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Mathematics · 2022 · 25 Jul · Shift 1

20 questions from this JEE Main paper

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2022 · 25 Jul · Shift 1
Mathematics

Mathematics · 2022 · 25 Jul · Shift 1

20 questions from this JEE Main paper

Functions1 questions Quadratic Equation and Inequalities1 questions Complex Numbers1 questions Matrices and Determinants2 questions Limits Continuity and Differentiability2 questions Application of Derivatives2 questions Area Under the Curves2 questions Definite Integration1 questions Differential Equations2 questions Straight Lines and Pair of Straight Lines1 questions Vector Algebra1 questions Probability1 questions Permutations and Combinations1 questions Binomial Theorem1 questions Sequences and Series1 questions

Q21.The total number of functions, $f : {1, 2, 3, 4} \to {1, 2, 3, 4, 5, 6}$ such that $f (1) + f (2) = f (3)$ , is equal to :
Mathematics · Functions · MCQ
Q22.If $α, β, γ, δ$ are the roots of the equation $x^{4} + x^{3} + x^{2} + x + 1 = 0$ , then $α^{2021} + β^{2021} + γ^{2021} + δ^{2021}$ is equal to :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q23.For $n \in N$ , let $S_{n} = {z \in C : ∣ z - 3 + 2 i ∣ = \frac{n}{4}}$ and $T_{n} = {z \in C : ∣ z - 2 + 3 i ∣ = \frac{1}{n}}$ . Then the number…
Mathematics · Complex Numbers · MCQ
Q24.The number of $θ \in (0, 4 π)$ for which the system of linear equations $3 (sin 3 θ) x - y + z = 2 3 (cos 2 θ) x + 4 y + 3 z = 3 6 x + 7 y + 7 z = 9$ has no solution, is :
Mathematics · Matrices and Determinants · MCQ
Q25.If $n \to \infty lim (n^{2} - n - 1 + n α + β) = 0$ , then $8 (α + β)$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q26.If the absolute maximum value of the function $f (x) = (x^{2} - 2 x + 7) e^{(4 x^{3} - 12 x^{2} - 180 x + 31)}$ in the interval $[- 3, 0]$ is $f (α)$ , then :
Mathematics · Application of Derivatives · MCQ
Q27.The curve $y (x) = a x^{3} + b x^{2} + c x + 5$ touches the $x$ -axis at the point $P (- 2, 0)$ and cuts the $y$ -axis at the point $Q$ , where $y^{'}$ is equal to 3 . Then the local maximum value of $y (x)$ is:
Mathematics · Application of Derivatives · MCQ
Q28.The area of the region given by $A = {(x, y) : x^{2} \leq y \leq min {x + 2, 4 - 3 x}}$ is :
Mathematics · Area Under the Curves · MCQ
Q29.For any real number $x$ , let $[x]$ denote the largest integer less than equal to $x$ . Let $f$ be a real valued function defined on the interval $[- 10, 10]$ by $f (x) = {x - [x], if [x] is odd 1 + [x] - x, if [x] is even .$ …
Mathematics · Definite Integration · MCQ
Q30.The slope of the tangent to a curve $C : y = y (x)$ at any point $(x, y)$ on it is $\frac{2 e ^{2 x} - 6 e ^{- x} + 9}{2 + 9 e ^{- 2 x}}$ . If $C$ passes through the points $$\left(0, \frac{1}{2}+\frac{\pi}{2…
Mathematics · Differential Equations · MCQ
Q31.The general solution of the differential equation $(x - y^{2}) d x + y (5 x + y^{2}) d y = 0$ is :
Mathematics · Differential Equations · MCQ
Q32.A line, with the slope greater than one, passes through the point $A (4, 3)$ and intersects the line $x - y - 2 = 0$ at the point B. If the length of the line segment $A B$ is $\frac{29}{3}$ , then $B$ also lies on the line :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q33.Let the locus of the centre $(α, β), β > 0$ , of the circle which touches the circle $x^{2} + (y - 1)^{2} = 1$ externally and also touches the $x$ -axis be $L$ . Then the area bounded by $L$ and the line $y = 4$ is:
Mathematics · Area Under the Curves · MCQ
Q34.Let $ABC$ be a triangle such that $BC = a, CA = b, AB = c, ∣ a ∣ = 62, ∣ b ∣ = 23$ …
Mathematics · Vector Algebra · MCQ
Q35.If the numbers appeared on the two throws of a fair six faced die are $α$ and $β$ , then the probability that $x^{2} + α x + β > 0$ , for all $x \in R$ , is :
Mathematics · Probability · MCQ
Q36.Let $A = 211 - 1 0 - 1 - 1 - 1 0$ and $B = A - I$ . If $ω = \frac{3 i - 1}{2}$ , then the number of elements in the $set {n \in {1, 2, \dots, 100} : A^{n} + (ω B)^{n} = A + B}$ …
Mathematics · Matrices and Determinants · Numerical
Q37.The letters of the word 'MANKIND' are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number of the word 'MANKIND' is .
Mathematics · Permutations and Combinations · Numerical
Q38.If the maximum value of the term independent of $t$ in the expansion of $(t^{2} x^{\frac{1}{5}} + \frac{( 1 - x ) ^{\frac{1}{10}}}{t})^{15}, x ⩾ 0$ , is $K$ , then is equal to …
Mathematics · Binomial Theorem · Numerical
Q39.Let $p$ be two non-zero real numbers. If $p$ and $r$ are the roots of the equation $x^{2} - 8 a x + 2 a = 0$ and $q$ and s are the roots of the equation $x^{2} + 12 b x + 6 b = 0$ , such that $\frac{1}{p}, \frac{1}{q}, \frac{1}{r}, \frac{1}{s}$ …
Mathematics · Sequences and Series · Numerical
Q40.Let $f (x) = {4 x^{2} - 8 x + 5, if 8 x^{2} - 6 x + 1 ⩾ 0 [4 x^{2} - 8 x + 5], if 8 x^{2} - 6 x + 1 < 0,$ where $[α]$ denotes the greatest integer less…
Mathematics · Limits Continuity and Differentiability · Numerical