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Mathematics · 2015 · Shift 0

20 questions from this JEE Main paper

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2015 · Shift 0
Mathematics

Mathematics · 2015 · Shift 0

20 questions from this JEE Main paper

Limits Continuity and Differentiability2 questions Statistics1 questions Quadratic Equation and Inequalities1 questions Probability1 questions Differential Equations1 questions Area Under the Curves1 questions Definite Integration1 questions Indefinite Integrals1 questions Matrices and Determinants2 questions Application of Derivatives1 questions Inverse Trigonometric Functions1 questions Parabola1 questions Circle1 questions Straight Lines and Pair of Straight Lines1 questions Sequences and Series1 questions Permutations and Combinations1 questions Complex Numbers1 questions Sets and Relations1 questions

Q23.If the function. $g (x) = {k x + 1, m x + 2, 0 \leq x \leq 3 3 < x \leq 5$ is differentiable, then the value of $k + m$ is :
Mathematics · Limits Continuity and Differentiability · MCQ
Q24.The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is :
Mathematics · Statistics · MCQ
Q25. $x \to 0 lim \frac{( 1 - c o s 2 x ) ( 3 + c o s x )}{x t a n 4 x}$ is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q26.Let $α$ and $β$ be the roots of equation $x^{2} - 6 x - 2 = 0$ . If $a_{n} = α^{n} - β^{n},$ for $n \geq 1,$ then the value of $\frac{a _{10} - 2 a _{8}}{2 a _{9}}$ is equal to :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q27.If $12$ different balls are to be placed in $3$ identical boxes, then the probability that one of the boxes contains exactly $3$ balls is :
Mathematics · Probability · MCQ
Q28.Let $y (x)$ be the solution of the differential equation $(x lo g x) \frac{d y}{d x} + y = 2 x lo g x, (x \geq 1) .$ Then $y (e)$ is equal to :
Mathematics · Differential Equations · MCQ
Q29.The area (in sq. units) of the region described by ${(x, y) : y^{2} \leq 2 x$ and $y \geq 4 x - 1}$ is :
Mathematics · Area Under the Curves · MCQ
Q30.The integral $2 \int 4 \frac{l o g x ^{2}}{l o g x ^{2} + l o g ( 36 - 12 x + x ^{2} )} d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q31.The integral $\int \frac{d x}{x ^{2} ( x ^{4} + 1 ) ^{3/4}}$ equals :
Mathematics · Indefinite Integrals · MCQ
Q32.If $A = 12 a 212 2 - 2 b$ is a matrix satisfying the equation $A A^{T} = 9 I,$ where $I$ is $3 \times 3$ identity matrix, then the…
Mathematics · Matrices and Determinants · MCQ
Q33.The set of all values of $λ$ for which the system of linear equations: $2 x_{1} - 2 x_{2} + x_{3} = λ x_{1} 2 x_{1} - 3 x_{2} + 2 x_{3} = λ x_{2} - x_{1} + 2 x_{2} = λ x_{3}$ …
Mathematics · Matrices and Determinants · MCQ
Q34.Let $f (x)$ be a polynomial of degree four having extreme values at $x = 1$ and $x = 2$ . If $x \to 0 lim [1 + \frac{f ( x )}{x ^{2}}] = 3$ , then f $(2)$ is equal to :
Mathematics · Application of Derivatives · MCQ
Q35.Let $tan^{- 1} y = tan^{- 1} x + tan^{- 1} (\frac{2 x}{1 - x ^{2}}),$ where $∣ x ∣ < \frac{1}{3} .$ Then a value of $y$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q36.Let $O$ be the vertex and $Q$ be any point on the parabola, $x^{2} = 8 y$ . If the point $P$ divides the line segment $O Q$ internally in the ratio $1 : 3$ , then locus of $P$ is :
Mathematics · Parabola · MCQ
Q37.Locus of the image of the point $(2, 3)$ in the line $(2 x - 3 y + 4) + k (x - 2 y + 3) = 0, k \in R,$ is a :
Mathematics · Circle · MCQ
Q38.The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices $(0, 0) (0, 41)$ and $(41, 0)$ is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q39.If m is the A.M. of two distinct real numbers l and n $(l, n > 1)$ and $G_{1}, G_{2}$ and $G_{3}$ are three geometric means between $l$ and n, then $G_{1}^{4} + 2 G_{2}^{4} + G_{3}^{4}$ equals:
Mathematics · Sequences and Series · MCQ
Q40.The number of integers greater than 6,000 that can be formed, using the digits 3, 5, 6, 7 and 8, without repetition, is:
Mathematics · Permutations and Combinations · MCQ
Q41.A complex number z is said to be unimodular if $∣ z ∣ = 1$ . Suppose $z_{1}$ and $z_{2}$ are complex numbers such that $\frac{z _{1} - 2 z _{2}}{2 - z _{1} z _{2}}$ is unimodular and $z_{2}$ is not unimodular.…
Mathematics · Complex Numbers · MCQ
Q42.Let A and B be two sets containing four and two elements respectively. Then, the number of subsets of the set A $\times$ B , each having atleast three elements are
Mathematics · Sets and Relations · MCQ