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Mathematics · 2022 · 28 Jul · Shift 1

24 questions from this JEE Main paper

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2022 · 28 Jul · Shift 1
Mathematics

Mathematics · 2022 · 28 Jul · Shift 1

24 questions from this JEE Main paper

Differential Equations2 questions Inverse Trigonometric Functions2 questions Vector Algebra2 questions Circle2 questions Sets and Relations1 questions Probability1 questions Binomial Theorem1 questions Complex Numbers1 questions Application of Derivatives1 questions Functions2 questions Definite Integration2 questions Permutations and Combinations1 questions 3D Geometry1 questions Limits Continuity and Differentiability2 questions Matrices and Determinants1 questions Statistics1 questions Quadratic Equation and Inequalities1 questions

Q23.Let the solution curve of the differential equation $x d y = (x^{2} + y^{2} + y) d x, x > 0$ , intersect the line $x = 1$ at $y = 0$ and the line $x = 2$ at $y = α$ . Then the value of $α$ is :
Mathematics · Differential Equations · MCQ
Q24.Considering only the principal values of the inverse trigonometric functions, the domain of the function $f (x) = cos^{- 1} (\frac{x ^{2} - 4 x + 2}{x ^{2} + 3})$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q25.Let the vectors $a = (1 + t) \hat{i} + (1 - t) \hat{j} + \hat{k}, b = (1 - t) \hat{i} + (1 + t) \hat{j} + 2 \hat{k}$ and $c = t \hat{i} - t \hat{j} + \hat{k}, t \in R$ be such that for $α, β, γ \in R, α a + β b + γ c = 0 \Rightarrow α = β = γ = 0$ …
Mathematics · Vector Algebra · MCQ
Q26.Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation $cos^{- 1} (x) - 2 sin^{- 1} (x) = cos^{- 1} (2 x)$ is equal to :
Mathematics · Inverse Trigonometric Functions · MCQ
Q27.Let a vector $a$ has magnitude 9. Let a vector $b$ be such that for every $(x, y) \in R \times R - {(0, 0)}$ , the vector $(x a + y b)$ is perpendicular to the vector $(6 y a - 18 x b)$ . Then…
Mathematics · Vector Algebra · MCQ
Q28.For $t \in (0, 2 π)$ , if $ABC$ is an equilateral triangle with vertices $A (sin t, - cos t), B (cost, sin t)$ and $C (a, b)$ such that its orthocentre lies on a circle with centre…
Mathematics · Circle · MCQ
Q29.For $α \in N$ , consider a relation $R$ on $N$ given by $R = {(x, y) : 3 x + α y$ is a multiple of 7 $}$ . The relation $R$ is an equivalence relation if and only if :
Mathematics · Sets and Relations · MCQ
Q30.Out of $60%$ female and $40%$ male candidates appearing in an exam, $60%$ candidates qualify it. The number of females qualifying the exam is twice the number of males qualifying it. A candidate is randomly chosen from the qualified…
Mathematics · Probability · MCQ
Q31.If $y = y (x), x \in (0, π /2)$ be the solution curve of the differential equation $(sin^{2} 2 x) \frac{d y}{d x} + (8 sin^{2} 2 x + 2 sin 4 x) y = 2 e^{- 4 x} (2 sin 2 x + cos 2 x)$ , with $y (π /4) = e^{- π}$ …
Mathematics · Differential Equations · MCQ
Q32.Let $C$ be the centre of the circle $x^{2} + y^{2} - x + 2 y = \frac{11}{4}$ and $P$ be a point on the circle. A line passes through the point $C$ , makes an angle of $\frac{π}{4}$ with the line $CP$ and intersects the circle at…
