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Mathematics · 2009 · Shift 2

19 questions from this JEE Advanced paper

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JEE Advanced
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2009 · Shift 2
Mathematics

Mathematics · 2009 · Shift 2

19 questions from this JEE Advanced paper

Definite Integration2 questions Trigonometric Functions and Equations2 questions Differential Equations1 questions 3D Geometry1 questions Application of Derivatives3 questions Functions1 questions Quadratic Equation and Inequalities1 questions Permutations and Combinations1 questions Sequences and Series1 questions Circle1 questions Ellipse2 questions Parabola2 questions Properties of Triangle1 questions

Q20.Let $f : R \to R$ be a continuous function which satisfies $f (x) = 0 \int x f (t) d t$ . Then, the value of $f (ln 5)$ is .
Mathematics · Definite Integration · Numerical
Q21.For $0 < θ < \frac{π}{2},$ the solution (s) of $m = 1 \sum 6 csc (θ + \frac{( m - 1 ) π}{4}) csc (θ + \frac{mπ}{4}) = 42$ is (are)
Mathematics · Trigonometric Functions and Equations · Multiple correct
Q22.Match the statements/expressions in Column I with the values given in Column II: Includes table
Mathematics · Differential Equations · MCQ
Q23.Match the statements/expressions in Column I with the values given in Column II: Includes table
Mathematics · Trigonometric Functions and Equations · MCQ
Q24.A line with positive direction cosines passes through the point P(2, $-$ 1, 2) and makes equal angles with the coordinate axes. The line meets the plane $2 x + y + z = 9$ at point Q. The length of the line segment PQ equals
Mathematics · 3D Geometry · MCQ
Q25.If $I_{n} = - π \int π \frac{s i n n x}{( 1 + π ^{x} ) s i n x} d x, n = 0, 1, 2,$ .... then
Mathematics · Definite Integration · Multiple correct
Q26.The maximum value of the function $f (x) = 2 x^{3} - 15 x^{2} + 36 x - 48$ on the set $A = {x ∣ x^{2} + 20 \leq 9 x ∣}$ is .
Mathematics · Application of Derivatives · Numerical
Q27.Let $p (x)$ be a polynomial of degree $4$ having extremum at $x = 1, 2$ and $x \to 0 lim (1 + \frac{p ( x )}{x ^{2}}) = 2$ . Then the value of $p (2)$ is
Mathematics · Application of Derivatives · Numerical
Q28.For the function $f (x) = x cos \frac{1}{x}, x \geq 1,$
Mathematics · Application of Derivatives · Multiple correct
Q29.If the function $f (x) = x^{3} + e^{x /2}$ and $g (x) = f^{- 1} (x)$ , then the value of $g^{'} (1)$ is .
Mathematics · Functions · Numerical
Q30.The smallest value of $k$ , for which both the roots of the equation $x^{2} - 8 k x + 16 (k^{2} - k + 1) = 0$ are real, distinct and have values at least 4, is
Mathematics · Quadratic Equation and Inequalities · Numerical
Q31.Let $(x, y, z)$ be points with integer coordinates satisfying the system of homogeneous equation: $3 x - y - z = 0 - 3 x + z = 0 - 3 x + 2 y + z = 0$ Then the number of such…
Mathematics · Permutations and Combinations · Numerical
Q32.If the sum of first $n$ terms of an A.P. is $c n^{2}$ , then the sum of squares of these $n$ terms is
Mathematics · Sequences and Series · MCQ
Q33.The centres of two circles $C_{1}$ and $C_{2}$ each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segement joining the centres of $C_{1}$ and $C_{2}$ and C a circle touching circles $C_{1}$ …
Mathematics · Circle · Numerical
Q34.The normal at a point $P$ on the ellipse $x^{2} + 4 y^{2} = 16$ meets the $x$ - axis $Q$ . If $M$ is the mid point of the line segment $P Q$ , then the locus of $M$ intersects the latus rectums of the given ellipse at the points
Mathematics · Ellipse · MCQ
Q35.The tangent $P T$ and the normal $P N$ to the parabola $y^{2} = 4 a x$ at a point $P$ on it meet its axis at points $T$ and $N$ , respectively. The locus of the centroid of the triangle $P T N$ is a parabola whose
Mathematics · Parabola · Multiple correct
Q36.An ellipse intersects the hyperbola $2 x^{2} - 2 y^{2} = 1$ orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinate axes then
Mathematics · Ellipse · Multiple correct
Q37.Let ABC and ABC' be two non-congruent triangles with sides AB = 4, AC = AC' = 2 $2$ and angle B = 30 $^{\circ}$ . The absolute value of the difference between the areas of these triangles is .
Mathematics · Properties of Triangle · Numerical
Q38.The locus of the orthocentre of the triangle formed by the lines $(1 + p) x - p y + p (1 + p) = 0, (1 + q) x - q y + q (1 + q) = 0$ and $y = 0$ , where $p e q$ , is :
Mathematics · Parabola · MCQ