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Mathematics · 2004 · Shift 0

50 questions from this JEE Main paper

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2004 · Shift 0
Mathematics

Mathematics · 2004 · Shift 0

50 questions from this JEE Main paper

Functions4 questions Limits Continuity and Differentiability2 questions Statistics2 questions Trigonometric Ratio and Identites2 questions Definite Integration4 questions Differentiation1 questions Application of Derivatives1 questions Matrices and Determinants3 questions Indefinite Integrals2 questions Ellipse1 questions Area Under the Curves1 questions Differential Equations1 questions Probability1 questions Vector Algebra4 questions 3D Geometry3 questions Sequences and Series1 questions Complex Numbers3 questions Quadratic Equation and Inequalities3 questions Permutations and Combinations2 questions Binomial Theorem2 questions Straight Lines and Pair of Straight Lines2 questions Circle3 questions Parabola1 questions Sets and Relations1 questions

Q67.The graph of the function y = f(x) is symmetrical about the line x = 2, then
Mathematics · Functions · MCQ
Q68.The range of the function f(x) = $^{7 - x} P_{x - 3}$ is
Mathematics · Functions · MCQ
Q69.If $f : R \to S$ , defined by $f (x) = sin x - 3 cos x + 1$ , is onto, then the interval of $S$ is
Mathematics · Functions · MCQ
Q70.The domain of the function $f (x) = \frac{s i n ^{- 1} ( x - 3 )}{9 - x ^{2}}$
Mathematics · Functions · MCQ
Q71.Let $f (x) = \frac{1 - t a n x}{4 x - π}$ , $x e \frac{π}{4}$ , $x \in [0, \frac{π}{2}]$ . If $f (x)$ is continuous in $[0, \frac{π}{2}]$ , then $f (\frac{π}{4})$ is
Mathematics · Limits Continuity and Differentiability · MCQ
Q72.If $x \to \infty lim (1 + \frac{a}{x} + \frac{b}{x ^{2}})^{2 x} = e^{2}$ , then the value of $a$ and $b$ , are
Mathematics · Limits Continuity and Differentiability · MCQ
Q73.Consider the following statements: (a) Mode can be computed from histogram (b) Median is not independent of change of scale (c) Variance is independent of change of origin and scale. Which of these is/are correct?
Mathematics · Statistics · MCQ
Q74.In a series of 2n observations, half of them equal $a$ and remaining half equal $- a$ . If the standard deviation of the observations is 2, then $∣ a ∣$ equals
Mathematics · Statistics · MCQ
Q75.If $u = a^{2} cos^{2} θ + b^{2} sin^{2} θ + a^{2} sin^{2} θ + b^{2} cos^{2} θ$ then the difference between the maximum and minimum values of $u^{2}$ is given by :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q76.The value of $I = 0 \int π /2 \frac{( s i n x + c o s x ) ^{2}}{1 + s i n 2 x} d x$ is
Mathematics · Definite Integration · MCQ
Q77.If $x = e^{y + e^{y} + e^{y + .....\infty}}$ , $x > 0,$ then $\frac{d y}{d x}$ is
Mathematics · Differentiation · MCQ
Q78.A point on the parabola $y^{2} = 18 x$ at which the ordinate increases at twice the rate of the abscissa is
Mathematics · Application of Derivatives · MCQ
Q79.Let $A = 121 - 1 11 1 - 3 1 .$ and $10$ $B = 4 - 5 1 20 - 2 2 α 3$ …
Mathematics · Matrices and Determinants · MCQ
Q80.Let $A = 00 - 1 0 - 1 0 - 1 00$ . The only correct statement about the matrix $A$ is
Mathematics · Matrices and Determinants · MCQ
Q81.If $a_{1}, a_{2}, a_{3}, ........., a_{n}, ......$ are in G.P., then the value of the determinant $lo g a_{n} lo g a_{n + 3} lo g a_{n + 6} lo g a_{n + 1} lo g a_{n + 4} lo g a_{n + 7} lo g a_{n + 2} lo g a_{n + 5} lo g a_{n + 8},$ …
Mathematics · Matrices and Determinants · MCQ
Q82.If $\int \frac{s i n x}{s i n ( x - α )} d x = A x + B lo g sin (x - α), + C,$ then value of $(A, B)$ is
Mathematics · Indefinite Integrals · MCQ
Q83. $\int \frac{d x}{c o s x - s i n x}$ is equal to
Mathematics · Indefinite Integrals · MCQ
Q84.The eccentricity of an ellipse, with its centre at the origin, is $\frac{1}{2}$ . If one of the directrices is $x = 4$ , then the equation of the ellipse is :
Mathematics · Ellipse · MCQ
Q85.The value of $- 2 \int 3 1 - x^{2} d x$ is
Mathematics · Definite Integration · MCQ
Q86.If $0 \int π x f (sin x) d x = A 0 \int π /2 f (sin x) d x,$ then $A$ is
Mathematics · Definite Integration · MCQ
Q87.If $f (x) = \frac{e ^{x}}{1 + e ^{x}}, I_{1} = f (- a) \int f (a) xg {x (1 - x)} d x$ and $I_{2} = f (- a) \int f (a) g {x (1 - x)} d x,$ …
Mathematics · Definite Integration · MCQ
Q88.The area of the region bounded by the curves $y = ∣ x - 2 ∣, x = 1, x = 3$ and the $x$ -axis is :
Mathematics · Area Under the Curves · MCQ
Q89.Solution of the differential equation $y d x + (x + x^{2} y) d y = 0$ is
Mathematics · Differential Equations · MCQ
