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Mathematics · 2022 · 29 Jul · Shift 1

23 questions from this JEE Main paper

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2022 · 29 Jul · Shift 1
Mathematics

Mathematics · 2022 · 29 Jul · Shift 1

23 questions from this JEE Main paper

Sets and Relations2 questions Complex Numbers1 questions Matrices and Determinants2 questions Quadratic Equation and Inequalities1 questions Limits Continuity and Differentiability2 questions Definite Integration2 questions Differential Equations1 questions Ellipse1 questions Straight Lines and Pair of Straight Lines1 questions Vector Algebra1 questions Area Under the Curves1 questions Parabola1 questions Probability1 questions Application of Derivatives1 questions Statistics1 questions Sequences and Series1 questions Binomial Theorem1 questions Permutations and Combinations1 questions Circle1 questions

Q25.Let R be a relation from the set ${1, 2, 3, \dots, 60}$ to itself such that $R = {(a, b) : b = pq$ , where $p, q ⩾ 3$ are prime numbers}. Then, the number of elements in R is :
Mathematics · Sets and Relations · MCQ
Q26.If $z = 2 + 3 i$ , then $z^{5} + (\overset{z}{ˉ})^{5}$ is equal to :
Mathematics · Complex Numbers · MCQ
Q27.Let A and B be two $3 \times 3$ non-zero real matrices such that AB is a zero matrix. Then
Mathematics · Matrices and Determinants · MCQ
Q28.If $\frac{1}{( 20 - a ) ( 40 - a )} + \frac{1}{( 40 - a ) ( 60 - a )} + \dots + \frac{1}{( 180 - a ) ( 200 - a )} = \frac{1}{256}$ , then the maximum value of $a$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q29.If $x \to 0 lim \frac{α e ^{x} + β e ^{- x} + γ s i n x}{x s i n ^{2} x} = \frac{2}{3}$ , where $α, β, γ \in R$ , then which of the following is NOT correct?
Mathematics · Limits Continuity and Differentiability · MCQ
Q30.The integral $0 \int \frac{π}{2} \frac{1}{3 + 2 s i n x + c o s x} d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q31.Let the solution curve $y = y (x)$ of the differential equation $(1 + e^{2 x}) (\frac{d y}{d x} + y) = 1$ pass through the point $(0, \frac{π}{2})$ . Then, $x \to \infty lim e^{x} y (x)$ …
Mathematics · Differential Equations · MCQ
Q32.Let a line L pass through the point of intersection of the lines $b x + 10 y - 8 = 0$ and $2 x - 3 y = 0, b \in R - {\frac{4}{3}}$ . If the line $L$ also passes through the point $(1, 1)$ and touches the circle…
Mathematics · Ellipse · MCQ
Q33.Let the circumcentre of a triangle with vertices A(a, 3), B(b, 5) and C(a, b), ab > 0 be P(1,1). If the line AP intersects the line BC at the point Q $(k_{1}, k_{2})$ , then $k_{1} + k_{2}$ is equal to :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q34.Let $\overset{a}{^}$ and $\hat{b}$ be two unit vectors such that the angle between them is $\frac{π}{4}$ . If $θ$ is the angle between the vectors $(\overset{a}{^} + \hat{b})$ and $(\overset{a}{^} + 2 \hat{b} + 2 (\overset{a}{^} \times \hat{b}))$ , then the value of $164 cos^{2} θ$ …
Mathematics · Vector Algebra · MCQ
Q35.If $f (α) = 1 \int α \frac{l o g _{10} t}{1 + t} dt, α > 0$ , then $f (e^{3}) + f (e^{- 3})$ is equal to :
Mathematics · Definite Integration · MCQ
Q36.The area of the region ${(x, y) : ∣ x - 1∣ \leq y \leq 5 - x^{2}}$ is equal to :
Mathematics · Area Under the Curves · MCQ
Q37.Let the focal chord of the parabola $P : y^{2} = 4 x$ along the line $L : y = m x + c, m > 0$ meet the parabola at the points M and N. Let the line L be a tangent to the hyperbola $H : x^{2} - y^{2} = 4$ …
Mathematics · Parabola · MCQ
Q38.The number of points, where the function $f : R \to R$ , $f (x) = ∣ x - 1∣ cos ∣ x - 2∣ sin ∣ x - 1∣ + (x - 3) x^{2} - 5 x + 4$ , is NOT differentiable, is :
Mathematics · Limits Continuity and Differentiability · MCQ
Q39.Let $S = {1, 2, 3, \dots, 2022}$ . Then the probability, that a randomly chosen number n from the set S such that $HCF (n, 2022) = 1$ , is :
Mathematics · Probability · MCQ
Q40.Let $f (x) = 3^{(x^{2} - 2)^{3} + 4}, x \in R$ . Then which of the following statements are true? $P : x = 0$ is a point of local minima of $f Q : x = 2$ is a point of inflection of $f R : f^{'}$ is…
Mathematics · Application of Derivatives · MCQ
Q41.Let the mean and the variance of 20 observations $x_{1}, x_{2}, \dots, x_{20}$ be 15 and 9 , respectively. For $α \in R$ , if the mean of $(x_{1} + α)^{2}, (x_{2} + α)^{2}, \dots, (x_{20} + α)^{2}$ …
Mathematics · Statistics · Numerical
Q42.Let $a_{1}, a_{2}, a_{3}, \dots$ be an A.P. If $r = 1 \sum \infty \frac{a _{r}}{2 ^{r}} = 4$ , then $4 a_{2}$ is equal to .
Mathematics · Sequences and Series · Numerical
Q43.Let the ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of $(42 + \frac{1}{4 3})^{n}$ , in the increasing powers of $\frac{1}{4 3}$ be $46 : 1$ …
Mathematics · Binomial Theorem · Numerical
Q44.The number of matrices of order $3 \times 3$ , whose entries are either 0 or 1 and the sum of all the entries is a prime number, is .
Mathematics · Permutations and Combinations · Numerical
Q45.Let p and p + 2 be prime numbers and let $Δ = p! (p + 1)! (p + 2)! (p + 1)! (p + 2)! (p + 3)! (p + 2)! (p + 3)! (p + 4)!$ …
Mathematics · Matrices and Determinants · Numerical
Q46.Let $S = {4, 6, 9}$ and $T = {9, 10, 11, \dots, 1000}$ . If $A = {a_{1} + a_{2} + \dots + a_{k} : k \in N, a_{1}, a_{2}, a_{3}, \dots, a_{k}$ $ϵ S}$ , then the sum of all the elements in the set $T - A$ is equal to …
Mathematics · Sets and Relations · Numerical
Q47.Let the mirror image of a circle $c_{1} : x^{2} + y^{2} - 2 x - 6 y + α = 0$ in line $y = x + 1$ be $c_{2} : 5 x^{2} + 5 y^{2} + 10 g x + 10 f y + 38 = 0$ . If $r$ is the radius of circle $c_{2}$ , then $α + 6 r^{2}$ is equal to …
Mathematics · Circle · Numerical