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Mathematics · 2019 · 10 Apr · Shift 2

21 questions from this JEE Main paper

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2019 · 10 Apr · Shift 2
Mathematics

Mathematics · 2019 · 10 Apr · Shift 2

21 questions from this JEE Main paper

Differentiation1 questions Application of Derivatives1 questions Quadratic Equation and Inequalities1 questions Limits Continuity and Differentiability1 questions Probability1 questions Indefinite Integrals1 questions Sequences and Series2 questions Vector Algebra1 questions Inverse Trigonometric Functions1 questions Statistics1 questions Straight Lines and Pair of Straight Lines1 questions Differential Equations1 questions Permutations and Combinations1 questions Definite Integration1 questions Area Under the Curves1 questions Complex Numbers1 questions Matrices and Determinants2 questions Hyperbola1 questions Binomial Theorem1 questions

Q23.Let f(x) = loge(sin x), (0 < x < $π$ ) and g(x) = sin–1 (e–x ), (x $\geq$ 0). If $α$ is a positive real number such that a = (fog)'( $α$ ) and b = (fog)( $α$ ), then :
Mathematics · Differentiation · MCQ
Q24.A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm3 /min. When the thickness of the ice is 5 cm, then the rate at which the thickness (in cm/min) of the ice decreases, is :
Mathematics · Application of Derivatives · MCQ
Q25.The number of real roots of the equation 5 + |2x – 1| = 2x (2x – 2) is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q26.If $x \to 1 lim \frac{x ^{2} - a x + b}{x - 1} = 5$ , then a + b is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q27.Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is :
Mathematics · Probability · MCQ
Q28.If $\int x^{5} e^{- x^{2}} d x = g (x) e^{- x^{2}} + c$ , where c is a constant of integration, then $g$ (–1) is equal to :
Mathematics · Indefinite Integrals · MCQ
Q29.Let a1, a2, a3,......be an A.P. with a6 = 2. Then the common difference of this A.P., which maximises the product a1a4a5, is :
Mathematics · Sequences and Series · MCQ
Q30.The distance of the point having position vector $- i + 2 j + 6 k$ from the straight line passing through the point (2, 3, – 4) and parallel to the vector, $6 i + 3 j - 4 k$ is :
Mathematics · Vector Algebra · MCQ
Q31.If $cos^{- 1} x - cos^{- 1} \frac{y}{2} = α$ ,where –1 $\leq$ x $\leq$ 1, – 2 $\leq$ y $\leq$ 2, x $\leq \frac{y}{2}$ , then for all x, y, 4x2 – 4xy cos $α$ + y2 is equal to :
Mathematics · Inverse Trigonometric Functions · MCQ
Q32.If both the mean and the standard deviation of 50 observations x1, x2,..., x50 are equal to 16, then the mean of (x1 – 4)2 , (x2 – 4)2 ,....., (x50 – 4)2 is :
Mathematics · Statistics · MCQ
Q33.Lines are drawn parallel to the line 4x – 3y + 2 = 0, at a distance $\frac{3}{5}$ from the origin. Then which one of the following points lies on any of these lines ?
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q34.Let y = y(x) be the solution of the differential equation, $\frac{d y}{d x} + y tan x = 2 x + x^{2} tan x$ , $x \in (- \frac{π}{2}, \frac{π}{2})$ , such that y(0) = 1. Then :
Mathematics · Differential Equations · MCQ
Q35.Let $a$ , b and c be in G.P. with common ratio r, where $a e$ 0 and 0 < r $\leq \frac{1}{2}$ . If 3 $a$ , 7b and 15c are the first three terms of an A.P., then the 4th term of this A.P. is :
Mathematics · Sequences and Series · MCQ
Q36.Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number of beams is :
Mathematics · Permutations and Combinations · MCQ
Q37.The integral $π /6 \int π /3 sec^{2/3} x cos e c^{4/3} x d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q38.The area (in sq.units) of the region bounded by the curves y = 2x and y = |x + 1|, in the first quadrant is :
Mathematics · Area Under the Curves · MCQ
Q39.If z and w are two complex numbers such that |zw| = 1 and arg(z) – arg(w) = $\frac{π}{2}$ , then :
Mathematics · Complex Numbers · MCQ
Q40.The sum of the real roots of the equation $x 2 - 3 - 6 - 3 x 2 x - 1 x - 3 x + 2 = 0$ , is equal to :
Mathematics · Matrices and Determinants · MCQ
Q41.If 5x + 9 = 0 is the directrix of the hyperbola 16x2 – 9y2 = 144, then its corresponding focus is :
Mathematics · Hyperbola · MCQ
Q42.The smallest natural number n, such that the coefficient of x in the expansion of $(x^{2} + \frac{1}{x ^{3}})^{n}$ is nC23, is :
Mathematics · Binomial Theorem · MCQ
Q43.Let $λ$ be a real number for which the system of linear equations x + y + z = 6, 4x + $λ$ y – $λ$ z = $λ$ – 2, 3x + 2y – 4z = – 5 has infinitely many solutions. Then $λ$ is a root of the quadratic equation:
Mathematics · Matrices and Determinants · MCQ