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Mathematics · 2020 · Shift 1

18 questions from this JEE Advanced paper

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JEE Advanced
Papers
2020 · Shift 1
Mathematics

Mathematics · 2020 · Shift 1

18 questions from this JEE Advanced paper

Quadratic Equation and Inequalities1 questions Functions3 questions Application of Integration1 questions Parabola1 questions Probability1 questions Application of Derivatives1 questions Limits Continuity and Differentiability2 questions Matrices and Determinants1 questions Complex Numbers1 questions Properties of Triangle2 questions 3D Geometry1 questions Definite Integration1 questions Sequences and Series2 questions

Q19.Suppose a, b denote the distinct real roots of the quadratic polynomial x2 + 20x $-$ 2020 and suppose c, d denote the distinct complex roots of the quadratic polynomial x2 $-$ 20x + 2020. Then the value of ac(a $-$ c) + ad(a $-$ d) + bc(b $-$ …
Mathematics · Quadratic Equation and Inequalities · MCQ
Q20.If the function f : R $\to$ R is defined by f(x) = |x| (x $-$ sin x), then which of the following statements is TRUE?
Mathematics · Functions · MCQ
Q21.Let the functions f : R $\to$ R and g : R $\to$ R be defined by f(x) = ex $-$ 1 $-$ e $-$ |x $-$ 1| and g(x) = $\frac{1}{2}$ (ex $-$ 1 + e1 $-$ x). The the area of the region in the first quadrant bounded by the curves y = f(x), y = g(x) and…
Mathematics · Application of Integration · MCQ
Q22.Let a, b and $λ$ be positive real numbers. Suppose P is an end point of the latus return of the parabola y2 = 4 $λ$ x, and suppose the ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ passes through the point…
Mathematics · Parabola · MCQ
Q23.Let C1 and C2 be two biased coins such that the probabilities of getting head in a single toss are $\frac{2}{3}$ and $\frac{1}{3}$ , respectively. Suppose $α$ is the number of heads that appear when C1 is tossed twice,…
Mathematics · Probability · MCQ
Q24.Consider the rectangles lying the region ${(x, y) \in R \times R : 0 \leq x \leq \frac{π}{2}$ and $0 \leq y \leq 2 sin (2 x)}$ and having one side on the X-axis. The area of the rectangle…
Mathematics · Application of Derivatives · MCQ
Q25.Let the function f : R $\to$ R be defined by f(x) = x3 $-$ x2 + (x $-$ 1)sin x and let g : R $\to$ R be an arbitrary function. Let fg : R $\to$ R be the product function defined by (fg)(x) = f(x)g(x). Then which of the following statements…
Mathematics · Limits Continuity and Differentiability · Multiple correct
Q26.Let M be a 3 $\times$ 3 invertible matrix with real entries and let I denote the 3 $\times$ 3 identity matrix. If M $-$ 1 = adj(adj M), then which of the following statements is/are ALWAYS TRUE?
Mathematics · Matrices and Determinants · Multiple correct
Q27.Let S be the set of all complex numbers z satisfying |z2 + z + 1| = 1. Then which of the following statements is/are TRUE?
Mathematics · Complex Numbers · Multiple correct
Q28.Let x, y and z be positive real numbers. Suppose x, y and z are the lengths of the sides of a triangle opposite to its angles X, Y, and Z, respectively. If $tan \frac{X}{2} + tan \frac{Z}{2} = \frac{2 y}{x + y + z}$ , then which of…
Mathematics · Properties of Triangle · Multiple correct
Q29.Let L1 and L2 be the following straight lines. $L_{1} : \frac{x - 1}{1} = \frac{y}{- 1} = \frac{z - 1}{3}$ and $L_{2} : \frac{x - 1}{- 3} = \frac{y}{- 1} = \frac{z - 1}{1}$ . Suppose the straight line $L : \frac{x - α}{l} = \frac{y - 1}{m} = \frac{z - γ}{- 2}$ …
Mathematics · 3D Geometry · Multiple correct
Q30.Which of the following inequalities is/are TRUE?
Mathematics · Definite Integration · Multiple correct
Q31.Let m be the minimum possible value of $lo g_{3} (3^{y_{1}} + 3^{y_{2}} + 3^{y_{3}})$ , where $y_{1}, y_{2}, y_{3}$ are real numbers for which $y_{1} + y_{2} + y_{3}$ = 9. Let M be the maximum possible value of $(lo g_{3} x_{1} + lo g_{3} x_{2} + lo g_{3} x_{3})$ …
Mathematics · Sequences and Series · Numerical
Q32.Let a1, a2, a3, .... be a sequence of positive integers in arithmetic progression with common difference 2. Also, let b1, b2, b3, .... be a sequence of positive integers in geometric progression with common ratio 2. If a1 = b1 = c, then…
Mathematics · Sequences and Series · Numerical
Q33.Let f : [0, 2] $\to$ R be the function defined by $f (x) = (3 - sin (2 π x)) sin (π x - \frac{π}{4}) - sin (3 π x + \frac{π}{4})$ If $α, β \in [0, 2]$ are such that ${x \in [0, 2] : f (x) \geq 0} = [α, β]$ …
Mathematics · Functions · Numerical
Q34.In a triangle PQR, let a = QR, b = RP, and c = PQ. If |a| = 3, |b| = 4 and $\frac{a . ( c - b )}{c . ( a - b )} = \frac{∣ a ∣}{∣ a ∣ + ∣ b ∣}$ , then the value of |a $\times$ b|2 is ......
Mathematics · Properties of Triangle · Numerical
Q35.For a polynomial g(x) with real coefficients, let mg denote the number of distinct real roots of g(x). Suppose S is the set of polynomials with real coefficients defined by $S = {(x^{2} - 1)^{2} (a_{0} + a_{1} x + a_{2} x^{2} + a_{3} x^{3}) : a_{0}, a_{1}, a_{2}, a_{3} \in R}$ …
Mathematics · Functions · Numerical
Q36.let e denote the base of the natural logarithm. The value of the real number a for which the right hand limit $x \to 0^{+} lim \frac{( 1 - x ) ^{1/ x} - e ^{- 1}}{x ^{a}}$ is equal to a non-zero real number,…
Mathematics · Limits Continuity and Differentiability · Numerical