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Mathematics · 2019 · Shift 2

18 questions from this JEE Advanced paper

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JEE Advanced
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2019 · Shift 2
Mathematics

Mathematics · 2019 · Shift 2

18 questions from this JEE Advanced paper

Trigonometric Functions and Equations3 questions Application of Derivatives2 questions 3D Geometry1 questions Limits Continuity and Differentiability2 questions Matrices and Determinants3 questions Vector Algebra1 questions Permutations and Combinations2 questions Definite Integration1 questions Inverse Trigonometric Functions1 questions Parabola2 questions

Q19.For non-negative integers n, let $f (n) = \frac{k = 0 \sum n s i n ( \frac{k + 1}{n + 2} π ) s i n ( \frac{k + 2}{n + 2} π )}{k = 0 \sum n s i n ^{2} ( \frac{k + 1}{n + 2} π )}$ …
Mathematics · Trigonometric Functions and Equations · Multiple correct
Q20.Let f : R $\to$ R be given by $f (x) = (x - 1) (x - 2) (x - 5)$ . Define $F (x) = 0 \int x f (t) d t$ , x > 0 Then which of the following options is/are correct?
Mathematics · Application of Derivatives · Multiple correct
Q21.Let, $f (x) = \frac{s i n π x}{x ^{2}}$ , x > 0 Let x1 < x2 < x3 < ... < xn < ... be all the points of local maximum of f and y1 < y2 < y3 < ... < yn < ... be all the points of local minimum of f. Then…
Mathematics · Application of Derivatives · Multiple correct
Q22.Three lines $L_{1} : r = λ i$ , $λ \in$ R, $L_{2} : r = k + μ j$ , $μ \in$ R and $L_{3} : r = i + j + v k$ , v $\in$ R are given. For which point(s) Q on L2 can we find a point P…
Mathematics · 3D Geometry · Multiple correct
Q23.For $a \in R, ∣ a ∣ > 1$ , let $n \to \infty lim (\frac{1 + 3 2 + ... 3 n}{n ^{7/3} ( \frac{1}{( an + 1 ) ^{2}} + \frac{1}{( an + 2 ) ^{2}} + ... + \frac{1}{( an + n ) ^{2}} )}) = 54$ …
Mathematics · Limits Continuity and Differentiability · Multiple correct
Q24.Let f : R be a function. We say that f has PROPERTY 1 if $h \to 0 lim \frac{f ( h ) - f ( 0 )}{∣ h ∣}$ exists and is finite, and PROPERTY 2 if $h \to 0 lim \frac{f ( h ) - f ( 0 )}{h ^{2}}$ …
Mathematics · Limits Continuity and Differentiability · Multiple correct
Q25.Let x $\in$ R and let $P = 100120123$ , $Q = 20 x x 4 x x 06$ …
Mathematics · Matrices and Determinants · Multiple correct
Q26. $P_{1} = I = 100010001, P_{2} = 100001010, P_{3} = 010100001, P_{4} = 001100010, P_{5} = 010001100, P_{6} = 001010100$ …
Mathematics · Matrices and Determinants · Multiple correct
Q27.Let $a = 2 i + j - k$ and $b = i + 2 j + k$ be two vectors. Consider a vector c = $α a$ + $β b$ , $α$ , $β \in$ …
Mathematics · Vector Algebra · Numerical
Q28.Let |X| denote the number of elements in a set X. Let S = {1, 2, 3, 4, 5, 6} be a sample space, where each element is equally likely to occur. If A and B are independent events associated with S, then the number of ordered pairs (A, B)…
Mathematics · Permutations and Combinations · Numerical
Q29.Suppose det $k = 0 \sum n k k = 0 \sum n^{n} C_{k} . k k = 0 \sum n^{n} C_{k} k^{2} k = 0 \sum n^{n} C_{k} 3^{k} = 0$ holds…
Mathematics · Matrices and Determinants · Numerical
Q30.Five persons A, B, C, D and E are seated in a circular arrangement. If each of them is given a hat of one of the three colours red, blue and green, then the number of ways of distributing the hats such that the persons seated in adjacent…
Mathematics · Permutations and Combinations · Numerical
Q31.The value of the integral $0 \int π /2 \frac{3 c o s θ}{( c o s θ + s i n θ ) ^{5}} d θ$ equals ..............
Mathematics · Definite Integration · Numerical
Q32.The value of $sec^{- 1} (\frac{1}{4} \sum_{k = 0}^{10} sec (\frac{7 π}{12} + \frac{k π}{2}) sec (\frac{7 π}{12} + \frac{( k + 1 ) π}{2}))$ in the interval $[- \frac{π}{4}, \frac{3 π}{4}]$ …
Mathematics · Inverse Trigonometric Functions · Numerical
Q33.Let f(x) = sin( $π$ cos x) and g(x) = cos(2 $π$ sin x) be two functions defined for x > 0. Define the following sets whose elements are written in the increasing order: X = {x : f(x) = 0}, Y = {x : f'(x) = 0} Z = {x : g(x) = 0}, W =… Includes diagram
Mathematics · Trigonometric Functions and Equations · MCQ
Q34.Let f(x) = sin( $π$ cos x) and g(x) = cos(2 $π$ sin x) be two functions defined for x > 0. Define the following sets whose elements are written in the increasing order : X = {x : f(x) = 0}, Y = {x : f'(x) = 0} Z = {x : g(x) = 0}, W =… Includes diagram
Mathematics · Trigonometric Functions and Equations · MCQ
Q35.Let the circles C1 : x2 + y2 = 9 and C2 : (x $-$ 3)2 + (y $-$ 4)2 = 16, intersect at the points X and Y. Suppose that another circle C3 : (x $-$ h)2 + (y $-$ k)2 = r2 satisfies the following conditions : (i) Centre of C3 is collinear with… Includes diagram
Mathematics · Parabola · MCQ
Q36.Let the circle C1 : x2 + y2 = 9 and C2 : (x $-$ 3)2 + (y $-$ 4)2 = 16, intersect at the points X and Y. Suppose that another circle C3 : (x $-$ h)2 + (y $-$ k)2 = r2 satisfies the following conditions : (i) centre of C3 is collinear with… Includes diagram
Mathematics · Parabola · MCQ