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Mathematics · 2007 · Shift 1

22 questions from this JEE Advanced paper

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JEE Advanced
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2007 · Shift 1
Mathematics

Mathematics · 2007 · Shift 1

22 questions from this JEE Advanced paper

Quadratic Equation and Inequalities1 questions Application of Derivatives1 questions Probability2 questions Parabola4 questions Definite Integration2 questions Hyperbola1 questions Vector Algebra2 questions Complex Numbers1 questions Trigonometric Functions and Equations1 questions Circle1 questions Inverse Trigonometric Functions1 questions Sequences and Series3 questions Straight Lines and Pair of Straight Lines1 questions Limits Continuity and Differentiability1 questions

Q23.Let $x^{2} - p x + r = 0$ be the roots of the equation $x^{2} - p x + r = 0$ and $\frac{α}{2}, 2 β$ be the roots of the equation $x^{2} - q x + r = 0$ . Then the value of r is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q24.Let $f (x)$ be differentiable on the interval (0, $\infty$ ) such that $f (1) = 1$ , and $t \to x lim \frac{t ^{2} f ( x ) - x ^{2} f ( t )}{t - x} = 1$ for each $x > 0$ . Then $f (x)$ is
Mathematics · Application of Derivatives · MCQ
Q25.One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his…
Mathematics · Probability · MCQ
Q26.The tangent to the curve $y = e^{x}$ drawn at the point ( $c, e^{c}$ ) intersects the line joining the points ( $c - 1, e^{c - 1}$ ) and ( $c + 1, e^{c + 1}$ )
Mathematics · Parabola · MCQ
Q27. $x \to \frac{π}{4} lim \frac{2 \int s e c ^{2} x f ( t ) d t}{x ^{2} - \frac{π ^{2}}{16}}$ equal
Mathematics · Definite Integration · MCQ
Q28.A hyperbola, having the transverse axis of the length $2 sin θ$ , is confocal with the ellipse $3 x^{2} + 4 y^{2} = 12$ . Then its equation is
Mathematics · Hyperbola · MCQ
Q29.The number of distinct real values of $λ$ , for which the vectors $- λ^{2} i + j + k, i - λ^{2} j + k$ and $i + j - λ^{2} k$ are…
Mathematics · Vector Algebra · MCQ
Q30.A man walks a distance of 3 units from the origin towards the north-east (N 45 $^{\circ}$ E) direction. From there, he walks a distance of 4 units towards the north-west (N 45 $^{\circ}$ W) direction to reach a point P. Then the position of P…
Mathematics · Complex Numbers · MCQ
Q31.The number of solutions of the pair of equations $2 sin^{2} θ - cos 2 θ = 02 cos^{2} θ - 3 sin θ = 0$ in the interval $[0, 2 π]$ is
Mathematics · Trigonometric Functions and Equations · MCQ
Q32.Let H $_{1}$ , H $_{2}$ , ..., H $_{n}$ be mutually exclusive and exhaustive events with P(H $_{i}$ ) > 0, i = 1, 2, ..., n. Let E be any other event with 0 Statement 1 : P(H $_{i}$ | E) > P(E | H $_{i}$ ). P(H $_{i}$ ) for $i = 1, 2, ..., n$ . Statement 2 :…
Mathematics · Probability · MCQ
Q33.Tangents are drawn from the point (17, 7) to the circle $x^{2} + y^{2} = 169$ . Statement 1 : The tangents are mutually perpendicular. Statement 2 : The locus of the points from which mutually perpendicular tangents can be drawn to the given circle…
Mathematics · Circle · MCQ
Q34.Let the vector $P Q, QR, R S, S T, T U$ and $U P$ , represent the sides of a regular hexagon. Statement 1 : $P Q \times (R S + S T) e 0$ …
Mathematics · Vector Algebra · MCQ
Q35.Let F(x) be an indefinite integral of $sin^{2} x$ . Statement 1 : The function F(x) satisfies F( $x + π$ ) = F( $x$ ) for all real x. Statement 2 : $sin^{2} (x + π) = sin^{2} x$ for all real x.
Mathematics · Inverse Trigonometric Functions · MCQ
Q36.Let V $_{r}$ denote the sum of the first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is ( $2 r - 1$ ). Let $T_{r} = V_{r + 1} - V_{r} - 2$ and $Q_{r} = T_{r + 1} - T_{r}$ for r = 1, 2, ...The…
Mathematics · Sequences and Series · MCQ
Q37.Let V $_{r}$ denote the sum of the first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is ( $2 r - 1$ ). Let $T_{r} = V_{r + 1} - V_{r} - 2$ and $Q_{r} = T_{r + 1} - T_{r}$ for r = 1, 2, ...T $_{r}$ …
Mathematics · Sequences and Series · MCQ
Q38.Let V $_{r}$ denote the sum of the first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is ( $2 r - 1$ ). Let $T_{r} = V_{r + 1} - V_{r} - 2$ and $Q_{r} = T_{r + 1} - T_{r}$ for r = 1, 2, ...Which…
Mathematics · Sequences and Series · MCQ
Q39.Consider the circle $x^{2} + y^{2} = 9$ and the parabola $y^{2} = 8 x$ . They intersect at P and Q in the first and the fourth quadrants, respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents to the parabola…
Mathematics · Parabola · MCQ
Q40.Consider the circle $x^{2} + y^{2} = 9$ and the parabola $y^{2} = 8 x$ . They intersect at P and Q in the first and the fourth quadrants, respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents to the parabola…
Mathematics · Parabola · MCQ
Q41.Consider the circle $x^{2} + y^{2} = 9$ and the parabola $y^{2} = 8 x$ . They intersect at P and Q in the first and the fourth quadrants, respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents to the parabola…
Mathematics · Parabola · MCQ
Q42.Consider the following linear equations $a x + b y + cz = 0$ $b x + cy + a z = 0$ $c x + a y + b z = 0$ Match the conditions/expressions in Column I with statements in Column II. Includes table
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q43.In the following [x] denotes the greatest integer less than or equal to x. Match the functions in Column I with the properties Column II. Includes table
Mathematics · Limits Continuity and Differentiability · MCQ
Q44.Match the integrals in Column I with the values in Column II. Includes table
Mathematics · Definite Integration · MCQ