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Mathematics · 2008 · Shift 0

27 questions from this JEE Main paper

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2008 · Shift 0
Mathematics

Mathematics · 2008 · Shift 0

27 questions from this JEE Main paper

Statistics1 questions Limits Continuity and Differentiability1 questions Functions1 questions Probability2 questions Differential Equations1 questions Area Under the Curves1 questions Indefinite Integrals1 questions Matrices and Determinants2 questions Application of Derivatives2 questions Inverse Trigonometric Functions1 questions Vector Algebra1 questions Parabola1 questions Ellipse1 questions Circle1 questions Straight Lines and Pair of Straight Lines1 questions Sequences and Series1 questions Permutations and Combinations2 questions Quadratic Equation and Inequalities2 questions Sets and Relations1 questions Complex Numbers1 questions 3D Geometry2 questions

Q30.The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?
Mathematics · Statistics · MCQ
Q31.Let $f (x) = {(x - 1) sin \frac{1}{x - 1} 0 i f x e 1 i f x = 1$ Then which one of the following is true?
Mathematics · Limits Continuity and Differentiability · MCQ
Q32.Let $f : N \to Y$ be a function defined as f(x) = 4x + 3 where Y = { y $\in$ N, y = 4x + 3 for some x $\in$ N }. Show that f is invertible and its inverse is
Mathematics · Functions · MCQ
Q33.A die is thrown. Let $A$ be the event that the number obtained is greater than $3.$ Let $B$ be the event that the number obtained is less than $5.$ Then $P (A \cup B)$ is :
Mathematics · Probability · MCQ
Q34.It is given that the events $A$ and $B$ are such that $P (A) = \frac{1}{4}, P (A ∣ B) = \frac{1}{2}$ and $P (B ∣ A) = \frac{2}{3} .$ Then $P (B)$ is :
Mathematics · Probability · MCQ
Q35.The solution of the differential equation $\frac{d y}{d x} = \frac{x + y}{x}$ satisfying the condition $y (1) = 1$ is :
Mathematics · Differential Equations · MCQ
Q36.The area of the plane region bounded by the curves $x + 2 y^{2} = 0$ and $x + 3 y^{2} = 1$ is equal to :
Mathematics · Area Under the Curves · MCQ
Q37.The value of $2 \int \frac{s i n x d x}{s i n ( x - \frac{π}{4} )}$ is
Mathematics · Indefinite Integrals · MCQ
Q38.Let $a, b, c$ be any real numbers. Suppose that there are real numbers $x, y, z$ not all zero such that $x = cy + b z, y = a z + c x,$ and $z = b x + a y .$ Then $a^{2} + b^{2} + c^{2} + 2 ab c$ is equal to :
Mathematics · Matrices and Determinants · MCQ
Q39.Let $A$ be $a 2 \times 2$ matrix with real entries. Let $I$ be the $2 \times 2$ identity matrix. Denote by tr $(A)$ , the sum of diagonal entries of $a$ . Assume that $a^{2} = I .$ Statement-1 : If $A e I$ and $A e - I$ , then det $(A) = - 1$ …
Mathematics · Matrices and Determinants · MCQ
Q40.Suppose the cubic $x^{3} - p x + q$ has three distinct real roots where $p > 0$ and $q > 0$ . Then which one of the following holds?
Mathematics · Application of Derivatives · MCQ
Q41.How many real solutions does the equation $x^{7} + 14 x^{5} + 16 x^{3} + 30 x - 560 = 0$ have?
Mathematics · Application of Derivatives · MCQ
Q42.The value of $co t (cos e c^{- 1} \frac{5}{3} + tan^{- 1} \frac{2}{3})$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q43.The non-zero vectors are $a, b$ and $c$ are related by $a = 8 b$ and $c = - 7 b .$ Then the angle between $a$ …
Mathematics · Vector Algebra · MCQ
Q44.A parabola has the origin as its focus and the line $x = 2$ as the directrix. Then the vertex of the parabola is at :
Mathematics · Parabola · MCQ
Q45.A focus of an ellipse is at the origin. The directrix is the line $x = 4$ and the eccentricity is $\frac{1}{2}$ . Then the length of the semi-major axis is :
Mathematics · Ellipse · MCQ
Q46.The point diametrically opposite to the point $P (1, 0)$ on the circle $x^{2} + y^{2} + 2 x + 4 y - 3 = 0$ is :
Mathematics · Circle · MCQ
Q47.The perpendicular bisector of the line segment joining P(1, 4) and Q(k, 3) has y-intercept -4. Then a possible value of k is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q48.The first two terms of a geometric progression add up to 12. the sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is
Mathematics · Sequences and Series · MCQ
Q49.How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?
Mathematics · Permutations and Combinations · MCQ
Q50.In a shop there are five types of ice-cream available. A child buys six ice-cream. Statement - 1: The number of different ways the child can buy the six ice-cream is $^{10} C_{5}$ . Statement - 2: The number of different ways the child can…
Mathematics · Permutations and Combinations · MCQ
Q51.The quadratic equations $x^{2} - 6 x + a = 0$ and $x^{2} - c x + 6 = 0$ have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q52.STATEMENT - 1 : For every natural number $n \geq 2, \frac{1}{1} + \frac{1}{2} + ........ + \frac{1}{n} > n .$ STATEMENT - 2 : For every natural number $n \geq 2,$ , $n (n + 1) < n + 1.$
Mathematics · Quadratic Equation and Inequalities · MCQ
Q53.Let R be the real line. Consider the following subsets of the plane $R \times R$ : $S = {(x, y) : y = x + 1 an d 0 < x < 2} T = {(x, y) : x - y i s an int e g er}$ , Which one…
Mathematics · Sets and Relations · MCQ
Q54.The conjugate of a complex number is $\frac{1}{i - 1}$ then that complex number is :
Mathematics · Complex Numbers · MCQ
Q55.If the straight lines $\frac{x - 1}{k} = \frac{y - 2}{2} = \frac{z - 3}{3}$ and $\frac{x - 2}{3} = \frac{y - 3}{k} = \frac{z - 1}{2}$ intersects at a point, then the integer…
Mathematics · 3D Geometry · MCQ
Q56.The line passing through the points $(5, 1, a)$ and $(3, b, 1)$ crosses the $y z$ -plane at the point $(0, \frac{17}{2}, - \frac{- 13}{2})$ . Then
Mathematics · 3D Geometry · MCQ