New chat PYQ Library Doubts Rank report

Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →

Mathematics · 2010 · Shift 0

24 questions from this JEE Main paper

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Main
Papers
2010 · Shift 0
Mathematics

Mathematics · 2010 · Shift 0

24 questions from this JEE Main paper

Statistics1 questions Limits Continuity and Differentiability1 questions Complex Numbers1 questions Application of Derivatives2 questions Probability2 questions Differential Equations1 questions Definite Integration1 questions Area Under the Curves1 questions Matrices and Determinants3 questions Differentiation1 questions Parabola1 questions Circle1 questions Straight Lines and Pair of Straight Lines1 questions Sequences and Series1 questions Permutations and Combinations1 questions Quadratic Equation and Inequalities1 questions Trigonometric Ratio and Identites1 questions 3D Geometry1 questions Vector Algebra1 questions Sets and Relations1 questions

Q27.For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is
Mathematics · Statistics · MCQ
Q28.Let $f : R \to R$ be a positive increasing function with $x \to \infty lim \frac{f ( 3 x )}{f ( x )} = 1$ . Then $x \to \infty lim \frac{f ( 2 x )}{f ( x )} =$
Mathematics · Limits Continuity and Differentiability · MCQ
Q29.The number of complex numbers z such that $∣ z - 1 ∣ = ∣ z + 1 ∣ = ∣ z - i ∣$ equals :
Mathematics · Complex Numbers · MCQ
Q30.Let $f : R \to R$ be defined by $f (x) = {k - 2 x, i f 2 x + 3, i f x \leq - 1 x > - 1$ If $f$ has a local minimum at $x = - 1$ , then a possible value of $k$ …
Mathematics · Application of Derivatives · MCQ
Q31.An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is :
Mathematics · Probability · MCQ
Q32.Four numbers are chosen at random (without replacement) from the set ${1, 2, 3, ....20} .$ Statement - 1: The probability that the chosen numbers when arranged in some order will form an AP is $\frac{1}{85} .$ Statement -…
Mathematics · Probability · MCQ
Q33.Solution of the differential equation $cos x d y = y (sin x - y) d x, 0 < x < \frac{π}{2}$ is :
Mathematics · Differential Equations · MCQ
Q34.Let $p (x)$ be a function defined on $R$ such that $p^{'} (x) = p^{'} (1 - x),$ for all $x \in [0, 1], p (0) = 1$ and $p (1) = 41.$ Then $0 \int 1 p (x) d x$ equals :
Mathematics · Definite Integration · MCQ
Q35.The area bounded by the curves $y = cos x$ and $y = sin x$ between the ordinates $x = 0$ and $x = \frac{3 π}{2}$ is
Mathematics · Area Under the Curves · MCQ
Q36.The number of $3 \times 3$ non-singular matrices, with four entries as $1$ and all other entries as $0$ , is :
Mathematics · Matrices and Determinants · MCQ
Q37.Consider the system of linear equations; $x_{1} + 2 x_{2} + x_{3} = 3 2 x_{1} + 3 x_{2} + x_{3} = 3 3 x_{1} + 5 x_{2} + 2 x_{3} = 1$ The system has :
Mathematics · Matrices and Determinants · MCQ
Q38.Let $A$ be a $2 \times 2$ matrix with non-zero entries and let $A^{2} = I,$ where $I$ is $2 \times 2$ identity matrix. Define $T r (A) =$ sum of diagonal elements of $A$ and $∣ A ∣ =$ determinant of matrix $A$ . Statement- 1: $T r (A) = 0$ …
Mathematics · Matrices and Determinants · MCQ
Q39.Let $f : R \to R$ be a continuous function defined by $f (x) = \frac{1}{e ^{x} + 2 e ^{- x}}$ Statement - 1 : $f (c) = \frac{1}{3},$ for some $c \in R$ . Statement - 2 : $0 < f (x) \leq \frac{1}{2 2},$ …
Mathematics · Application of Derivatives · MCQ
Q40.Let $f : (- 1, 1) \to R$ be a differentiable function with $f (0) = - 1$ and $f^{'} (0) = 1$ . Let $g (x) = [f (2 f (x) + 2)]^{2}$ . Then $g^{'} (0) =$ …
Mathematics · Differentiation · MCQ
Q41.If two tangents drawn from a point $P$ to the parabola $y^{2} = 4 x$ are at right angles, then the locus of $P$ is
Mathematics · Parabola · MCQ
Q42.The circle $x^{2} + y^{2} = 4 x + 8 y + 5$ intersects the line $3 x - 4 y = m$ at two distinct points if :
Mathematics · Circle · MCQ
Q43.The line $L$ given by $\frac{x}{5} + \frac{y}{b} = 1$ passes through the point $(13, 32)$ . The line K is parrallel to $L$ and has the equation $\frac{x}{c} + \frac{y}{3} = 1.$ Then the distance between $L$ and $K$ is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q44.A person is to count 4500 currency notes. Let $a_{n}$ denote the number of notes he counts in the $n^{t h}$ minute. If $a_{1}$ = $a_{2}$ = ....= $a_{10}$ = 150 and $a_{10}$ , $a_{11}$ ,.... are in an AP with common difference - 2, then the…
Mathematics · Sequences and Series · MCQ
Q45.There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is
Mathematics · Permutations and Combinations · MCQ
Q46.If $α$ and $β$ are the roots of the equation $x^{2} - x + 1 = 0,$ then $α^{2009} + β^{2009} =$
Mathematics · Quadratic Equation and Inequalities · MCQ
Q47.Let $cos (α + β) = \frac{4}{5}$ and $sin (α - β) = \frac{5}{13},$ where $0 \leq α, β \leq \frac{π}{4} .$ Then $t an 2 α$ =
Mathematics · Trigonometric Ratio and Identites · MCQ
Q48.A line $A B$ in three-dimensional space makes angles $4 5^{\circ}$ and $12 0^{\circ}$ with the positive $x$ -axis and the positive $y$ -axis respectively. If $A B$ makes an acute angle $θ$ with the positive $z$ -axis, then $θ$ …
Mathematics · 3D Geometry · MCQ
Q49.If the vectors $a = i - j + 2 k, b = 2 i + 4 j + k$ and $c = λ i + j + μ k$ are…
Mathematics · Vector Algebra · MCQ
Q50.Consider the following relations $R = {(x, y) ∣ x, y$ are real numbers and $x = w y$ for some rational number $w}$ ; $S = {(\frac{m}{n}, \frac{p}{q}) ∣ m, n, p$ and $q$ are integers such that $n, q e q 0$ and $q m = p m}$ …
Mathematics · Sets and Relations · MCQ