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Mathematics · 2007 · Shift 0

24 questions from this JEE Main paper

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2007 · Shift 0
Mathematics

Mathematics · 2007 · Shift 0

24 questions from this JEE Main paper

Statistics1 questions Limits Continuity and Differentiability2 questions Functions1 questions Inverse Trigonometric Functions1 questions 3D Geometry2 questions Probability1 questions Definite Integration3 questions Area Under the Curves1 questions Indefinite Integrals1 questions Matrices and Determinants1 questions Application of Derivatives2 questions Vector Algebra1 questions Hyperbola1 questions Straight Lines and Pair of Straight Lines1 questions Sequences and Series1 questions Permutations and Combinations1 questions Binomial Theorem1 questions Quadratic Equation and Inequalities1 questions Complex Numbers1 questions

Q39.The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is
Mathematics · Statistics · MCQ
Q40.The function $f : R / {0} \to R$ given by $f (x) = \frac{1}{x} - \frac{2}{e ^{2 x} - 1}$ can be made continuous at $x$ = 0 by defining $f$ (0) as
Mathematics · Limits Continuity and Differentiability · MCQ
Q41.Let $f : R \to R$ be a function defined by $f (x) = min {x + 1, ∣ x ∣ + 1}$ , then which of the following is true?
Mathematics · Limits Continuity and Differentiability · MCQ
Q42.The largest interval lying in $(- \frac{π}{2}, \frac{π}{2})$ for which the function $f (x) = 4^{- x^{2}} + cos^{- 1} (\frac{x}{2} - 1) + lo g (cos x)$ , is defined, is
Mathematics · Functions · MCQ
Q43.If sin-1 $(\frac{x}{5})$ + cosec-1 $(\frac{5}{4})$ = $\frac{π}{2}$ , then the value of x is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q44.If a line makes an angle of $π /4$ with the positive directions of each of $x$ -axis and $y$ -axis, then the angle that the line makes with the positive direction of the $z$ -axis is :
Mathematics · 3D Geometry · MCQ
Q45.Two aeroplanes $I$ and $I I$ bomb a target in succession. The probabilities of $I$ and $I I$ scoring a hit correctly are $0.3$ and $0.2,$ respectively. The second plane will bomb only if the first misses…
Mathematics · Probability · MCQ
Q46.Let $I = 0 \int 1 \frac{s i n x}{x} d x$ and $J = 0 \int 1 \frac{c o s x}{x} d x .$ Then which one of the following is true?
Mathematics · Definite Integration · MCQ
Q47.The area enclosed between the curves $y^{2} = x$ and $y = ∣ x ∣$ is :
Mathematics · Area Under the Curves · MCQ
Q48.The solution for $x$ of the equation $2 \int x \frac{d t}{t t ^{2} - 1} = \frac{π}{2}$ is
Mathematics · Definite Integration · MCQ
Q49.Let $F (x) = f (x) + f (\frac{1}{x}),$ where $f (x) = l \int x \frac{l o g t}{1 + t} d t,$ Then $F (e)$ equals
Mathematics · Definite Integration · MCQ
Q50. $\int \frac{d x}{c o s x + 3 s i n x}$ equals
Mathematics · Indefinite Integrals · MCQ
Q51.If $D = 111 1 1 + x 1 11 1 + y$ for $x e 0, y e 0,$ then $D$ is :
Mathematics · Matrices and Determinants · MCQ
Q52.If $p$ and $q$ are positive real numbers such that $p^{2} + q^{2} = 1$ , then the maximum value of $(p + q)$ is
Mathematics · Application of Derivatives · MCQ
Q53.The function $f (x) = tan^{- 1} (sin x + cos x)$ is an incresing function in
Mathematics · Application of Derivatives · MCQ
Q54.If $u$ and $v$ are unit vectors and $θ$ is the acute angle between them, then $2 u \times 3 v$ is a unit vector for :
Mathematics · Vector Algebra · MCQ
Q55.For the Hyperbola $\frac{x ^{2}}{c o s ^{2} α} - \frac{y ^{2}}{s i n ^{2} α} = 1$ , which of the following remains constant when $α$ varies $=$ ?
Mathematics · Hyperbola · MCQ
Q56.Let A $(h, k)$ , B $(1, 1)$ and C $(2, 1)$ be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is $1$ square unit, then the set of values which $^{'} k^{'}$ can take is…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q57.In a geometric progression consisting of positive terms, each term equals the sum of the next two terns. Then the common ratio of its progression is equals
Mathematics · Sequences and Series · MCQ
Q58.The set S = {1, 2, 3, ........., 12} is to be partitioned into three sets A, B, C of equal size. Thus $A \cup B \cup C = S, A \cap B = B \cap C = A \cap C = ϕ$ . The number of ways to partition S is
Mathematics · Permutations and Combinations · MCQ
Q59.In the binomial expansion of $(a - b)^{n}, n \geq 5,$ the sum of $5^{t h}$ and $6^{t h}$ terms is zero, then $a / b$ equals
Mathematics · Binomial Theorem · MCQ
Q60.If the difference between the roots of the equation $x^{2} + a x + 1 = 0$ is less than $5,$ then the set of possible values of $a$ is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q61.If $∣ z + 4 ∣ \leq 3$ , then the maximum value of $∣ z + 1 ∣$ is :
Mathematics · Complex Numbers · MCQ
Q62.Let $L$ be the line of intersection of the planes $2 x + 3 y + z = 1$ and $x + 3 y + 2 z = 2.$ If $L$ makes an angle $α$ with the positive $x$ -axis, then cos $α$ equals
Mathematics · 3D Geometry · MCQ