Q90.The probability that $A$ speaks truth is $\frac{4}{5},$ while the probability for $B$ is $\frac{3}{4} .$ The probability that they contradict each other when asked to speak on a fact is :
Mathematics · Probability · MCQ
Q91.A particle acted on by constant forces $4 i + j - 3 k$ and $3 i + j - k$ is displaced from the point $i + 2 j + 3 k$ to the point $5 i + 4 j + k .$ …
Mathematics · Vector Algebra · MCQ
Q92.Let $u, v, w$ be such that $u = 1, v 2, w 3.$ If the projection $v$ …
Mathematics · Vector Algebra · MCQ
Q93.A line with direction cosines proportional to $2, 1, 2$ meets each of the lines $x = y + a = z$ and $x + a = 2 y = 2 z$ . The co-ordinates of each of the points of intersection are given by :
Mathematics · 3D Geometry · MCQ
Q94.Let $T_{r}$ be the rth term of an A.P. whose first term is a and common difference is d. If for some positive integers m, n, $m e n, T_{m} = \frac{1}{n} an d T_{n} = \frac{1}{m},$ then a - d equals
Mathematics · Sequences and Series · MCQ
Q95.Let $α, β$ be such that $π < α - β < 3 π$ . If $s in α + sin β = - \frac{21}{65}$ and $cos α + cos β = - \frac{27}{65}$ then the value of $\cos {{\alpha - \beta } \over…
Mathematics · Trigonometric Ratio and Identites · MCQ
Q96.A line makes the same angle $θ$ , with each of the $x$ and $z$ axis. If the angle $β$ , which it makes with y-axis, is such that $sin^{2} β = 3 sin^{2} θ,$ then $cos^{2} θ$ equals :
Mathematics · 3D Geometry · MCQ
Q97.Let z and w be complex numbers such that $\overline{z} + i \overline{w} = 0$ and arg zw = $π$ . Then arg z equals :
Mathematics · Complex Numbers · MCQ
Q98.If $z = x - i y$ and $z^{\frac{1}{3}} = p + i q$ , then $\frac{( \frac{x}{p} + \frac{y}{q} )}{( p ^{2} + q ^{2} )}$ is equal to :
Mathematics · Complex Numbers · MCQ
Q99.If $z^{2} - 1 = ∣ z ∣^{2} + 1$ , then z lies on :
Mathematics · Complex Numbers · MCQ
Q100.Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation
Mathematics · Quadratic Equation and Inequalities · MCQ
Q101.If $(1 - p)$ is a root of quadratic equation $x^{2} + p x + (1 - p) = 0$ then its root are
Mathematics · Quadratic Equation and Inequalities · MCQ
Q102.If one root of the equation $x^{2} + p x + 12 = 0$ is 4, while the equation $x^{2} + p x + q = 0$ has equal roots, then the value of $^{'} q^{'}$ is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q103.How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical order
Mathematics · Permutations and Combinations · MCQ
Q104.The coefficient of the middle term in the binomial expansion in powers of $x$ of $(1 + α x)^{4}$ and $(1 - α x)^{6}$ is the same if $α$ equals
Mathematics · Binomial Theorem · MCQ
Q105.The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is
Mathematics · Permutations and Combinations · MCQ
Q106.The coefficient of $x^{n}$ in expansion of $(1 + x) (1 - x)^{n}$ is
Mathematics · Binomial Theorem · MCQ
Q107.The equation of the straight line passing through the point $(4, 3)$ and making intercepts on the co-ordinate axes whose sum is $- 1$ is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q108.Let $A (2, - 3)$ and $B (- 2, 1)$ be vertices of a triangle $A B C$ . If the centroid of this triangle moves on the line $2 x + 3 y = 1$ , then the locus of the vertex $C$ is the line :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q109.If the lines 2x + 3y + 1 + 0 and 3x - y - 4 = 0 lie along diameter of a circle of circumference $10 π$ , then the equation of the circle is :
Mathematics · Circle · MCQ
Q110.If a circle passes through the point (a, b) and cuts the circle $x^{2} + y^{2} = 4$ orthogonally, then the locus of its centre is :
Mathematics · Circle · MCQ
Q111.Intercept on the line y = x by the circle $x^{2} + y^{2} - 2 x = 0$ is AB. Equation of the circle on AB as a diameter is :
Mathematics · Circle · MCQ
Q112.If $a e 0$ and the line $2 b x + 3 cy + 4 d = 0$ passes through the points of intersection of the parabolas $y^{2} = 4 a x$ and $x^{2} = 4 a y$ , then :
Mathematics · Parabola · MCQ
Q113.Let $a, b$ and $c$ be non-zero vectors such that $(a \times b) \times c = \frac{1}{3} b c a .$ …
Mathematics · Vector Algebra · MCQ
Q114.If the straight lines $x = 1 + s, y = - 3 - λ s, z = 1 + λ s$ and $x = \frac{t}{2}, y = 1 + t, z = 2 - t,$ with parameters $s$ and $t$ respectively, are co-planar, then $λ$ equals :
Mathematics · 3D Geometry · MCQ
Q115.Let $a, b$ and $c$ be three non-zero vectors such that no two of these are collinear. If the vector $a + 2 b$ is collinear with $c$ and $b + 3 c$ …
Mathematics · Vector Algebra · MCQ
Q116.Let $R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)}$ be a relation on the set $A = {1, 2, 3, 4}$ . The relation $R$ is :
Mathematics · Sets and Relations · MCQ