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Mathematics · 2002 · Shift 0

53 questions from this JEE Main paper

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2002 · Shift 0
Mathematics

Mathematics · 2002 · Shift 0

53 questions from this JEE Main paper

Limits Continuity and Differentiability8 questions Statistics1 questions Functions3 questions Straight Lines and Pair of Straight Lines2 questions Definite Integration5 questions Differentiation1 questions Inverse Trigonometric Functions1 questions Application of Derivatives1 questions Matrices and Determinants1 questions Circle2 questions Area Under the Curves1 questions Differential Equations2 questions Probability2 questions Vector Algebra5 questions Permutations and Combinations4 questions Complex Numbers3 questions Quadratic Equation and Inequalities5 questions Binomial Theorem2 questions Sequences and Series4 questions

Q62.f(x) and g(x) are two differentiable functions on [0, 2] such that f''(x) - g''(x) = 0, f'(1) = 2, g'(1) = 4, f(2) = 3, g(2) = 9 then f(x) - g(x) at x = $\frac{3}{2}$ is
Mathematics · Limits Continuity and Differentiability · MCQ
Q63.In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average marks of the girls?
Mathematics · Statistics · MCQ
Q64. $x \to 0 lim \frac{1 - c o s 2 x}{2 x}$ is
Mathematics · Limits Continuity and Differentiability · MCQ
Q65.The domain of $sin^{- 1} [lo g_{3} (\frac{x}{3})]$ is
Mathematics · Functions · MCQ
Q66.Let $f (2) = 4$ and $f^{'} (x) = 4.$ Then $x \to 2 lim \frac{x f ( 2 ) - 2 f ( x )}{x - 2}$ is given by
Mathematics · Limits Continuity and Differentiability · MCQ
Q67. $x \to \infty lim (\frac{x ^{2} + 5 x + 3}{x ^{2} + x + 2})^{x}$
Mathematics · Limits Continuity and Differentiability · MCQ
Q68. $x \to 0 lim \frac{l o g x ^{n} - [ x ]}{[ x ]}$ , $n \in N$ , ( [x] denotes the greatest integer less than or equal to x )
Mathematics · Limits Continuity and Differentiability · MCQ
Q69.If $f (1) = 1, f^{'} (1) = 2,$ then $x \to 1 lim \frac{f ( x ) - 1}{x - 1}$ is
Mathematics · Limits Continuity and Differentiability · MCQ
Q70. $f$ is defined in $[- 5, 5]$ as $f (x) = x$ if $x$ is rational $= - x$ if $x$ is irrational. Then
Mathematics · Limits Continuity and Differentiability · MCQ
Q71.If f(x + y) = f(x).f(y) $\forall$ x, y and f(5) = 2, f'(0) = 3, then f'(5) is
Mathematics · Limits Continuity and Differentiability · MCQ
Q72.A triangle with vertices $(4, 0), (- 1, - 1), (3, 5)$ is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q73.Locus of mid point of the portion between the axes of $x cos α + y sin α = p$ where $p$ is constant is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q74.If $y = f (x)$ makes + $v e$ intercept of $2$ and $0$ unit on $x$ and $y$ axes and encloses an area of $3/4$ square unit with the axes then $0 \int 2 x f^{'} (x) d x$ is
Mathematics · Definite Integration · MCQ
Q75.If $y = (x + 1 + x^{2})^{n},$ then $(1 + x^{2}) \frac{d ^{2} y}{d x ^{2}} + x \frac{d y}{d x}$ is
Mathematics · Differentiation · MCQ
Q76. $cot^{- 1} (cos α) - tan^{- 1} (cos α) = x,$ then sin x is equal to :
Mathematics · Inverse Trigonometric Functions · MCQ
Q77.The maximum distance from origin of a point on the curve $x = a sin t - b sin (\frac{a t}{b}) y = a cos t - b cos (\frac{a t}{b}),$ both $a, b > 0$ is
Mathematics · Application of Derivatives · MCQ
Q78.If $a > 0$ and discriminant of $a x^{2} + 2 b x + c$ is $- v e$ , then $a b a x + b b c b x + c a x + b b x + c 0$ is equal to
Mathematics · Matrices and Determinants · MCQ
Q79. $I_{n} = 0 \int π /4 tan^{n} x d x$ then $n \to \infty lim n [I_{n} + I_{n + 2}]$ equals
Mathematics · Definite Integration · MCQ
Q80. $0 \int 10 π ∣ sin x ∣ d x$ is
Mathematics · Definite Integration · MCQ
Q81. $0 \int 2 [x^{2}] d x$ is
Mathematics · Definite Integration · MCQ
Q82. $\int_{- π}^{π} \frac{2 x ( 1 + s i n x )}{1 + c o s ^{2} x} d x$ is
Mathematics · Definite Integration · MCQ
Q83.The equation of a circle with origin as a center and passing through an equilateral triangle whose median is of length $3 a$ is :
Mathematics · Circle · MCQ
Q84.The area bounded by the curves $y = ln x, y = ln ∣ x ∣, y = ∣ ln x ∣$ and $y = ∣ ln ∣ x ∣ ∣$ is :
Mathematics · Area Under the Curves · MCQ
Q85.The solution of the equation $\frac{d ^{2} y}{d x ^{2}} = e^{- 2 x}$
