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Mathematics · 2019 · Shift 1

18 questions from this JEE Advanced paper

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JEE Advanced
Papers
2019 · Shift 1
Mathematics

Mathematics · 2019 · Shift 1

18 questions from this JEE Advanced paper

Complex Numbers2 questions Matrices and Determinants2 questions Circle2 questions Application of Integration1 questions Differential Equations1 questions Ellipse1 questions Properties of Triangle1 questions Quadratic Equation and Inequalities1 questions 3D Geometry2 questions Probability2 questions Limits Continuity and Differentiability1 questions Definite Integration1 questions Sequences and Series1 questions

Q19.Let S be the set of all complex numbers z satisfying $∣ z - 2 + i ∣ \geq 5$ . If the complex number z0 is such that $\frac{1}{∣ z _{0} - 1 ∣}$ is the maximum of the set ${\frac{1}{∣ z _{0} - 1 ∣} : z \in S}$ …
Mathematics · Complex Numbers · MCQ
Q20.Let $M = [sin^{4} θ 1 + cos^{2} θ - 1 - sin^{2} θ cos^{4} θ] = α I + β M^{- 1}$ , where $α$ = $α$ …
Mathematics · Matrices and Determinants · MCQ
Q21.A line y = mx + 1 intersects the circle $(x - 3)^{2} + (y + 2)^{2}$ = 25 at the points P and Q. If the midpoint of the line segment PQ has x-coordinate $- \frac{3}{5}$ , then which one of the following options is correct?
Mathematics · Circle · MCQ
Q22.The area of the region {(x, y) : xy $\leq$ 8, 1 $\leq$ y $\leq$ x2} is
Mathematics · Application of Integration · MCQ
Q23.Let $Γ$ denote a curve y = y(x) which is in the first quadrant and let the point (1, 0) lie on it. Let the tangent to I` at a point P intersect the y-axis at YP. If PYP has length 1 for each point P on I`, then which of the following…
Mathematics · Differential Equations · Multiple correct
Q24.Define the collections {E1, E2, E3, ...} of ellipses and {R1, R2, R3.....} of rectangles as follows : $E_{1} : \frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ R1 : rectangle of largest area, with sides parallel to the axes, inscribed in E1; En :…
Mathematics · Ellipse · Multiple correct
Q25.In a non-right-angled triangle $Δ$ PQR, let p, q, r denote the lengths of the sides opposite to the angles At P, Q, R respectively. The median from R meets the side PQ at S, the perpendicular from P meets the side QR at E, and RS and…
Mathematics · Properties of Triangle · Multiple correct
Q26.Let $α$ and $β$ be the roots of $x^{2} - x - 1 = 0$ , with $α$ > $β$ . For all positive integers n, define $a_{n} = \frac{α ^{n} - β ^{n}}{α - β}, n \geq 1 b_{1} = 1 an d b_{n} = a_{n - 1} + a_{n + 1}, n \geq 2$ …
Mathematics · Quadratic Equation and Inequalities · Multiple correct
Q27.Let L1 and L2 denote the lines $r = i + λ (- i + 2 j + 2 k)$ , $λ \in$ R and $r = μ (2 i - j + 2 k), μ \in R$ respectively. If L3 is a line which is…
Mathematics · 3D Geometry · Multiple correct
Q28.There are three bags B1, B2 and B3. The bag B1 contains 5 red and 5 green balls, B2 contains 3 red and 5 green balls, and B3 contains 5 red and 3 green balls. Bags B1, B2 and B3 have probabilities $\frac{3}{10}$ , $\frac{3}{10}$ and $\frac{4}{10}$ …
Mathematics · Probability · Multiple correct
Q29.Let $M = 013 12 b a 31$ and adj $M = - 1 8 - 5 1 - 6 3 - 1 2 - 1$ …
Mathematics · Matrices and Determinants · Multiple correct
Q30.Let f : R $\to$ R be given by $f (x) = ⎩ ⎨ ⎧ x^{5} + 5 x^{4} + 10 x^{3} + 10 x^{2} + 3 x + 1, x^{2} - x + 1, \frac{2}{3} x^{3} - 4 x^{2} + 7 x - \frac{8}{3}, (x - 2) lo g_{e} (x - 2) - x + \frac{10}{3}, x < 0; 0 \leq x < 1; 1 \leq x < 3; x \geq 3; ⎭ ⎬ ⎫$ …
Mathematics · Limits Continuity and Differentiability · Multiple correct
Q31.Let S be the sample space of all 3 $\times$ 3 matrices with entries from the set {0, 1}. Let the events E1 and E2 be given by E1 = {A $\in$ S : det A = 0} and E2 = {A $\in$ S : sum of entries of A is 7}. If a matrix is chosen at random…
Mathematics · Probability · Numerical
Q32.Let the point B be the reflection of the point A(2, 3) with respect to the line $8 x - 6 y - 23 = 0$ . Let $Γ_{A}$ and $Γ_{B}$ be circles of radii 2 and 1 with centres A and B respectively. Let T be a common tangent to the circles $Γ_{A}$ …
Mathematics · Circle · Numerical
Q33.Let $ω e 1$ be a cube root of unity. Then the minimum of the set ${a + bω + c ω^{2}^{2} : a, b, c$ distinct non-zero integers} equals ..................
Mathematics · Complex Numbers · Numerical
Q34.If $I = \frac{2}{π} - π /4 \int π /4 \frac{d x}{( 1 + e ^{s i n x} ) ( 2 - c o s 2 x )}$ , then 27I2 equals .................
Mathematics · Definite Integration · Numerical
Q35.Three lines are given by $r = λ i, λ \in R$ , $r = μ (i + j), μ \in R$ and $r = v (i + j + k), v \in R$ Let the lines cut the plane x + y + z = 1 at the points A, B…
Mathematics · 3D Geometry · Numerical
Q36.Let AP(a; d) denote the set of all the terms of an infinite arithmetic progression with first term a and common difference d > 0. If $A P (1; 3) \cap A P (2; 5) \cap A P (3; 7)$ = AP(a ; d), then a + d equals ..............
Mathematics · Sequences and Series · Numerical