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Mathematics · 2014 · Shift 1

20 questions from this JEE Advanced paper

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JEE Advanced
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2014 · Shift 1
Mathematics

Mathematics · 2014 · Shift 1

20 questions from this JEE Advanced paper

Permutations and Combinations2 questions Circle1 questions Sequences and Series1 questions Straight Lines and Pair of Straight Lines1 questions Definite Integration3 questions Application of Derivatives1 questions 3D Geometry1 questions Vector Algebra2 questions Limits Continuity and Differentiability3 questions Functions2 questions Matrices and Determinants2 questions Inverse Trigonometric Functions1 questions

Q21.Let $n_{1} < n_{2} < n_{3} < n_{4} < n_{5}$ be positive integers such that $n_{1} + n_{2} + n_{3} + n_{4} + n_{5}$ = 20. Then the number of such destinct arrangements $(n_{1}, n_{2}, n_{3}, n_{4}, n_{5})$ …
Mathematics · Permutations and Combinations · Numerical
Q22.A circle S passes through the point (0, 1) and is orthogonal to the circles $(x - 1)^{2} + y^{2} = 16 an d x^{2} + y^{2} = 1$ . Then
Mathematics · Circle · Multiple correct
Q23.Let $n \geq 2$ be an integer. Take n distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line…
Mathematics · Permutations and Combinations · Numerical
Q24.Let a, b, c be positive integers such that $\frac{b}{a}$ is an integer. If a, b, c are in geometric progression and the arithmetic mean of a, b, c is b + 2, then the value of $\frac{a ^{2} + a - 14}{a + 1}$ is
Mathematics · Sequences and Series · Numerical
Q25.For a point $P$ in the plane, Let $d_{1} (P)$ and $d_{2} (P)$ be the distance of the point $P$ from the lines $x - y = 0$ and $x + y = 0$ respectively. The area of the region $R$ consisting of all points $P$ …
Mathematics · Straight Lines and Pair of Straight Lines · Numerical
Q26.Let $f : (0, \infty) \to R$ be given by $f (x)$ = $\frac{1}{x} \int x \frac{e ^{- (t + \frac{1}{t})}}{t} d t$ . Then
Mathematics · Definite Integration · Multiple correct
Q27.The slope of the tangent to the curve $(y - x^{5})^{2} = x (1 + x^{2})^{2}$ at the point $(1, 3)$ is
Mathematics · Application of Derivatives · Numerical
Q28.The value of $0 \int 1 4 x^{3} {\frac{d ^{2}}{d x ^{2}} (1 - x^{2})^{5}} d x$ is
Mathematics · Definite Integration · Numerical
Q29.From a point $P (λ, λ, λ),$ perpendicular $P Q$ and $P R$ are drawn respectively on the lines $y = x, z = 1$ and $y = - x, z = - 1.$ If $P$ is such that $∠ QP R$ is a right angle, then the possible value(s) of $λ$ …
Mathematics · 3D Geometry · Multiple correct
Q30.Let $x, y$ and $z$ be three vectors each of magnitude $2$ and the angle between each pair of them is $\frac{π}{3}$ . If $a$ is a non-zero vector perpendicular to $x$ …
Mathematics · Vector Algebra · Multiple correct
Q31.Let $a, b$ and $c$ be three non-coplanar unit vectors such that the angle between every pair of them is $\frac{π}{3} .$ If $a \times b + b \times c = p a + q b + r c,$ …
Mathematics · Vector Algebra · Numerical
Q32.Let $f : (a, b) \to [1, \infty)$ be a continuous function and g : R $\to$ R be defined as $g (x) = {0, x b$ Then,
Mathematics · Limits Continuity and Differentiability · Multiple correct
Q33.For every pair of continuous function f, g : [0, 1] $\to$ R such that max {f(x) : x $\in$ [0, 1]} = max {g(x) : x $\in$ [0, 1]}. The correct statement(s) is (are)
Mathematics · Functions · Multiple correct
Q34.Let M be a 2 $\times$ 2 symmetric matrix with integer entries. Then, M is invertible, if
Mathematics · Matrices and Determinants · Multiple correct
Q35.Let M and N be two 3 $\times$ 3 matrices such that MN = NM. Further, if M $e$ N2 and M2 = N4, then
Mathematics · Matrices and Determinants · Multiple correct
Q36.Let $f : (- \frac{π}{2}, \frac{π}{2}) \to R$ be given by $f (x) = [lo g (sec x + tan x)]^{3}$ . Then,
Mathematics · Functions · Multiple correct
Q37.Let a $\in$ R and f : R $\to$ R be given by f(x) = x5 $-$ 5x + a. Then,
Mathematics · Definite Integration · Multiple correct
Q38.Let f : [0, 4 $π$ ] $\to$ [0, $π$ ] be defined by f(x) = cos $-$ 1 (cos x). The number of points x $\in$ [0, 4 $π$ ] satisfying the equation $f (x) = \frac{10 - x}{10}$ is
Mathematics · Inverse Trigonometric Functions · Numerical
Q39.The largest value of the non-negative integer a for which $x \to 1 lim {\frac{- a x + s i n ( x - 1 ) + a}{x + s i n ( x - 1 ) - 1}}^{\frac{1 - x}{1 - x}} = \frac{1}{4}$ is
Mathematics · Limits Continuity and Differentiability · Numerical
Q40.Let f : R $\to$ R and g : R $\to$ R be respectively given by f(x) = | x | + 1 and g(x) = x2 + 1. Define h : R $\to$ R by $h (x) = {max {f (x), g (x)}, min {f (x), g (x)}, i f x \leq 0. i f x > 0.$ …
Mathematics · Limits Continuity and Differentiability · Numerical