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Mathematics · 2010 · Shift 2

19 questions from this JEE Advanced paper

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JEE Advanced
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2010 · Shift 2
Mathematics

Mathematics · 2010 · Shift 2

19 questions from this JEE Advanced paper

3D Geometry2 questions Complex Numbers1 questions Application of Derivatives1 questions Trigonometric Functions and Equations1 questions Mathematical Induction and Binomial Theorem1 questions Sequences and Series1 questions Ellipse3 questions Properties of Triangle1 questions Definite Integration1 questions Matrices and Determinants1 questions Functions3 questions Application of Integration1 questions Probability1 questions Vector Algebra1 questions

Q20.Match the statement in Column- $I$ with the values in Column- $I I$ Column- $I$ (A) A line from the origin meets the lines $\frac{x - 2}{1} = \frac{y - 1}{- 2} = \frac{z + 1}{1}$ and $\frac{x - \frac{8}{3}}{2} = \frac{y + 3}{- 1} = \frac{z - 1}{1}$ …
Mathematics · 3D Geometry · MCQ
Q21.Match the statements in Column I with those in Column II. [Note : Here z takes value in the complex plane and Im z and Re z denotes, respectively, the imaginary part and the real part of z.] Column I (A) The set of points z satisfying $∣ z - i ∣ z ∥ = ∣ z + i ∣ z ∥$ …
Mathematics · Complex Numbers · MCQ
Q22.Let $f$ be a function defined on $R$ (the set of all real numbers) such that $f^{'} (x) = 2010 (x - 2009) (x - 2010)^{2} (x - 2011)^{3} (x - 2012)^{4}$ for all $x \in R$ If $g$ …
Mathematics · Application of Derivatives · Numerical
Q23.If the distance of the point $P (1, - 2, 1)$ from the plane $x + 2 y - 2 z = α,$ where $α > 0,$ is $5,$ then the foot of the perpendicular from $P$ to the planes is
Mathematics · 3D Geometry · MCQ
Q24.Two parallel chords of a circle of radius 2 are at a distance $3 + 1$ apart. If the chords subtend at the center , angles of $\frac{π}{k}$ and $\frac{2 π}{k},$ where $k > 0,$ then the value of $[k]$ is [Note…
Mathematics · Trigonometric Functions and Equations · Numerical
Q25.For $r = 0, 1, ....,$ let $A_{r}, B_{r}$ and $C_{r}$ denote, respectively, the coefficient of $X^{r}$ in the expansions of $(1 + x)^{10}, (1 + x)^{20}$ and $(1 + x)^{30} .$ Then $r = 1 \sum 10 A_{r} (B_{10} B_{r} - C_{10} A_{r})$ …
Mathematics · Mathematical Induction and Binomial Theorem · MCQ
Q26.Let $a_{1}, a_{2}, a_{3}$ ......, $a_{11}$ be real numbers satisfying $a_{1} = 15, 27 - 2 a_{2} > 0 an d a_{k} = 2 a_{k - 1} - a_{k - 2} f or k = 3, 4, ........11$ . if $\frac{a _{1}^{2} + a _{2}^{2} + .... + a _{11}^{2}}{11} = 90$ …
Mathematics · Sequences and Series · Numerical
Q27.Tangents are drawn from the point $P (3, 4)$ to the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ touching the ellipse at points $A$ and $B$ . The coordinates of $A$ and $B$ are
Mathematics · Ellipse · MCQ
Q28.Tangents are drawn from the point $P (3, 4)$ to the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ touching the ellipse at points $A$ and $B$ . The orthocentre of the triangle $P A B$ is
Mathematics · Ellipse · MCQ
Q29.Tangents are drawn from the point $P (3, 4)$ to the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ touching the ellipse at points $A$ and $B$ . The equation of the locus of the point whose distances from the point $P$ and the line $A B$ …
Mathematics · Ellipse · MCQ
Q30.Consider a triangle $A B C$ and let $a, b$ and $c$ denote the lengths of the sides opposit to vertices $A, B$ and $C$ respectively. Suppose $a = 6, b = 10$ and the area of the triangle is $153$ , if $∠ A C B$ is obtuse and if $r$ …
Mathematics · Properties of Triangle · Numerical
Q31.Let $f$ be a real-valued function defined on the interval $(- 1, 1)$ such that $e^{- x} f (x) = 2 + 0 \int x t^{4} + 1 d t,$ for all $x \in (- 1, 1)$ , and let $f^{- 1}$ be the inverse…
Mathematics · Definite Integration · MCQ
Q32.Let $k$ be a positive real number and let $A B = 2 k - 1 2 k - 2 k 2 k 1 2 k 2 k - 2 k - 1 and = 0 1 - 2 k - k 2 k - 1 0 - 2 k k 2 k 0 .$ …
Mathematics · Matrices and Determinants · Numerical
Q33.Let $S = {1, 2, 3, 4}$ . The total number of unordered pairs of disjoint subsets of $S$ is equal to :
Mathematics · Functions · MCQ
Q34.Consider the polynomial $f (x) = 1 + 2 x + 3 x^{2} + 4 x^{3} .$ Let $s$ be the sum of all distinct real roots of $f (x)$ and let $t = ∣ s ∣ .$ The area bounded by the curve $y = f (x)$ and the lines $x = 0, y = 0$ and $x = t,$ …
Mathematics · Application of Integration · MCQ
Q35.Consider the polynomial $f (x) = 1 + 2 x + 3 x^{2} + 4 x^{3} .$ Let $s$ be the sum of all distinct real roots of $f (x)$ and let $t = ∣ s ∣ .$ The real numbers lies in the interval
Mathematics · Functions · MCQ
Q36.Consider the polynomial $f (x) = 1 + 2 x + 3 x^{2} + 4 x^{3} .$ Let $s$ be the sum of all distinct real roots of $f (x)$ and let $t = ∣ s ∣ .$ The function $f^{'} (x)$ is
Mathematics · Functions · MCQ
Q37.A signal which can be green or red with probability $\frac{4}{5}$ and $\frac{1}{5}$ respectively, is received by station A and then transmitted to station $B$ . The probability of each station receving the signal correctly is $\frac{3}{4}$ .…
Mathematics · Probability · MCQ
Q38.Two adjacent sides of a parallelogram $A B C D$ are given by $A B = 2 i + 10 j + 11 k$ and $A D = - i + 2 j + 2 k$ The side $A D$ is rotated by an acute…
Mathematics · Vector Algebra · MCQ