Straight Lines and Pair of Straight Lines1 questions Matrices and Determinants1 questions Area Under the Curves1 questions Definite Integration2 questions Functions1 questions Statistics1 questions Sets and Relations1 questions Differentiation1 questions Inverse Trigonometric Functions1 questions Differential Equations1 questions

Q21.Let a $_{1}$ , a $_{2}$ , a $_{3}$ , .... be a G.P. of increasing positive numbers. Let the sum of its 6th and 8th terms be 2 and the product of its 3rd and 5th terms be $\frac{1}{9}$ . Then $6 (a_{2} + a_{4}) (a_{4} + a_{6})$ is equal to
Mathematics · Sequences and Series · MCQ
Q22.Let $∣ a ∣ = 2, ∣ b ∣ = 3$ and the angle between the vectors $a$ and $b$ be $\frac{π}{4}$ . Then $∣ (a + 2 b) \times (2 a - 3 b) ∣^{2}$ is equal to :
Mathematics · Vector Algebra · MCQ
Q23.All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written as in a dictionary with serial numbers. The serial number of the word MONDAY is :
Mathematics · Permutations and Combinations · MCQ
Q24.Let $S = {z \in C : \overset{z}{ˉ} = i (z^{2} + Re (\overset{z}{ˉ}))}$ . Then $\sum_{z \in S} ∣ z ∣^{2}$ is equal to :
Mathematics · Complex Numbers · MCQ
Q25.If $lim_{x \to 0} \frac{e ^{a x} - c o s ( b x ) - \frac{c x e ^{- c x}}{2}}{1 - c o s ( 2 x )} = 17$ , then $5 a^{2} + b^{2}$ is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q26.The line, that is coplanar to the line $\frac{x + 3}{- 3} = \frac{y - 1}{1} = \frac{z - 5}{5}$ , is :
Mathematics · 3D Geometry · MCQ
Q27.The coefficient of $x^{5}$ in the expansion of $(2 x^{3} - \frac{1}{3 x ^{2}})^{5}$ is :
Mathematics · Binomial Theorem · MCQ
Q28.Let $α, β$ be the roots of the equation $x^{2} - 2 x + 2 = 0$ . Then $α^{14} + β^{14}$ is equal to
Mathematics · Quadratic Equation and Inequalities · MCQ
Q29.Let $(α, β)$ be the centroid of the triangle formed by the lines $15 x - y = 82, 6 x - 5 y = - 4$ and $9 x + 4 y = 17$ . Then $α + 2 β$ and $2 α - β$ are the roots of the equation :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q30.If the system of equations $2 x + y - z = 52 x - 5 y + λ z = μx + 2 y - 5 z = 7$ has infinitely many solutions, then $(λ + μ)^{2} + (λ - μ)^{2}$ is equal to
Mathematics · Matrices and Determinants · MCQ
Q31.The area of the region ${(x, y) : x^{2} \leq y \leq x^{2} - 4, y \geq 1}$ is
Mathematics · Area Under the Curves · MCQ
Q32.The value of $\frac{e ^{- \frac{π}{4}} + 0 \int \frac{π}{4} e ^{- x} t a n ^{50} x d x}{0 \int \frac{π}{4} e ^{- x} ( t a n ^{49} x + t a n ^{51} x ) d x}$ is
Mathematics · Definite Integration · MCQ
Q33.The range of $f (x) = 4 sin^{- 1} (\frac{x ^{2}}{x ^{2} + 1})$ is
Mathematics · Functions · MCQ
Q34.Let for a triangle $ABC$ , $AB = - 2 \hat{i} + \hat{j} + 3 \hat{k} CB = α \hat{i} + β \hat{j} + γ \hat{k} CA = 4 \hat{i} + 3 \hat{j} + δ \hat{k}$ If $δ > 0$ …
Mathematics · Vector Algebra · MCQ
Q35.The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks 20 and 25 were wrongly read as 45 and 50 respectively. Then the correct variance is …
Mathematics · Statistics · Numerical
Q36.Let $A = {- 4, - 3, - 2, 0, 1, 3, 4}$ and $R = {(a, b) \in A \times A : b = ∣ a ∣$ or $b^{2} = a + 1}$ be a relation on $A$ . Then the minimum number of elements, that must be added to…
Mathematics · Sets and Relations · Numerical
Q37.Let $f_{n} = \int_{0}^{\frac{π}{2}} (\sum_{k = 1}^{n} sin^{k - 1} x) (\sum_{k = 1}^{n} (2 k - 1) sin^{k - 1} x) cos x d x, n \in N$ . Then $f_{21} - f_{20}$ is equal to
Mathematics · Definite Integration · Numerical
Q38.The remainder, when $7^{103}$ is divided by 17, is
Mathematics · Binomial Theorem · Numerical
Q39.Let $f (x) = \sum_{k = 1}^{10} k x^{k}, x \in R$ . If $2 f (2) + f^{'} (2) = 119 (2)^{n} + 1$ then $n$ is equal to
Mathematics · Differentiation · Numerical
Q40.For $x \in (- 1, 1]$ , the number of solutions of the equation $sin^{- 1} x = 2 tan^{- 1} x$ is equal to .
Mathematics · Inverse Trigonometric Functions · Numerical
Q41.If $y = y (x)$ is the solution of the differential equation $\frac{d y}{d x} + \frac{4 x}{( x ^{2} - 1 )} y = \frac{x + 2}{( x ^{2} - 1 ) ^{\frac{5}{2}}}, x > 1$ such that $y (2) = \frac{2}{9} lo g_{e} (2 + 3) and y (2) = α lo g_{e} (α + β) + β - γ, α, β, γ \in N, then α β γ is equal to$ …
Mathematics · Differential Equations · Numerical
Q42.Let $[α]$ denote the greatest integer $\leq α$ . Then $[1] + [2] + [3] + \dots + [120]$ is equal to
Mathematics · Quadratic Equation and Inequalities · Numerical
Q43.Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits $1, 2, 3, 4, 5$ with repetition, is .
Mathematics · Permutations and Combinations · Numerical