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Mathematics · 2013 · Shift 0

21 questions from this JEE Main paper

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2013 · Shift 0
Mathematics

Mathematics · 2013 · Shift 0

21 questions from this JEE Main paper

Permutations and Combinations2 questions Statistics1 questions Limits Continuity and Differentiability1 questions Differential Equations1 questions Area Under the Curves1 questions Definite Integration1 questions Indefinite Integrals1 questions Inverse Trigonometric Functions1 questions Differentiation1 questions Ellipse1 questions Straight Lines and Pair of Straight Lines2 questions Binomial Theorem1 questions Quadratic Equation and Inequalities1 questions Matrices and Determinants1 questions Application of Derivatives1 questions Complex Numbers1 questions Trigonometric Ratio and Identites1 questions Vector Algebra1 questions 3D Geometry1 questions

Q27.Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A $\times$ B having 3 or more elements is :
Mathematics · Permutations and Combinations · MCQ
Q28.All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?
Mathematics · Statistics · MCQ
Q29. $x \to 0 lim \frac{( 1 - c o s 2 x ) ( 3 + c o s x )}{x t a n 4 x}$ is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q30.At present, a firm is manufacturing $2000$ items. It is estimated that the rate of change of production P w.r.t. additional number of workers $x$ is given by $\frac{d p}{d x} = 100 - 12 x .$ If the firm employs $25$ more workers,…
Mathematics · Differential Equations · MCQ
Q31.The area (in square units) bounded by the curves $y = x, 2 y - x + 3 = 0, x$ -axis, and lying in the first quadrant is :
Mathematics · Area Under the Curves · MCQ
Q32.Statement-1 : The value of the integral $π /6 \int π /3 \frac{d x}{1 + t a n x}$ is equal to $π /6$ Statement-2 : $a \int b f (x) d x = a \int b f (a + b - x) d x .$ …
Mathematics · Definite Integration · MCQ
Q33.If $\int f (x) d x = ψ (x),$ then $\int x^{5} f (x^{3}) d x$ is equal to
Mathematics · Indefinite Integrals · MCQ
Q34.If $x, y, z$ are in A.P. and $tan^{- 1} x, tan^{- 1} y$ and $tan^{- 1} z$ are also in A.P., then :
Mathematics · Inverse Trigonometric Functions · MCQ
Q35.If $y = sec (tan^{- 1} x),$ then $\frac{d y}{d x}$ at $x = 1$ is equal to :
Mathematics · Differentiation · MCQ
Q36.The equation of the circle passing through the foci of the ellipse $\frac{x ^{2}}{16} + \frac{y ^{2}}{9} = 1$ , and having centre at $(0, 3)$ is :
Mathematics · Ellipse · MCQ
Q37.The $x$ -coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as $(0, 1) (1, 1)$ and $(1, 0)$ is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q38.A ray of light along $x + 3 y = 3$ gets reflected upon reaching $X$ -axis, the equation of the reflected ray is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q39.The term independent of $x$ in expansion of $(\frac{x + 1}{x ^{2/3} - x ^{1/3} + 1} - \frac{x - 1}{x - x ^{1/2}})^{10}$ is
Mathematics · Binomial Theorem · MCQ
Q40.Let $T_{n}$ be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If $T_{n + 1} - T_{n}$ = 10, then the value of n is :
Mathematics · Permutations and Combinations · MCQ
Q41.If the equations $x^{2} + 2 x + 3 = 0$ and $a x^{2} + b x + c = 0, a, b, c \in R,$ have a common root, then $a : b : c$ is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q42.The number of values of $k$ , for which the system of equations : $(k + 1) x + 8 y = 4 k k x + (k + 3) y = 3 k - 1$ has no solution, is
Mathematics · Matrices and Determinants · MCQ
Q43.The real number $k$ for which the equation, $2 x^{3} + 3 x + k = 0$ has two distinct real roots in $[0, 1]$
Mathematics · Application of Derivatives · MCQ
Q44.If z is a complex number of unit modulus and argument $θ$ , then arg $(\frac{1 + z}{1 + z})$ equals :
Mathematics · Complex Numbers · MCQ
Q45.The expression $\frac{t a n A}{1 - c o t A} + \frac{c o t A}{1 - t a n A}$ can be written as:
Mathematics · Trigonometric Ratio and Identites · MCQ
Q46.If the vectors $A B = 3 i + 4 k$ and $A C = 5 i - 2 j + 4 k$ are the sides of a triangle $A B C,$ then the length of the median through $A$ is :
Mathematics · Vector Algebra · MCQ
Q47.If the lines $\frac{x - 2}{1} = \frac{y - 3}{1} = \frac{z - 4}{- k}$ and $\frac{x - 1}{k} = \frac{y - 4}{2} = \frac{z - 5}{1}$ are coplanar, then $k$ can have :
Mathematics · 3D Geometry · MCQ