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Mathematics · 2009 · Shift 0

22 questions from this JEE Main paper

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JEE Main
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2009 · Shift 0
Mathematics

Mathematics · 2009 · Shift 0

22 questions from this JEE Main paper

Statistics2 questions Functions2 questions Complex Numbers1 questions Differentiation1 questions Probability1 questions Definite Integration1 questions Area Under the Curves1 questions Matrices and Determinants1 questions Application of Derivatives1 questions Limits Continuity and Differentiability1 questions Ellipse1 questions Circle1 questions Straight Lines and Pair of Straight Lines2 questions Binomial Theorem1 questions Permutations and Combinations1 questions Quadratic Equation and Inequalities1 questions Trigonometric Ratio and Identites1 questions 3D Geometry1 questions Sets and Relations1 questions

Q26.Statement - 1 : The variance of first n even natural numbers is $\frac{n ^{2} - 1}{4}$ Statement - 2 : The sum of first n natural numbers is $\frac{n ( n + 1 )}{2}$ and the sum of squares of first n natural numbers is $\frac{n ( n + 1 ) ( 2 n + 1 )}{6}$ …
Mathematics · Statistics · MCQ
Q27.If the mean deviation of number 1, 1 + d, 1 + 2d,........, 1 + 100d from their mean is 255, then the d is equal to
Mathematics · Statistics · MCQ
Q28.For real x, let f(x) = x3 + 5x + 1, then
Mathematics · Functions · MCQ
Q29.Let $f (x) = (x + 1)^{2} - 1, x \geq - 1$ Statement - 1 : The set ${x : f (x) = f^{- 1} (x)} = {0, - 1}$ . Statement - 2 : $f$ is a bijection.
Mathematics · Functions · MCQ
Q30.If $z - \frac{4}{z} = 2,$ then the maximum value of $∣ z ∣$ is equal to :
Mathematics · Complex Numbers · MCQ
Q31.Let $y$ be an implicit function of $x$ defined by $x^{2 x} - 2 x^{x} cot y - 1 = 0$ . Then $y^{'} (1)$ equals
Mathematics · Differentiation · MCQ
Q32.One ticket is selected at random from $50$ tickets numbered $00, 01, 02, ...., 49.$ Then the probability that the sum of the digits on the selected ticket is $8$ , given that the product of these digits is zer, equals :
Mathematics · Probability · MCQ
Q33. $0 \int π [cot x] d x,$ where $[.]$ denotes the greatest integer function, is equal to:
Mathematics · Definite Integration · MCQ
Q34.The area of the region bounded by the parabola $(y - 2)^{2} = x - 1,$ the tangent of the parabola at the point $(2, 3)$ and the $x$ -axis is :
Mathematics · Area Under the Curves · MCQ
Q35.Let $a, b, c$ be such that $b (a + c) e 0$ if $a - b c a + 1 b + 1 c - 1 a - 1 b - 1 c + 1 + a + 1 a - 1 (- 1)^{n + 2} a b + 1 b - 1 (- 1)^{n + 1} b c - 1 c + 1 (- 1)^{n} c = 0$ …
Mathematics · Matrices and Determinants · MCQ
Q36.Given $P (x) = x^{4} + a x^{3} + b x^{2} + c x + d$ such that $x = 0$ is the only real root of $P^{'} (x) = 0.$ If $P (- 1) < P (1),$ then in the interval $[- 1, 1] :$
Mathematics · Application of Derivatives · MCQ
Q37.Let $f (x) = x ∣ x ∣$ and $g (x) = sin x .$ Statement-1: gof is differentiable at $x = 0$ and its derivative is continuous at that point. Statement-2: gof is twice differentiable at $x = 0$ .
Mathematics · Limits Continuity and Differentiability · MCQ
Q38.The ellipse $x^{2} + 4 y^{2} = 4$ is inscribed in a rectangle aligned with the coordinate axex, which in turn is inscribed in another ellipse that passes through the point $(4, 0)$ . Then the equation of the ellipse is :
Mathematics · Ellipse · MCQ
Q39.Three distinct points A, B and C are given in the 2 -dimensional coordinates plane such that the ratio of the distance of any one of them from the point $(1, 0)$ to the distance from the point $(- 1, 0)$ is equal to $\frac{1}{3}$ . Then the…
Mathematics · Circle · MCQ
Q40.The lines $p (p^{2} + 1) x - y + q = 0$ and $(p^{2} + 1)^{2} x + (p^{2} + 1) y + 2 q$ $= 0$ are perpendicular to a common line for :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q41.The shortest distance between the line $y - x = 1$ and the curve $x = y^{2}$ is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q42.The remainder left out when $8^{2 n} - (62)^{2 n + 1}$ is divided by 9 is :
Mathematics · Binomial Theorem · MCQ
Q43.From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangement is :
Mathematics · Permutations and Combinations · MCQ
Q44.If the roots of the equation $b x^{2} + c x + a = 0$ imaginary, then for all real values of $x$ , the expression $3 b^{2} x^{2} + 6 b c x + 2 c^{2}$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q45.Let A and B denote the statements A: $cos α + cos β + cos γ = 0$ B: $sin α + sin β + sin γ = 0$ If $cos (β - γ) + cos (γ - α) + cos (α - β) = - \frac{3}{2},$ …
Mathematics · Trigonometric Ratio and Identites · MCQ
Q46.The projections of a vector on the three coordinate axis are $6, - 3, 2$ respectively. The direction cosines of the vector are :
Mathematics · 3D Geometry · MCQ
Q47.If $A, B$ and $C$ are three sets such that $A \cap B = A \cap C$ and $A \cup B = A \cup C$ , then :
Mathematics · Sets and Relations · MCQ