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Mathematics · 2022 · Shift 1

18 questions from this JEE Advanced paper

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JEE Advanced
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2022 · Shift 1
Mathematics

Mathematics · 2022 · Shift 1

18 questions from this JEE Advanced paper

Inverse Trigonometric Functions1 questions Limits Continuity and Differentiability1 questions Probability2 questions Complex Numbers2 questions Sequences and Series2 questions Permutations and Combinations1 questions Circle1 questions Definite Integration1 questions 3D Geometry2 questions Parabola1 questions Functions1 questions Trigonometric Functions and Equations1 questions Matrices and Determinants1 questions Ellipse1 questions

Q19.Considering only the principal values of the inverse trigonometric functions, the value of $\frac{3}{2} cos^{- 1} \frac{2}{2 + π ^{2}} + \frac{1}{4} sin^{- 1} \frac{2 2 π}{2 + π ^{2}} + tan^{- 1} \frac{2}{π}$ is
Mathematics · Inverse Trigonometric Functions · Numerical
Q20.Let $α$ be a positive real number. Let $f : R \to R$ and $g : (α, \infty) \to R$ be the functions defined by $f (x) = sin (\frac{π x}{12}) and g (x) = \frac{2 l o g _{e} ( x - α )}{l o g _{e} ( e ^{x} - e ^{α} )} .$ …
Mathematics · Limits Continuity and Differentiability · Numerical
Q21.In a study about a pandemic, data of 900 persons was collected. It was found that 190 persons had symptom of fever, 220 persons had symptom of cough, 220 persons had symptom of breathing problem, 330 persons had symptom of fever or cough…
Mathematics · Probability · Numerical
Q22.Let $z$ be a complex number with a non-zero imaginary part. If $\frac{2 + 3 z + 4 z ^{2}}{2 - 3 z + 4 z ^{2}}$ is a real number, then the value of $∣ z ∣^{2}$ is .
Mathematics · Complex Numbers · Numerical
Q23.Let $\overset{z}{ˉ}$ denote the complex conjugate of a complex number $z$ and let $i = - 1$ . In the set of complex numbers, the number of distinct roots of the equation $\overset{z}{ˉ} - z^{2} = i (\overset{z}{ˉ} + z^{2})$ is …
Mathematics · Complex Numbers · Numerical
Q24.Let $l_{1}, l_{2}, \dots, l_{100}$ be consecutive terms of an arithmetic progression with common difference $d_{1}$ , and let $w_{1}, w_{2}, \dots, w_{100}$ be consecutive terms of another arithmetic progression with common difference $d_{2}$ …
Mathematics · Sequences and Series · Numerical
Q25.The number of 4-digit integers in the closed interval [2022, 4482] formed by using the digits $0, 2, 3, 4, 6, 7$ is .
Mathematics · Permutations and Combinations · Numerical
Q26.Let $A B C$ be the triangle with $A B = 1, A C = 3$ and $∠ B A C = \frac{π}{2}$ . If a circle of radius $r > 0$ touches the sides $A B, A C$ and also touches internally the circumcircle of the triangle $A B C$ , then the value of $r$ is …
Mathematics · Circle · Numerical
Q27.Consider the equation $\int_{1}^{e} \frac{( l o g _{e} x ) ^{1/2}}{x ( a - ( l o g _{e} x ) ^{3/2} ) ^{2}} d x = 1, a \in (- \infty, 0) \cup (1, \infty)$ Which of the following statements is/are…
Mathematics · Definite Integration · Multiple correct
Q28.Let $a_{1}, a_{2}, a_{3}, \dots$ be an arithmetic progression with $a_{1} = 7$ and common difference 8. Let $T_{1}, T_{2}, T_{3}, \dots$ be such that $T_{1} = 3$ and $T_{n + 1} - T_{n} = a_{n}$ for $n \geq 1$ . Then, which of the following is/are…
Mathematics · Sequences and Series · Multiple correct
Q29.Let $P_{1}$ and $P_{2}$ be two planes given by $P_{1} : 10 x + 15 y + 12 z - 60 = 0 P_{2} : - 2 x + 5 y + 4 z - 20 = 0$ Which of the following straight lines can be an edge of some tetrahedron whose two faces lie…
Mathematics · 3D Geometry · Multiple correct
Q30.Let $S$ be the reflection of a point $Q$ with respect to the plane given by $r = - (t + p) \overset{}{^} + t \overset{}{^} + (1 + p) \hat{k}$ where $t, p$ are real parameters and $\overset{}{^}, \overset{}{^}, \hat{k}$ are the unit vectors along…
Mathematics · 3D Geometry · Multiple correct
Q31.Consider the parabola $y^{2} = 4 x$ . Let $S$ be the focus of the parabola. A pair of tangents drawn to the parabola from the point $P = (- 2, 1)$ meet the parabola at $P_{1}$ and $P_{2}$ . Let $Q_{1}$ and $Q_{2}$ be points on the lines $S P_{1}$ …
Mathematics · Parabola · Multiple correct
Q32.Let $∣ M ∣$ denote the determinant of a square matrix $M$ . Let $g : [0, \frac{π}{2}] \to R$ be the function defined by $g (θ) = f (θ) - 1 + f (\frac{π}{2} - θ) - 1$ where $f (θ) = \frac{1}{2} 1 - sin θ - 1 sin θ 1 - sin θ 1 sin θ 1 + sin π sin (θ - \frac{π}{4}) cot (θ + \frac{π}{4}) cos (θ + \frac{π}{4}) - cos \frac{π}{2} lo g_{e} (\frac{π}{4}) tan (θ - \frac{π}{4}) lo g_{e} (\frac{4}{π}) tan π .$ …
Mathematics · Functions · Multiple correct
Q33.Consider the following lists : The correct option is: Includes table
Mathematics · Trigonometric Functions and Equations · MCQ
Q34.Two players, $P_{1}$ and $P_{2}$ , play a game against each other. In every round of the game, each player rolls a fair die once, where the six faces of the die have six distinct numbers. Let $x$ and $y$ denote the readings on the die… Includes table
Mathematics · Probability · MCQ
Q35.Let $p, q, r$ be nonzero real numbers that are, respectively, the $1 0^{th}, 10 0^{th}$ and $100 0^{th}$ terms of a harmonic progression. Consider the system of linear equations $x + y + z = 1 10 x + 100 y + 1000 z = 0 q r x + p r y + pq z = 0$ … Includes table
Mathematics · Matrices and Determinants · MCQ
Q36.Consider the ellipse $\frac{x ^{2}}{4} + \frac{y ^{2}}{3} = 1$ Let $H (α, 0), 0 < α < 2$ , be a point. A straight line drawn through $H$ parallel to the $y$ -axis crosses the ellipse and its auxiliary circle at points $E$ and $F$ … Includes table
Mathematics · Ellipse · MCQ