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Mathematics · 2012 · Shift 2

20 questions from this JEE Advanced paper

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JEE Advanced
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2012 · Shift 2
Mathematics

Mathematics · 2012 · Shift 2

20 questions from this JEE Advanced paper

Permutations and Combinations2 questions 3D Geometry2 questions Vector Algebra1 questions Probability2 questions Definite Integration1 questions Application of Derivatives3 questions Properties of Triangle1 questions Circle2 questions Sequences and Series1 questions Matrices and Determinants2 questions Quadratic Equation and Inequalities1 questions Limits Continuity and Differentiability1 questions Functions1 questions

Q21.Let $a_{n}$ denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0.Let $b_{n}$ = the number of such n-digit integers ending with digit 1 and $c_{n}$ =the…
Mathematics · Permutations and Combinations · MCQ
Q22.If the straight lines $\frac{x - 1}{2} = \frac{y + 1}{k} = \frac{z}{2}$ and $\frac{x + 1}{5} = \frac{y + 1}{2} = \frac{z}{k}$ are coplanar, then the plane (s) containing these two lines is (are)
Mathematics · 3D Geometry · Multiple correct
Q23.The equation of a plane passing through the line of intersection of the planes $x + 2 y + 3 z = 2$ and $x - y + z = 3$ and at a distance $\frac{2}{3}$ from the point $(3, 1, - 1)$ is
Mathematics · 3D Geometry · MCQ
Q24.If $a$ and $b$ are vectors such that $a + b = 29$ and $a \times (2 i + 3 j + 4 k) = (2 i + 3 j + 4 k) \times b,$ …
Mathematics · Vector Algebra · MCQ
Q25.Let $X$ and $Y$ be two events such that $P (X ∣ Y) = \frac{1}{2}, P (Y ∣ X) = \frac{1}{3}$ and $P (X \cap Y) = \frac{1}{6} .$ Which of the following is (are) correct ?
Mathematics · Probability · Multiple correct
Q26.Four fair dice $D_{1}, D_{2}, D_{3}$ and $D_{4}$ ; each having six faces numbered $1, 2, 3, 4, 5$ and $6$ are rolled simultaneously. The probability that $D_{4}$ shows a number appearing on one of $D_{1}, D_{2}$ and $D_{3}$ is
Mathematics · Probability · MCQ
Q27.The value of the integral $- π /2 \int π /2 (x^{2} + 1 n \frac{π + x}{π - x}) cos x d x$ is
Mathematics · Definite Integration · MCQ
Q28.Let $f (x) = (1 - x)^{2} sin^{2} x + x^{2}$ for all $x \in I R$ and let $g (x) = 1 \int x (\frac{2 ( t - 1 )}{t + 1} - I n t) f (t) d t$ for…
Mathematics · Application of Derivatives · MCQ
Q29.Let $f (x) = (1 - x)^{2} sin^{2} x + x^{2}$ for all $x \in I R$ and let $g (x) = 1 \int x (\frac{2 ( t - 1 )}{t + 1} - I n t) f (t) d t$ for…
Mathematics · Application of Derivatives · MCQ
Q30.If $f (x) = \int_{0}^{x} e^{t^{2}} (t - 2) (t - 3) d t$ for all $x \in (0, \infty),$ then
Mathematics · Application of Derivatives · Multiple correct
Q31.Let $P QR$ be a triangle of area $Δ$ with $a = 2$ , $b = \frac{7}{2}$ and $c = \frac{5}{2}$ ; where $a, b,$ and $c$ are the lengths of the sides of the triangle opposite to the angles at $P . Q$ and $R$ respectively. Then $\frac{2 s i n P - s i n 2 P}{2 s i n P + s i n 2 P}$ …
Mathematics · Properties of Triangle · MCQ
Q32.A tangent PT is drawn to the circle $x^{2} + y^{2} = 4$ at the point P $(3, 1)$ . A straight line L, perpendicular to PT is a tangent to the circle $(x - 3)^{2}$ + $y^{2}$ = 1 A common tangent of the two circles is
Mathematics · Circle · MCQ
Q33.A tangent PT is drawn to the circle $x^{2} + y^{2} = 4$ at the point P $(3, 1)$ . A straight line L, perpendicular to PT is a tangent to the circle $(x - 3)^{2}$ + $y^{2}$ = 1. A possible equation of L is
Mathematics · Circle · MCQ
Q34.Let $a_{1}, a_{2}, a_{3}, .....$ be in harmonic progression with $a_{1} = 5$ and $a_{20} = 25.$ The least positive integer $n$ for which $a_{n} < 0$ is
Mathematics · Sequences and Series · MCQ
Q35.Let $a_{n}$ denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0.Let $b_{n}$ = the number of such n-digit integers ending with digit 1 and $c_{n}$ =the…
Mathematics · Permutations and Combinations · MCQ
Q36.If P is a 3 $\times$ 3 matrix such that PT = 2P + I, where PT is the transpose of P and I is the 3 $\times$ 3 identity matrix, then there exists a column matrix $X = x y z e 000$ …
Mathematics · Matrices and Determinants · MCQ
Q37.Let $α$ (a) and $β$ (a) be the roots of the equation $(3 1 + a - 1) x^{2} + (1 + a - 1) x + (6 1 + a - 1) = 0$ where $a > - 1$ . Then $a \to 0^{+} lim α (a)$ and $a \to 0^{+} lim β (a)$ …
Mathematics · Quadratic Equation and Inequalities · MCQ
Q38.For every integer n, let an and bn be real numbers. Let function f : R $\to$ R be given by $f (x) = {a_{n} + sin π x, b_{n} + cos π x, f or x \in [2 n, 2 n + 1] f or x \in (2 n - 1, 2 n)$ …
Mathematics · Limits Continuity and Differentiability · Multiple correct
Q39.If the ad joint of a 3 $\times$ 3 matrix P is $121411473$ , then the possible value(s) of the determinant of P is(are)
Mathematics · Matrices and Determinants · Multiple correct
Q40.Let $f : (- 1, 1) \to R$ be such that $f (cos 4 θ) = \frac{2}{2 - s e c ^{2} θ}$ for $θ \in (0, \frac{π}{4}) \cup (\frac{π}{4}, \frac{π}{2})$ . Then the value(s) of $f (\frac{1}{3})$ …
Mathematics · Functions · Multiple correct