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Mathematics · 2009 · Shift 1

20 questions from this JEE Advanced paper

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JEE Advanced
Papers
2009 · Shift 1
Mathematics

Mathematics · 2009 · Shift 1

20 questions from this JEE Advanced paper

Complex Numbers2 questions 3D Geometry1 questions Vector Algebra1 questions Probability3 questions Application of Integration2 questions Ellipse3 questions Circle1 questions Permutations and Combinations1 questions Trigonometric Functions and Equations1 questions Differential Equations1 questions Limits Continuity and Differentiability1 questions Matrices and Determinants3 questions

Q21.Let $z = x + i y$ be a complex number where x and y are integers. Then the area of the rectangle whose vertices are the roots of the equation $\overline{z} z^{3} + z \overline{z}^{3} = 350$ is
Mathematics · Complex Numbers · MCQ
Q22.Let $z = cos θ + i sin θ$ . Then the value of $m = 1 \sum 15 Im o l imi t s (z^{2 m - 1}) a t θ = 2^{\circ}$ is
Mathematics · Complex Numbers · MCQ
Q23.Let $P (3, 2, 6)$ be a point in space and $Q$ be a point on the line $r = (i - j + 2 k) + μ (- 3 i + j + 5 k)$ Then the value of $μ$ for which the…
Mathematics · 3D Geometry · MCQ
Q24.If $a, b, c$ and $d$ are unit vectors such that $(a \times b) . (c \times d) = 1$ and $a . c = \frac{1}{2}$ …
Mathematics · Vector Algebra · MCQ
Q25.A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.The conditional probability that $X \geq 6$ given $X > 3$ equals :
Mathematics · Probability · MCQ
Q26.A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.The probability that $X \geq 3$ equals :
Mathematics · Probability · MCQ
Q27.A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.The probability that X = 3 equals
Mathematics · Probability · MCQ
Q28.Area of the region bounded by the curve $y = e^{x}$ and lines $x = 0$ and $y = e$ is
Mathematics · Application of Integration · Multiple correct
Q29.Let $f$ be a non-negative function defined on the interval $[0, 1]$ . If $0 \int x 1 - (f^{'} (t))^{2} d t = 0 \int x f (t) d t, 0 \leq x \leq 1$ , and $f (0) = 0$ , then
Mathematics · Application of Integration · MCQ
Q30.Match the conics in Column I with the statements/expressions in Column II : Includes table
Mathematics · Ellipse · MCQ
Q31.In a triangle $A B C$ with fixed base $B C$ , the vertex $A$ moves such that $cos B + cos C = 4 sin^{2} \frac{A}{2} .$ If $a, b$ and $c$ denote the lengths of the sides of the triangle opposite to the angles $A, B$ and $C$ , respectively,…
Mathematics · Ellipse · Multiple correct
Q32.The line passing through the extremity $A$ of the major axis and extremity $B$ of the minor axis of the ellipse $x^{2} + 9 y^{2} = 9$ meets its auxiliary circle at the point $M$ . Then the area of the triangle with vertices at $A$ , $M$ and…
Mathematics · Ellipse · MCQ
Q33.Tangents drawn from the point P (1, 8) to the circle $x^{2} + y^{2} - 6 x - 4 y - 11 = 0$ touch the circle at the points A and B. The equation of the cirumcircle of the triangle PAB is
Mathematics · Circle · MCQ
Q34.The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is
Mathematics · Permutations and Combinations · MCQ
Q35.If $\frac{s i n ^{4} x}{2} + \frac{c o s ^{4} x}{3} = \frac{1}{5},$ then
Mathematics · Trigonometric Functions and Equations · Multiple correct
Q36.Match the statements/expressions in Column I with the open intervals in Column II : Includes table
Mathematics · Differential Equations · MCQ
Q37.Let $L = x \to 0 lim \frac{a - a ^{2} - x ^{2} - \frac{x ^{2}}{4}}{x ^{4}}, a > 0$ . If L is finite, then
Mathematics · Limits Continuity and Differentiability · Multiple correct
Q38.Let A be the set of all 3 $\times$ 3 symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0.The number of matrices in A is
Mathematics · Matrices and Determinants · MCQ
Q39.Let A be the set of all 3 $\times$ 3 symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0.The number of matrices A in A for which the system of linear equations $A x y z = 100$ …
Mathematics · Matrices and Determinants · MCQ
Q40.Let A be the set of all 3 $\times$ 3 symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0.The number of matrices A in A for which the system of linear equations $A x y z = 100$ …
Mathematics · Matrices and Determinants · MCQ