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Mathematics · 2019 · 11 Jan · Shift 2

22 questions from this JEE Main paper

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2019 · 11 Jan · Shift 2
Mathematics

Mathematics · 2019 · 11 Jan · Shift 2

22 questions from this JEE Main paper

Sequences and Series2 questions Hyperbola2 questions Probability1 questions Ellipse1 questions Application of Derivatives1 questions Definite Integration1 questions Functions2 questions Indefinite Integrals1 questions Area Under the Curves1 questions Limits Continuity and Differentiability2 questions Quadratic Equation and Inequalities1 questions Matrices and Determinants1 questions Complex Numbers1 questions Differential Equations1 questions Parabola1 questions Straight Lines and Pair of Straight Lines1 questions Inverse Trigonometric Functions1 questions Vector Algebra1 questions

Q21.Let x, y be positive real numbers and m, n positive integers. The maximum value of the expression $\frac{x ^{m} y ^{n}}{( 1 + x ^{2 m} ) ( 1 + y ^{2 n} )}$ is :
Mathematics · Sequences and Series · MCQ
Q22.If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is :
Mathematics · Hyperbola · MCQ
Q23.Let S = {1, 2, . . . . . ., 20}. A subset B of S is said to be "nice", if the sum of the elements of B is 203. Then the probability that a randonly chosen subset of S is "nice" is :
Mathematics · Probability · MCQ
Q24.Let the length of the latus rectum of an ellipse with its major axis along x-axis and centre at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following…
Mathematics · Ellipse · MCQ
Q25.Let f(x) = $\frac{x}{a ^{2} + x ^{2}} - \frac{d - x}{b ^{2} + ( d - x ) ^{2}},$ x $\in$ R, where a, b and d are non-zero real constants. Then :
Mathematics · Application of Derivatives · MCQ
Q26.The integral $π /6 \int π /4 \frac{d x}{s i n 2 x ( t a n ^{5} x + c o t ^{5} x )}$ equals :
Mathematics · Definite Integration · MCQ
Q27.Let a function f : (0, $\infty$ ) $\to$ (0, $\infty$ ) be defined by f(x) = $1 - \frac{1}{x}$ . Then f is :
Mathematics · Functions · MCQ
Q28.If $\int \frac{x + 1}{2 x - 1} d x$ = f(x) $2 x - 1$ + C, where C is a constant of integration, then f(x) is equal to :
Mathematics · Indefinite Integrals · MCQ
Q29.The area (in sq. units) in the first quadrant bounded by the parabola, y = x2 + 1, the tangent to it at the point (2, 5) and the coordinate axes is :
Mathematics · Area Under the Curves · MCQ
Q30. $x \to 0 lim \frac{x c o t ( 4 x )}{s i n ^{2} x c o t ^{2} ( 2 x )}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q31.Let $α$ and $β$ be the roots of the quadratic equation x2 sin $θ$ – x(sin $θ$ cos $θ$ + 1) + cos $θ$ = 0 (0 < $θ$ < 45o), and $α$ < $β$ . Then $n = 0 \sum \infty (α^{n} + \frac{( - 1 ) ^{n}}{β ^{n}})$ …
Mathematics · Quadratic Equation and Inequalities · MCQ
Q32.If $a - b - c 2 b 2 c 2 a b - c - a 2 c 2 a 2 b c - a - b$ = (a + b + c) (x + a + b + c)2, x $e$ 0, then x is equal to :
Mathematics · Matrices and Determinants · MCQ
Q33.If 19th term of a non-zero A.P. is zero, then its (49th term) : (29th term) is :
Mathematics · Sequences and Series · MCQ
Q34.Let z be a complex number such that |z| + z = 3 + i (where i = $- 1$ ). Then |z| is equal to :
Mathematics · Complex Numbers · MCQ
Q35.Let K be the set of all real values of x where the function f(x) = sin |x| – |x| + 2(x – $π$ ) cos |x| is not differentiable. Then the set K is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q36.The number of functions f from {1, 2, 3, ...., 20} onto {1, 2, 3, ...., 20} such that f(k) is a multiple of 3, whenever k is a multiple of 4, is :
Mathematics · Functions · MCQ
Q37.The solution of the differential equation, $\frac{d y}{d x}$ = (x – y)2, when y(1) = 1, is :
Mathematics · Differential Equations · MCQ
Q38.A circle cuts a chord of length 4a on the x-axis and passes through a point on the y-axis, distant 2b from the origin. Then the locus of the centre of this circle, is :
Mathematics · Hyperbola · MCQ
Q39.If the area of the triangle whose one vertex is at the vertex of the parabola, y2 + 4(x – a2) = 0 and the othertwo vertices are the points of intersection of the parabola and y-axis, is 250 sq. units, then a value of 'a' is :
Mathematics · Parabola · MCQ
Q40.If in a parallelogram ABDC, the coordinates of A, B and C are respectively (1, 2), (3, 4) and (2, 5), then the equation of the diagonal AD is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q41.All x satisfying the inequality (cot–1 x)2– 7(cot–1 x) + 10 > 0, lie in the interval :
Mathematics · Inverse Trigonometric Functions · MCQ
Q42.Let $3 i + j, i + 3 j$ and $β i + (1 - β) j$ respectively be the position vectors of the points A, B and C with respect to the origin O. If the…
Mathematics · Vector Algebra · MCQ