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Mathematics · 2020 · Shift 2

18 questions from this JEE Advanced paper

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JEE Advanced
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2020 · Shift 2
Mathematics

Mathematics · 2020 · Shift 2

18 questions from this JEE Advanced paper

Complex Numbers1 questions Probability2 questions Circle1 questions Matrices and Determinants1 questions Limits Continuity and Differentiability3 questions Definite Integration2 questions Hyperbola1 questions 3D Geometry1 questions Vector Algebra1 questions Mathematical Induction and Binomial Theorem1 questions Permutations and Combinations2 questions Functions2 questions

Q19.For a complex number z, let Re(z) denote that real part of z. Let S be the set of all complex numbers z satisfying $z^{4} - ∣ z ∣^{4} = 4 i z^{2}$ , where i = $- 1$ . Then the minimum possible value of |z1 $-$ z2|2, where z1, z2 $\in$ S…
Mathematics · Complex Numbers · Numerical
Q20.The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of…
Mathematics · Probability · Numerical
Q21.Let O be the centre of the circle x2 + y2 = r2, where $r > \frac{5}{2}$ . Suppose PQ is a chord of this circle and the equation of the line passing through P and Q is 2x + 4y = 5. If the centre of the circumcircle of the triangle…
Mathematics · Circle · Numerical
Q22.The trace of a square matrix is defined to be the sum of its diagonal entries. If A is a 2 $\times$ 2 matrix such that the trace of A is 3 and the trace of A3 is $-$ 18, then the value of the determinant of A is .............
Mathematics · Matrices and Determinants · Numerical
Q23.Let the functions $f : (- 1, 1) \to R$ and $g : (- 1, 1) \to (- 1, 1)$ be defined by $f (x) = ∣2 x - 1∣ + ∣2 x + 1∣$ and $g (x) = x - [x]$ , where [x] denotes the greatest integer less than or equal to x. Let $f o g : (- 1, 1) \to R$ be the…
Mathematics · Limits Continuity and Differentiability · Numerical
Q24.The value of the limit $x \to \frac{π}{2} lim \frac{4 2 ( s i n 3 x + s i n x )}{( 2 s i n 2 x s i n \frac{3 x}{2} + c o s \frac{5 x}{2} ) - ( 2 + 2 c o s 2 x + c o s \frac{3 x}{2} )}$ …
Mathematics · Limits Continuity and Differentiability · Numerical
Q25.Let b be a nonzero real number. Suppose f : R $\to$ R is a differentiable function such that f(0) = 1. If the derivative f' of f satisfies the equation $f^{'} (x) = \frac{f ( x )}{b ^{2} + x ^{2}}$ for all x $\in$ R, then which of the following…
Mathematics · Definite Integration · Multiple correct
Q26.Let a and b be positive real numbers such that a > 1 and b < a. Let P be a point in the first quadrant that lies on the hyperbola $\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ . Suppose the tangent to the hyperbola at P…
Mathematics · Hyperbola · Multiple correct
Q27.Let f : R $\to$ R and g : R $\to$ R be functions satisfying f(x + y) = f(x) + f(y) + f(x)f(y) and f(x) = xg(x) for all x, y $\in$ R. If $x \to 0 lim g (x) = 1$ , then which of the following statements is/are TRUE?
Mathematics · Limits Continuity and Differentiability · Multiple correct
Q28.Let $α$ 2 + $β$ 2 + $γ$ 2 $e$ 0 and $α$ + $γ$ = 1. Suppose the point (3, 2, $-$ 1) is the mirror image of the point (1, 0, $-$ 1) with respect to the plane $α$ x + $β$ y + $γ$ z = $δ$ . Then which of…
Mathematics · 3D Geometry · Multiple correct
Q29.Let a and b be positive real numbers. Suppose $P Q = a i + b j$ and $P S = a i - b j$ are adjacent sides of a parallelogram PQRS. Let u and v be the projection vectors of $w = i + j$ along PQ…
Mathematics · Vector Algebra · Multiple correct
Q30.For non-negative integers s and r, let $(s r) = {\frac{s !}{r ! ( s - r )!} 0 i f r \leq s, i f r > s$ For…
Mathematics · Mathematical Induction and Binomial Theorem · Multiple correct
Q31.An engineer is required to visit a factory for exactly four days during the first 15 days of every month and it is mandatory that no two visits take place on consecutive days. Then the number of all possible ways in which such visits to…
Mathematics · Permutations and Combinations · Numerical
Q32.In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons. Then the number of all possible ways in which this…
Mathematics · Permutations and Combinations · Numerical
Q33.Two fair dice, each with faces numbered 1, 2, 3, 4, 5 and 6, are rolled together and the sum of the numbers on the faces is observed. This process is repeated till the sum is either a prime number or a perfect square. Suppose the sum turns…
Mathematics · Probability · Numerical
Q34.Let the function f : [0, 1] $\to$ R be defined by $f (x) = \frac{4 ^{x}}{4 ^{x} + 2}$ Then the value of $f (\frac{1}{40}) + f (\frac{2}{40}) + f (\frac{3}{40}) + ... + f (\frac{39}{40}) - f (\frac{1}{2})$ …
Mathematics · Functions · Numerical
Q35.Let $f : R \to R$ be a differentiable function such that its derivative f' is continuous and f( $π$ ) = $-$ 6. If $F : [0, π] \to R$ is defined by $F (x) = \int_{0}^{x} f (t) d t$ , and if $\int_{0}^{π} (f^{'} (x) + F (x)) cos x d x$ = 2 then the value…
Mathematics · Definite Integration · Numerical
Q36.Let the function $f : (0, π) \to R$ be defined by $f (θ) = (sin θ + cos θ)^{2} + (sin θ - cos θ)^{4}$ Suppose the function f has a local minimum at $θ$ precisely when $θ \in {λ_{1} π, ...., λ_{r} π}$ …
Mathematics · Functions · Numerical