Mathematics · Differential Equations · MCQ
Q86.The order and degree of the differential equation $(1 + 3 \frac{d y}{d x})^{2/3} = 4 \frac{d ^{3} y}{d x ^{3}}$ are
Mathematics · Differential Equations · MCQ
Q87.A problem in mathematics is given to three students $A, B, C$ and their respective probability of solving the problem is $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4} .$ Probability that the problem is solved is :
Mathematics · Probability · MCQ
Q88. $A$ and $B$ are events such that $P (A \cup B) = 3/4$ , $P (A \cap B) = 1/4, P (\overline{A}) = 2/3$ then $P (\overline{A} \cap B)$ is :
Mathematics · Probability · MCQ
Q89.If $a = 4, b = 2$ and the angle between $a$ and $b$ is $π /6$ then $(a \times b)^{2}$ …
Mathematics · Vector Algebra · MCQ
Q90.If the vectors $a, b$ and $c$ from the sides $B C, C A$ and $A B$ respectively of a triangle $A B C$ , then :
Mathematics · Vector Algebra · MCQ
Q91.If $a = 5, b = 4, c = 3$ thus what will be the value of $a . b + b . c + c . a,$ …
Mathematics · Vector Algebra · MCQ
Q92. $a = 3 i - 5 j$ and $b = 6 i + 3 j$ are two vectors and $c$ is a vector such that $c = a \times b$ then $a : b : c$ …
Mathematics · Vector Algebra · MCQ
Q93.If the vectors $c, a = x i + y j + z k$ and $b = j$ are such that $a, c$ and $b$ form a right handed system then $c$ …
Mathematics · Vector Algebra · MCQ
Q94.Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 (using repetition allowed) are :
Mathematics · Permutations and Combinations · MCQ
Q95.The period of $sin^{2} θ$ is
Mathematics · Functions · MCQ
Q96.Which one is not periodic?
Mathematics · Functions · MCQ
Q97.z and w are two nonzero complex numbers such that $∣ z ∣ = ∣ w ∣$ and Arg z + Arg w = $π$ then z equals
Mathematics · Complex Numbers · MCQ
Q98.If $∣ z - 4 ∣ < ∣ z - 2 ∣$ , its solution is given by :
Mathematics · Complex Numbers · MCQ
Q99.The locus of the centre of a circle which touches the circle $∣ z - z_{1} ∣ = a$ and $∣ z - z_{2} ∣ = b$ externally ( $z, z_{1} & z_{2}$ are complex numbers) will be :
Mathematics · Complex Numbers · MCQ
Q100.If $α e β$ but $α^{2} = 5 α - 3$ and $β^{2} = 5 β - 3$ then the equation having $α / β$ and $β / α$ as its roots is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q101.Product of real roots of equation $t^{2} x^{2} + ∣ x ∣ + 9 = 0$
Mathematics · Quadratic Equation and Inequalities · MCQ
Q102.Difference between the corresponding roots of $x^{2} + a x + b = 0$ and $x^{2} + b x + a = 0$ is same and $a e b,$ then
Mathematics · Quadratic Equation and Inequalities · MCQ
Q103.If $p$ and $q$ are the roots of the equation $x^{2} + p x + q = 0,$ then
Mathematics · Quadratic Equation and Inequalities · MCQ
Q104.If $a, b, c$ are distinct $+ v e$ real numbers and $a^{2} + b^{2} + c^{2} = 1$ then $ab + b c + c a$ is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q105.The coefficients of $x^{p}$ and $x^{q}$ in the expansion of $(1 + x)^{p + q}$ are
Mathematics · Binomial Theorem · MCQ
Q106.The positive integer just greater than $(1 + 0.0001)^{10000}$ is
Mathematics · Binomial Theorem · MCQ
Q107.Number greater than 1000 but less than 4000 is formed using the digits 0, 1, 2, 3, 4 (repetition allowed). Their number is :
Mathematics · Permutations and Combinations · MCQ
Q108.The sum of integers from 1 to 100 that are divisible by 2 or 5 is :
Mathematics · Permutations and Combinations · MCQ
Q109.Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4 and 5 without repetition. Total number of such numbers are :
Mathematics · Permutations and Combinations · MCQ
Q110.If 1, $lo g_{9} (3^{1 - x} + 2), lo g_{3} (4. 3^{x} - 1)$ are in A.P. then x equals
Mathematics · Sequences and Series · MCQ
Q111.l, m, n are the $p^{t h}$ , $q^{t h}$ and $r^{t h}$ term of a G.P all positive, $t h e n lo g l lo g m lo g n p q r 111 e q u a l s$
Mathematics · Sequences and Series · MCQ
Q112.Fifth term of a GP is 2, then the product of its 9 terms is
Mathematics · Sequences and Series · MCQ
Q113.Sum of infinite number of terms of GP is 20 and sum of their square is 100. The common ratio of GP is
Mathematics · Sequences and Series · MCQ
Q114.If the chord y = mx + 1 of the circle $x^{2} + y^{2} = 1$ subtends an angle of measure $4 5^{\circ}$ at the major segment of the circle then value of m is :
Mathematics · Circle · MCQ