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Mathematics · 2011 · Shift 1

23 questions from this JEE Advanced paper

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JEE Advanced
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2011 · Shift 1
Mathematics

Mathematics · 2011 · Shift 1

23 questions from this JEE Advanced paper

Complex Numbers1 questions Trigonometric Functions and Equations2 questions Quadratic Equation and Inequalities3 questions Sequences and Series1 questions Straight Lines and Pair of Straight Lines1 questions Hyperbola1 questions Parabola1 questions Differentiation1 questions Definite Integration1 questions Application of Integration1 questions Probability2 questions Vector Algebra2 questions Limits Continuity and Differentiability1 questions Matrices and Determinants4 questions Differential Equations1 questions

Q24.If z is any complex number satisfying $∣ z - 3 - 2 i ∣ \leq 2$ , then the minimum value of $∣ 2 z - 6 + 5 i ∣$ is
Mathematics · Complex Numbers · Numerical
Q25.The positive integer value of $n > 3$ satisfying the equation $\frac{1}{s i n ( \frac{π}{n} )} = \frac{1}{s i n ( \frac{2 π}{n} )} + \frac{1}{s i n ( \frac{3 π}{n} )}$ is
Mathematics · Trigonometric Functions and Equations · Numerical
Q26.The minimum value of the sum of real numbers $a^{- 5}, a^{- 4}, 3 a^{- 3}, 1, a^{8}$ and $a^{10}$ where $a > 0$ is
Mathematics · Quadratic Equation and Inequalities · Numerical
Q27.Let $α$ and $β$ be the roots of $x^{2} - 6 x - 2 = 0,$ with $α > β .$ If $a_{n} = α^{n} - β^{n}$ for $n \geq 1$ then the value of $\frac{a _{10} - 2 a _{8}}{2 a _{9}}$ is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q28.Let $(x_{0}, y_{0})$ be the solution of the following equations $(2 x)^{ℓ n 2} = (3 y)^{ℓ n 3} 3^{ℓ n x} = 2^{ℓ n y}$ Then $x_{0}$ …
Mathematics · Quadratic Equation and Inequalities · MCQ
Q29.Let $a_{1}$ , $a_{2}$ , $a_{3}$ ........ $a_{100}$ be an arithmetic progression with $a_{1}$ = 3 and $S_{p} = i = 1 \sum p a_{i}, 1 \leq p \leq 100$ . For any integer n with $1 \leq n \leq 20$ , let m = 5n. If $\frac{S _{m}}{S _{n}}$ …
Mathematics · Sequences and Series · Numerical
Q30.A straight line $L$ through the point $(3, - 2)$ is inclined at an angle $6 0^{\circ}$ to the line $3 x + y = 1.$ If $L$ also intersects the x-axis, then the equation of $L$ is
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q31.Let the eccentricity of the hyperbola $\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ be reciprocal to that of the ellipse $x^{2} + 4 y^{2} = 4$ . If the hyperbola passes through a focus of the ellipse, then
Mathematics · Hyperbola · Multiple correct
Q32.Consider the parabola $y^{2} = 8 x$ . Let $Δ_{1}$ be the area of the triangle formed by the end points of its latus rectum and the point $P (\frac{1}{2}, 2)$ on the parabola and $Δ_{2}$ be the area of the triangle…
Mathematics · Parabola · Numerical
Q33.Let $f (θ) = sin (tan^{- 1} (\frac{s i n θ}{c o s 2 θ})),$ where $- \frac{π}{4} < θ < \frac{π}{4} .$ Then the value of $\frac{d}{d ( t a n θ )} (f (θ))$ …
Mathematics · Differentiation · Numerical
Q34.The value of $ℓ n 2 \int ℓ n 3 \frac{x s i n x ^{2}}{s i n x ^{2} + s i n ( ℓ n 6 - x ^{2} )} d x$ is
Mathematics · Definite Integration · MCQ
Q35.Let the straight line $x = b$ divide the area enclosed by $y = (1 - x)^{2}, y = 0,$ and $x = 0$ into two parts $R_{1} (0 \leq x \leq b)$ and $R_{2} (b \leq x \leq 1)$ such that $R_{1} - R_{2} = \frac{1}{4} .$ …
Mathematics · Application of Integration · MCQ
Q36.Let $U_{1}$ and $U_{2}$ be two urns such that $U_{1}$ contains $3$ white and $2$ red balls, and $U_{2}$ contains only $1$ white ball. A fair coin is tossed. If head appears then $1$ ball is drawn at random from $U_{1}$ and put into…
Mathematics · Probability · MCQ
Q37.Let $U_{1}$ and $U_{2}$ be two urns such that $U_{1}$ contains $3$ white and $2$ red balls, and $U_{2}$ contains only $1$ white ball. A fair coin is tossed. If head appears then $1$ ball is drawn at random from $U_{1}$ and put into…
Mathematics · Probability · MCQ
Q38.Let $a = i + j + k, b = i - j + k$ and $c = i - j - k$ be three vectors. A vector $v$ in…
Mathematics · Vector Algebra · MCQ
Q39.The vector (s) which is/are coplanar with vectors $i + j + 2 k$ and $i + 2 j + k,$ and perpendicular to the vector $i + j + k$ is/are
Mathematics · Vector Algebra · Multiple correct
Q40.Let $P = {θ : sin θ - cos θ = 2 cos θ}$ and $Q = {θ : sin θ + cos θ = 2 sin θ}$ be two sets. Then
Mathematics · Trigonometric Functions and Equations · MCQ
Q41.Let f : R $\to$ R be a function such that $f (x + y) = f (x) + f (y), \forall x, y \in R$ . If f(x) is differentiable at x = 0, then
Mathematics · Limits Continuity and Differentiability · Multiple correct
Q42.Let M and N be two 3 $\times$ 3 non-singular skew symmetric matrices such that MN = NM. If PT denotes the transpose of P, then M2N2(MTN) $-$ 1(MN $-$ 1)T is equal to
Mathematics · Matrices and Determinants · Multiple correct
Q43.Let a, b and c be three real numbers satisfying $[a b c] 187923777 = [000]$ …
Mathematics · Matrices and Determinants · MCQ
Q44.Let a, b and c be three real numbers satisfying $[a b c] 187923777 = [000]$ …
Mathematics · Matrices and Determinants · MCQ
Q45.Let a, b and c be three real numbers satisfying $[a b c] 187923777 = [000]$ …
Mathematics · Matrices and Determinants · MCQ
Q46.Let $f : [1, \infty) \to [2, \infty)$ be a differentiable function such that $f (1) = 2$ . If $6 1 \int x f (t) d t = 3 x f (x) - x^{3} - 5$ for all $x \geq 1$ , then the value of f(2) is .
Mathematics · Differential Equations · Numerical