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Mathematics · 2021 · Shift 1

19 questions from this JEE Advanced paper

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JEE Advanced
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2021 · Shift 1
Mathematics

Mathematics · 2021 · Shift 1

19 questions from this JEE Advanced paper

Circle1 questions Application of Integration1 questions Probability4 questions Complex Numbers2 questions Matrices and Determinants4 questions Straight Lines and Pair of Straight Lines2 questions Limits Continuity and Differentiability1 questions Sequences and Series1 questions Quadratic Equation and Inequalities1 questions Properties of Triangle1 questions Vector Algebra1 questions

Q20.Consider a triangle $Δ$ whose two sides lie on the x-axis and the line x + y + 1 = 0. If the orthocenter of $Δ$ is (1, 1), then the equation of the circle passing through the vertices of the triangle $Δ$ is
Mathematics · Circle · MCQ
Q21.The area of the region ${(x, y) : 0 \leq x \leq \frac{9}{4}, 0 \leq y \leq 1, x \geq 3 y, x + y \geq 2}$ is
Mathematics · Application of Integration · MCQ
Q22.Consider three sets E1 = {1, 2, 3}, F1 = {1, 3, 4} and G1 = {2, 3, 4, 5}. Two elements are chosen at random, without replacement, from the set E1, and let S1 denote the set of these chosen elements. Let E2 = E1 $-$ S1 and F2 = F1 $\cup$ …
Mathematics · Probability · MCQ
Q23.Let $θ_{1}, θ_{2}, \dots, θ_{10}$ be positive valued angles (in radian) such that $θ_{1} + θ_{2} + \dots + θ_{10} = 2 π$ . Define the complex numbers $z_{1} = e^{i θ_{1}}, z_{k} = z_{k - 1} e^{i θ_{k}}$ for $k=2,3, \ldots,…
Mathematics · Complex Numbers · MCQ
Q24.Three numbers are chosen at random, one after another with replacement, from the set S = {1, 2, 3, ......, 100}. Let p1 be the probability that the maximum of chosen numbers is at least 81 and p2 be the probability that the minimum of…
Mathematics · Probability · Numerical
Q25.Three numbers are chosen at random, one after another with replacement, from the set S = {1, 2, 3, ......, 100}. Let p1 be the probability that the maximum of chosen numbers is at least 81 and p2 be the probability that the minimum of…
Mathematics · Probability · Numerical
Q26.Let $α$ , $β$ and $γ$ be real numbers such that the system of linear equations x + 2y + 3z = $α$ 4x + 5y + 6z = $β$ 7x + 8y + 9z = $γ -$ 1 is consistent. Let | M | represent the determinant of the matrix $M = α β - 1 210 γ 01$ …
Mathematics · Matrices and Determinants · Numerical
Q27.Let $α$ , $β$ and $γ$ be real numbers such that the system of linear equations x + 2y + 3z = $α$ 4x + 5y + 6z = $β$ 7x + 8y + 9z = $γ -$ 1 is consistent. Let | M | represent the determinant of the matrix $M = α β - 1 210 γ 01$ …
Mathematics · Matrices and Determinants · Numerical
Q28.Consider the lines L1 and L2 defined by $L_{1} : x 2 + y - 1 = 0$ and $L_{2} : x 2 - y + 1 = 0$ For a fixed constant $λ$ , let C be the locus of a point P such that the product of the distance of P from L1 and the distance of P…
Mathematics · Straight Lines and Pair of Straight Lines · Numerical
Q29.Consider the lines L1 and L2 defined by $L_{1} : x 2 + y - 1 = 0$ and $L_{2} : x 2 - y + 1 = 0$ For a fixed constant $λ$ , let C be the locus of a point P such that the product of the distance of P from L1 and the distance of P…
Mathematics · Straight Lines and Pair of Straight Lines · Numerical
Q30.For any 3 $\times$ 3 matrix M, let | M | denote the determinant of M. Let $E = 12823133418$ , $P = 100001010$ …
Mathematics · Matrices and Determinants · Multiple correct
Q31.Let f : R $\to$ R be defined by $f (x) = \frac{x ^{2} - 3 x - 6}{x ^{2} + 2 x + 4}$ Then which of the following statements is (are) TRUE?
Mathematics · Limits Continuity and Differentiability · Multiple correct
Q32.Let E, F and G be three events having probabilities $P (E) = \frac{1}{8}$ , $P (F) = \frac{1}{6}$ and $P (G) = \frac{1}{4}$ , and let P (E $\cap$ F $\cap$ G) = $\frac{1}{10}$ . For any event H, if Hc denotes the complement, then which of the…
Mathematics · Probability · Multiple correct
Q33.For any 3 $\times$ 3 matrix M, let |M| denote the determinant of M. Let I be the 3 $\times$ 3 identity matrix. Let E and F be two 3 $\times$ 3 matrices such that (I $-$ EF) is invertible. If G = (I $-$ EF) $-$ 1, then which of the…
Mathematics · Matrices and Determinants · Multiple correct
Q34.For any positive integer n, let Sn : (0, $\infty$ ) $\to$ R be defined by $S_{n} (x) = \sum o l imi t s_{k = 1}^{n} cot^{- 1} (\frac{1 + k ( k + 1 ) x ^{2}}{x})$ , where for any x $\in$ R, $cot^{- 1} (x) \in (0, π)$ and $tan^{- 1} (x) \in (- \frac{π}{2}, \frac{π}{2})$ …
Mathematics · Sequences and Series · Multiple correct
Q35.For any complex number w = c + id, let $ar g (w) \in (- π, π]$ , where $i = - 1$ . Let $α$ and $β$ be real numbers such that for all complex numbers z = x + iy satisfying $ar g (\frac{z + α}{z + β}) = \frac{π}{4}$ …
Mathematics · Complex Numbers · Multiple correct
Q36.For x $\in$ R, the number of real roots of the equation $3 x^{2} - 4 x^{2} - 1 + x - 1 = 0$ is .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q37.In a triangle ABC, let AB = $23$ , BC = 3 and CA = 4. Then the value of $\frac{c o t A + c o t C}{c o t B}$ is .
Mathematics · Properties of Triangle · Numerical
Q38.Let $u$ , $v$ and $w$ be vectors in three-dimensional space, where $u$ and $v$ are unit vectors which are not perpendicular to each other and $\overrightarrow…
Mathematics · Vector Algebra · Numerical