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Mathematics · 2008 · Shift 2

22 questions from this JEE Advanced paper

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JEE Advanced
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2008 · Shift 2
Mathematics

Mathematics · 2008 · Shift 2

22 questions from this JEE Advanced paper

Limits Continuity and Differentiability2 questions Complex Numbers1 questions Vector Algebra3 questions 3D Geometry1 questions Differential Equations1 questions Definite Integration1 questions Differentiation2 questions Application of Integration1 questions Indefinite Integrals1 questions Hyperbola1 questions Circle1 questions Sequences and Series1 questions Permutations and Combinations1 questions Quadratic Equation and Inequalities1 questions Straight Lines and Pair of Straight Lines2 questions Probability1 questions Trigonometric Functions and Equations1 questions

Q23.Consider the function $f : (- \infty, \infty) \to (- \infty, \infty)$ defined by $f (x) = \frac{x ^{2} - a x + 1}{x ^{2} + a x + 1}, 0 < a < 2.$ Which of the following is true?
Mathematics · Limits Continuity and Differentiability · MCQ
Q24.A particle P stats from the point $z_{0}$ = 1 +2i, where $i = - 1$ . It moves horizontally away from origin by 5 unit and then vertically away from origin by 3 units to reach a point $z_{1}$ . From $z_{1}$ the particle moves $\sqrt…
Mathematics · Complex Numbers · MCQ
Q25.Consider the lines, $L_{1} : \frac{x + 1}{3} = \frac{y + 2}{1} = \frac{z + 1}{2} L_{2} : \frac{x - 2}{1} = \frac{y - 2}{2} = \frac{z - 3}{3}$ The shortest distance between $L_{1}$ and $L_{2}$ is :
Mathematics · Vector Algebra · MCQ
Q26.Consider the lines, $L_{1} : \frac{x + 1}{3} = \frac{y + 2}{1} = \frac{z + 1}{2} L_{2} : \frac{x - 2}{1} = \frac{y - 2}{2} = \frac{z - 3}{3}$ The distance of the point $(1, 1, 1)$ from the plane passing through the point $(- 1, - 2, - 1)$ …
Mathematics · 3D Geometry · MCQ
Q27.Consider the lines $L_{1} : \frac{x + 1}{3} = \frac{y + 2}{1} = \frac{z + 1}{2} L_{2} : \frac{x - 2}{1} = \frac{y + 2}{2} = \frac{z - 3}{3}$ The unit vector perpendicular to both $L_{1}$ and $L_{2}$ is :
Mathematics · Vector Algebra · MCQ
Q28.Let two non-collinear unit vectors $a$ and $b$ form an acute angle. A point $P$ moves so that at any time $t$ the position vector $O P$ (where $O$ is the origin) is given by $a cos t + b sin t .$ …
Mathematics · Vector Algebra · MCQ
Q29.Let a solution $y = y (x)$ of the differential equation, $x x^{2} - 1 d y - y y^{2} - 1 d x = 0$ satify $y (2) = \frac{2}{3} .$ STATEMENT-1 : $y (x) = sec (sec^{- 1} x - \frac{π}{6})$ …
Mathematics · Differential Equations · MCQ
Q30.Consider the function $f : (- \infty, \infty) \to (- \infty, \infty)$ defined by $f (x) = \frac{x ^{2} - a x + 1}{x ^{2} + a x + 1}, 0 < a < 2.$ Let $g (x) = 0 \int e^{x} \frac{f ^{'} ( t )}{1 + t ^{2}} d t .$ …
Mathematics · Definite Integration · MCQ
Q31.Consider the function $f : (- \infty, \infty) \to (- \infty, \infty)$ defined by $f (x) = \frac{x ^{2} - a x + 1}{x ^{2} + a x + 1}, 0 < a < 2.$ Which of the following is true?
Mathematics · Differentiation · MCQ
Q32.The area of the region between the curves $y = \frac{1 + s i n x}{c o s x}$ and $y = \frac{1 - s i n x}{c o s x}$ bounded by the lines $x = 0$ and $x = \frac{π}{4}$ is
Mathematics · Application of Integration · MCQ
Q33.Let $I = \int \frac{e ^{x}}{e ^{4 x} + e ^{2 x} + 1} d x, J = \int \frac{e ^{- x}}{e ^{- 4 x} + e ^{- 2 x} + 1} d x .$ Then for an arbitrary constant $C$ , the value of $J - I$ equals :
Mathematics · Indefinite Integrals · MCQ
Q34.Let the function $g : (- \infty, \infty) \to (- \frac{π}{2}, \frac{π}{2})$ be given by $g (u) = 2 tan^{- 1} (e^{u}) - \frac{π}{2} .$ Then, $g$ is
Mathematics · Limits Continuity and Differentiability · MCQ
Q35.Let $g (x) = lo g f (x)$ , where $f (x)$ is a twice differentiable positive function on (0, $\infty$ ) such that $f (x + 1) = x f (x)$ . Then for N = 1, 2, 3, ..., $g^{''} (N + \frac{1}{2}) - g^{''} (\frac{1}{2}) =$
Mathematics · Differentiation · MCQ
Q36.Consider a branch of the hyperbola $x^{2} - 2 y^{2} - 22 x - 42 y - 6 = 0$ with vertex at the point $A$ . Let $B$ be one of the end points of its latus rectum. If $C$ is the focus of the hyperbola nearest to the point $A$ , then…
Mathematics · Hyperbola · MCQ
Q37.Consider $L_{1} : 2 x + 3 y + p - 3 = 0 L_{2} : 2 x + 3 y + p + 3 = 0$ where p is a real number, and $C : x^{2} + y^{2} + 6 x - 10 y + 30 = 0$ STATEMENT-1 : If line $L_{1}$ is a…
Mathematics · Circle · MCQ
Q38.Suppose four distinct positive numbers $a_{1}, a_{2}, a_{3}, a_{4}$ are in G.P. Let $b_{1} = a_{1}, b_{2} = b_{1} + a_{2}, b_{3} = b_{2} + a_{3} an d b_{4} = b_{3} + a_{4}$ . STATEMENT-1: The numbers $b_{1}, b_{2}, b_{3}, b_{4}$ …
Mathematics · Sequences and Series · MCQ
Q39.Consider all possible permutations of the letters of the word ENDEANOEL. Match the Statements/Expressions in Column I with the Statements/Expressions in Column II. Includes table
Mathematics · Permutations and Combinations · MCQ
Q40.Let $a, b, c$ , $α, β$ be real numbers. Suppose $α, β$ are the roots of the equation $x^{2} + 2 p x + q = 0$ and $α, \frac{1}{β}$ are the roots of the equation $a x^{2} + 2 b x + c = 0,$ where $β^{2} \in {- 1, 0, 1}$ …
Mathematics · Quadratic Equation and Inequalities · MCQ
Q41.Consider three points $P = (- sin (β - α), - cos β), Q = (cos (β - α), sin β)$ and $R = (cos (β - α + θ), sin (β - θ))$ where $0 < α, β, θ < \frac{π}{4}$ . Then :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q42.An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent is :
Mathematics · Probability · MCQ
Q43.Consider the lines given by: $L_{1} : x + 3 y - 5 = 0$ $L_{2} : 3 x - k y - 1 = 0$ $L_{3} : 5 x + 2 y - 12 = 0$ Match the Statement/Expressions in Column I with the Statements/Expressions in Column II. Includes table
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q44.Match the Statements/Expressions in Column I with the Statements/Expressions in Column II. Includes table
Mathematics · Trigonometric Functions and Equations · MCQ