Mathematics · Circle · MCQ
Q33.The remainder when $7^{2022} + 3^{2022}$ is divided by 5 is :
Mathematics · Binomial Theorem · MCQ
Q34.Let $S_{1} = {z_{1} \in C : ∣ z_{1} - 3 ∣ = \frac{1}{2}}$ and $S_{2} = {z_{2} \in C : ∣ z_{2} - ∣ z_{2} + 1∣∣ = ∣ z_{2} + ∣ z_{2} - 1∣∣}$ . Then, for $z_{1} \in S_{1}$ and $z_{2} \in S_{2}$ …
Mathematics · Complex Numbers · MCQ
Q35.If the minimum value of $f (x) = \frac{5 x ^{2}}{2} + \frac{α}{x ^{5}}, x > 0$ , is 14 , then the value of $α$ is equal to :
Mathematics · Application of Derivatives · MCQ
Q36.Let $γ$ and $γ$ be three positive real numbers. Let $f (x) = α x^{5} + β x^{3} + γ x, x \in R$ and $g : R \to R$ be such that $g (f (x)) = x$ for all $x \in R$ . If $a_{1}, a_{2}, a_{3}, \dots, a_{n}$ …
Mathematics · Functions · MCQ
Q37.The minimum value of the twice differentiable function $f (x) = 0 \int x e^{x - t} f^{'} (t) dt - (x^{2} - x + 1) e^{x}$ , $x \in R$ , is :
Mathematics · Definite Integration · MCQ
Q38.Let $S$ be the set of all passwords which are six to eight characters long, where each character is either an alphabet from ${A, B, C, D, E}$ or a number from ${1, 2, 3, 4, 5}$ with the repetition of characters allowed. If the number of…
Mathematics · Permutations and Combinations · Numerical
Q39.Let $P (- 2, - 1, 1)$ and $Q (\frac{56}{17}, \frac{43}{17}, \frac{111}{17})$ be the vertices of the rhombus PRQS. If the direction ratios of the diagonal RS are $α, - 1, β$ , where both $α$ and $β$ …
Mathematics · 3D Geometry · Numerical
Q40.Let $f : [0, 1] \to R$ be a twice differentiable function in $(0, 1)$ such that $f (0) = 3$ and $f (1) = 5$ . If the line $y = 2 x + 3$ intersects the graph of $f$ at only two distinct points in $(0, 1)$ , then the least number of points…
Mathematics · Limits Continuity and Differentiability · Numerical
Q41.If $0 \int 3 \frac{15 x ^{3}}{1 + x ^{2} + ( 1 + x ^{2} ) ^{3}} d x = α 2 + β 3$ , where $α + β$ are integers, then $α + β$ is equal to .
Mathematics · Definite Integration · Numerical
Q42.Let $A = [12 - 1 α]$ and $B = [β 1 10], α, β \in R$ . Let $α_{1}$ be the value of $α$ which…
Mathematics · Matrices and Determinants · Numerical
Q43.For $p, q \in R$ , consider the real valued function $f (x) = (x - p)^{2} - q, x \in R$ and $q > 0$ . Let $a_{1}$ , $a_{2^{'}} a_{3}$ and $a_{4}$ …
Mathematics · Functions · Numerical
Q44.Let $x_{1}, x_{2}, x_{3}, \dots, x_{20}$ be in geometric progression with $x_{1} = 3$ and the common ratio $\frac{1}{2}$ . A new data is constructed replacing each $x_{i}$ by $(x_{i} - i)^{2}$ . If $\overset{x}{ˉ}$ is the mean of new…
Mathematics · Statistics · Numerical
Q45. $x \to 0 lim (\frac{( x + 2 c o s x ) ^{3} + 2 ( x + 2 c o s x ) ^{2} + 3 s i n ( x + 2 c o s x )}{( x + 2 ) ^{3} + 2 ( x + 2 ) ^{2} + 3 s i n ( x + 2 )})^{\frac{100}{x}}$ is equal to .
Mathematics · Limits Continuity and Differentiability · Numerical
Q46.The sum of all real values of $x$ for which $\frac{3 x ^{2} - 9 x + 17}{x ^{2} + 3 x + 10} = \frac{5 x ^{2} - 7 x + 19}{3 x ^{2} + 5 x + 12}$ is equal to .
Mathematics · Quadratic Equation and Inequalities · Numerical