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Mathematics · 2006 · Shift 0

31 questions from this JEE Main paper

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2006 · Shift 0
Mathematics

Mathematics · 2006 · Shift 0

31 questions from this JEE Main paper

Statistics1 questions Trigonometric Ratio and Identites1 questions Definite Integration3 questions Limits Continuity and Differentiability1 questions Differentiation1 questions Application of Derivatives2 questions Matrices and Determinants2 questions Differential Equations1 questions Probability1 questions Vector Algebra1 questions 3D Geometry1 questions Complex Numbers2 questions Quadratic Equation and Inequalities3 questions Permutations and Combinations1 questions Binomial Theorem1 questions Sequences and Series2 questions Straight Lines and Pair of Straight Lines2 questions Circle2 questions Parabola1 questions Ellipse1 questions Sets and Relations1 questions

Q52.Suppose a population A has 100 observations 101, 102,........, 200, and another population B has 100 observations 151, 152,......., 250. If VA and VB represent the variances of the two populations, respectively, then $\frac{V _{A}}{V _{B}}$ …
Mathematics · Statistics · MCQ
Q53.If $0 < x < π$ and $cos x + sin x = \frac{1}{2},$ then $tan x$ is :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q54.The value of $1 \int a [x] f^{'} (x) d x, a > 1$ where $[x]$ denotes the greatest integer not exceeding $x$ is
Mathematics · Definite Integration · MCQ
Q55.The set of points where $f (x) = \frac{x}{1 + ∣ x ∣}$ is differentiable is
Mathematics · Limits Continuity and Differentiability · MCQ
Q56.If $x^{m} . y^{n} = (x + y)^{m + n},$ then $\frac{d y}{d x}$ is
Mathematics · Differentiation · MCQ
Q57.The function $f (x) = \frac{x}{2} + \frac{2}{x}$ has a local minimum at
Mathematics · Application of Derivatives · MCQ
Q58.A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length $x$ . The maximum area enclosed by the park is
Mathematics · Application of Derivatives · MCQ
Q59.If $A$ and $B$ are square matrices of size $n \times n$ such that $A^{2} - B^{2} = (A - B) (A + B),$ then which of the following will be always true?
Mathematics · Matrices and Determinants · MCQ
Q60.Let $A = (1324)$ and $B = (a 0 0 b), a, b \in N .$ Then
Mathematics · Matrices and Determinants · MCQ
Q61. $0 \int π x f (sin x) d x$ is equal to
Mathematics · Definite Integration · MCQ
Q62. $- \frac{3 π}{2} \int - \frac{π}{2} [(x + π)^{3} + cos^{2} (x + 3 π)] d x$ is equal to
Mathematics · Definite Integration · MCQ
Q63.The differential equation whose solution is $A x^{2} + B y^{2} = 1$ where $A$ and $B$ are arbitrary constants is of
Mathematics · Differential Equations · MCQ
Q64.At a telephone enquiry system the number of phone cells regarding relevant enquiry follow Poisson distribution with an average of $5$ phone calls during $10$ minute time intervals. The probability that there is at the most one phone call…
Mathematics · Probability · MCQ
Q65.The values of a, for which the points $A, B, C$ with position vectors $2 i - j + k, i - 3 j - 5 k$ and $a i - 3 j + k$ respectively are the vertices of a…
Mathematics · Vector Algebra · MCQ
Q66.The two lines $x = a y + b, z = cy + d;$ and $x = a^{'} y + b^{'}, z = c^{'} y + d^{'}$ are perpendicular to each other if :
Mathematics · 3D Geometry · MCQ
Q67.If $z^{2} + z + 1 = 0$ , where z is complex number, then value of $(z + \frac{1}{z})^{2} + (z^{2} + \frac{1}{z ^{2}})^{2} + (z^{3} + \frac{1}{z ^{3}})^{2} + .......... + (z^{6} + \frac{1}{z ^{6}})^{2}$ …
Mathematics · Complex Numbers · MCQ
Q68.The value of $k = 1 \sum 10 (sin \frac{2 k π}{11} + i cos \frac{2 k π}{11})$ is :
Mathematics · Complex Numbers · MCQ
Q69.If the roots of the quadratic equation $x^{2} + p x + q = 0$ are $tan 3 0^{\circ}$ and $tan 1 5^{\circ}$ , respectively, then the value of $2 + q - p$ is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q70.All the values of $m$ for which both roots of the equation $x^{2} - 2 m x + m^{2} - 1 = 0$ are greater than $- 2$ but less then 4, lie in the interval
Mathematics · Quadratic Equation and Inequalities · MCQ
Q71.If $x$ is real, the maximum value of $\frac{3 x ^{2} + 9 x + 17}{3 x ^{2} + 9 x + 7}$ is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q72.At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he…
Mathematics · Permutations and Combinations · MCQ
Q73.If the expansion in powers of $x$ of the function $\frac{1}{( 1 - a x ) ( 1 - b x )}$ is $a_{0} + a_{1} x + a_{2} x^{2} + a_{3} x^{3} .....$ then $a_{n}$ is
Mathematics · Binomial Theorem · MCQ
Q74.If $a_{1}, a_{2}, .... a_{n}$ are in H.P., then the expression $a_{1} a_{2} + a_{2} a_{3} + .... + a_{n - 1} a_{n}$ is equal to
Mathematics · Sequences and Series · MCQ
Q75.Let $a_{1}$ , $a_{2}$ , $a_{3}$ .....be terms on A.P. If $\frac{a _{1} + a _{2} + ..... a _{p}}{a _{1} + a _{2} + ..... a _{q}} = \frac{p ^{2}}{q ^{2}}, p e q, t h e n \frac{a _{6}}{a _{21}}$ equals
Mathematics · Sequences and Series · MCQ
Q76.A straight line through the point $A (3, 4)$ is such that its intercept between the axes is bisected at $A$ . Its equation is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q77.If $(a, a^{2})$ falls inside the angle made by the lines $y = \frac{x}{2}, x > 0$ and $y = 3 x, x > 0,$ then a belong to :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q78.If the lines $3 x - 4 y - 7 = 0$ and $2 x - 3 y - 5 = 0$ are two diameters of a circle of area $49 π$ square units, the equation of the circle is :
Mathematics · Circle · MCQ
Q79.Let $C$ be the circle with centre $(0, 0)$ and radius $3$ units. The equation of the locus of the mid points of the chords of the circle $C$ that subtend an angle of $\frac{2 π}{3}$ at its center is :
Mathematics · Circle · MCQ
Q80.The locus of the vertices of the family of parabolas $y = \frac{a ^{3} x ^{2}}{3} + \frac{a ^{2} x}{2} - 2 a$ is :
Mathematics · Parabola · MCQ
Q81.In the ellipse, the distance between its foci is $6$ and minor axis is $8$ . Then its eccentricity is :
Mathematics · Ellipse · MCQ
Q82.Let $W$ denote the words in the English dictionary. Define the relation $R$ by $R = {(x, y) \in W \times W ∣$ the words $x$ and $y$ have at least one letter in common}. Then, $R$ is
Mathematics · Sets and Relations · MCQ